(* ----Theorem clauses *)
theorem c_16:
- ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp32 X).less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp31 X).less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than X (half Xa).∀_:less_than Y (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than X Y.∀_:less_than Y Z.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than n0 X) (less_than (add (absolute (add (f (fp33 X)) (minus l1))) (absolute (add (g (fp33 X)) (minus l2)))) b)
+ ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than (absolute (add Y (minus a))) (fp32 X).∀_:less_than n0 X.less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than (absolute (add Y (minus a))) (fp31 X).∀_:less_than n0 X.less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than Y (half Xa).∀_:less_than X (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than Y Z.∀_:less_than X Y.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than (add (absolute (add (f (fp33 X)) (minus l1))) (absolute (add (g (fp33 X)) (minus l2)))) b) (less_than n0 X)
.
intros.
exists[
(* ----Clauses from the theorem *)
theorem c_16:
- ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp32 X).less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp31 X).less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than X (half Xa).∀_:less_than Y (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than X Y.∀_:less_than Y Z.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than n0 X) (less_than (absolute (add (add (f (fp33 X)) (minus l1)) (add (g (fp33 X)) (minus l2)))) b)
+ ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than (absolute (add Y (minus a))) (fp32 X).∀_:less_than n0 X.less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than (absolute (add Y (minus a))) (fp31 X).∀_:less_than n0 X.less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than Y (half Xa).∀_:less_than X (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than Y Z.∀_:less_than X Y.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than (absolute (add (add (f (fp33 X)) (minus l1)) (add (g (fp33 X)) (minus l2)))) b) (less_than n0 X)
.
intros.
exists[
(* ----Clauses from the theorem *)
theorem c_16:
- ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp32 X).less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp31 X).less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than X (half Xa).∀_:less_than Y (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than X Y.∀_:less_than Y Z.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than n0 X) (less_than (absolute (add (add (f (fp33 X)) (g (fp33 X))) (minus (add l1 l2)))) b)
+ ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than (absolute (add Y (minus a))) (fp32 X).∀_:less_than n0 X.less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than (absolute (add Y (minus a))) (fp31 X).∀_:less_than n0 X.less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than Y (half Xa).∀_:less_than X (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 Y.∀_:less_than n0 X.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than Y Z.∀_:less_than X Y.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than (absolute (add (add (f (fp33 X)) (g (fp33 X))) (minus (add l1 l2)))) b) (less_than n0 X)
.
intros.
exists[
(* ------------------------------------------------------------------------------ *)
theorem cls_conjecture_1:
- ∀Univ:Set.∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀c_0:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀class_OrderedGroup_Oab__semigroup__mult:∀_:Univ.Prop.∀class_OrderedGroup_Olordered__ab__group__abs:∀_:Univ.Prop.∀class_OrderedGroup_Osemigroup__mult:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__semiring:∀_:Univ.Prop.∀t_b:Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:Univ.∀H0:c_lessequals (c_HOL_Oabs (v_b v_x) t_b) (c_times v_c (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b.∀H1:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀_:class_Ring__and__Field_Opordered__semiring T_a.∀_:c_lessequals V_a V_b T_a.∀_:c_lessequals c_0 V_c T_a.c_lessequals (c_times V_c V_a T_a) (c_times V_c V_b T_a) T_a.∀H2:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_OrderedGroup_Oab__semigroup__mult T_a.eq Univ (c_times V_a V_b T_a) (c_times V_b V_a T_a).∀H3:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀_:class_OrderedGroup_Osemigroup__mult T_a.eq Univ (c_times (c_times V_a V_b T_a) V_c T_a) (c_times V_a (c_times V_b V_c T_a) T_a).∀H4:∀T_a:Univ.∀V_a:Univ.∀_:class_OrderedGroup_Olordered__ab__group__abs T_a.c_lessequals c_0 (c_HOL_Oabs V_a T_a) T_a.c_lessequals (c_times (c_HOL_Oabs (v_b v_x) t_b) (c_HOL_Oabs (v_f v_x) t_b) t_b) (c_times v_c (c_times (c_HOL_Oabs (v_f v_x) t_b) (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b) t_b
+ ∀Univ:Set.∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀c_0:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀class_OrderedGroup_Oab__semigroup__mult:∀_:Univ.Prop.∀class_OrderedGroup_Olordered__ab__group__abs:∀_:Univ.Prop.∀class_OrderedGroup_Osemigroup__mult:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__semiring:∀_:Univ.Prop.∀t_b:Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:Univ.∀H0:c_lessequals (c_HOL_Oabs (v_b v_x) t_b) (c_times v_c (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b.∀H1:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀_:c_lessequals c_0 V_c T_a.∀_:c_lessequals V_a V_b T_a.∀_:class_Ring__and__Field_Opordered__semiring T_a.c_lessequals (c_times V_c V_a T_a) (c_times V_c V_b T_a) T_a.∀H2:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_OrderedGroup_Oab__semigroup__mult T_a.eq Univ (c_times V_a V_b T_a) (c_times V_b V_a T_a).∀H3:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀_:class_OrderedGroup_Osemigroup__mult T_a.eq Univ (c_times (c_times V_a V_b T_a) V_c T_a) (c_times V_a (c_times V_b V_c T_a) T_a).∀H4:∀T_a:Univ.∀V_a:Univ.∀_:class_OrderedGroup_Olordered__ab__group__abs T_a.c_lessequals c_0 (c_HOL_Oabs V_a T_a) T_a.c_lessequals (c_times (c_HOL_Oabs (v_b v_x) t_b) (c_HOL_Oabs (v_f v_x) t_b) t_b) (c_times v_c (c_times (c_HOL_Oabs (v_f v_x) t_b) (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b) t_b
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* ------------------------------------------------------------------------------ *)
theorem cls_conjecture_5:
- ∀Univ:Set.∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀V_x:Univ.∀V_y:Univ.∀c_0:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_less:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀class_OrderedGroup_Olordered__ab__group__abs:∀_:Univ.Prop.∀class_Orderings_Oorder:∀_:Univ.Prop.∀class_Ring__and__Field_Oordered__idom:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__cancel__semiring:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__semiring:∀_:Univ.Prop.∀t_b:Univ.∀v_a:∀_:Univ.Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_ca:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:Univ.∀H0:eq Univ (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) (c_times (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b).∀H1:c_lessequals (c_HOL_Oabs (v_b v_x) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b.∀H2:c_lessequals (c_HOL_Oabs (v_a v_x) t_b) (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) t_b.∀H3:c_less c_0 v_c t_b.∀H4:∀T_a:Univ.∀V_a:Univ.∀_:class_OrderedGroup_Olordered__ab__group__abs T_a.c_lessequals c_0 (c_HOL_Oabs V_a T_a) T_a.∀H5:∀T_a:Univ.∀V_x:Univ.∀V_y:Univ.∀_:class_Orderings_Oorder T_a.∀_:c_less V_x V_y T_a.c_lessequals V_x V_y T_a.∀H6:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_Ring__and__Field_Opordered__cancel__semiring T_a.∀_:c_lessequals c_0 V_b T_a.∀_:c_lessequals c_0 V_a T_a.c_lessequals c_0 (c_times V_a V_b T_a) T_a.∀H7:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀_:class_Ring__and__Field_Opordered__semiring T_a.∀_:c_lessequals V_c V_d T_a.∀_:c_lessequals V_a V_b T_a.∀_:c_lessequals c_0 V_c T_a.∀_:c_lessequals c_0 V_b T_a.c_lessequals (c_times V_a V_c T_a) (c_times V_b V_d T_a) T_a.∀H8:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_Ring__and__Field_Oordered__idom T_a.eq Univ (c_HOL_Oabs (c_times V_a V_b T_a) T_a) (c_times (c_HOL_Oabs V_a T_a) (c_HOL_Oabs V_b T_a) T_a).c_lessequals (c_HOL_Oabs (c_times (v_a v_x) (v_b v_x) t_b) t_b) (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) t_b
+ ∀Univ:Set.∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀V_x:Univ.∀V_y:Univ.∀c_0:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_less:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀class_OrderedGroup_Olordered__ab__group__abs:∀_:Univ.Prop.∀class_Orderings_Oorder:∀_:Univ.Prop.∀class_Ring__and__Field_Oordered__idom:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__cancel__semiring:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__semiring:∀_:Univ.Prop.∀t_b:Univ.∀v_a:∀_:Univ.Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_ca:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:Univ.∀H0:eq Univ (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) (c_times (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b).∀H1:c_lessequals (c_HOL_Oabs (v_b v_x) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b.∀H2:c_lessequals (c_HOL_Oabs (v_a v_x) t_b) (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) t_b.∀H3:c_less c_0 v_c t_b.∀H4:∀T_a:Univ.∀V_a:Univ.∀_:class_OrderedGroup_Olordered__ab__group__abs T_a.c_lessequals c_0 (c_HOL_Oabs V_a T_a) T_a.∀H5:∀T_a:Univ.∀V_x:Univ.∀V_y:Univ.∀_:c_less V_x V_y T_a.∀_:class_Orderings_Oorder T_a.c_lessequals V_x V_y T_a.∀H6:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:c_lessequals c_0 V_a T_a.∀_:c_lessequals c_0 V_b T_a.∀_:class_Ring__and__Field_Opordered__cancel__semiring T_a.c_lessequals c_0 (c_times V_a V_b T_a) T_a.∀H7:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀_:c_lessequals c_0 V_b T_a.∀_:c_lessequals c_0 V_c T_a.∀_:c_lessequals V_a V_b T_a.∀_:c_lessequals V_c V_d T_a.∀_:class_Ring__and__Field_Opordered__semiring T_a.c_lessequals (c_times V_a V_c T_a) (c_times V_b V_d T_a) T_a.∀H8:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_Ring__and__Field_Oordered__idom T_a.eq Univ (c_HOL_Oabs (c_times V_a V_b T_a) T_a) (c_times (c_HOL_Oabs V_a T_a) (c_HOL_Oabs V_b T_a) T_a).c_lessequals (c_HOL_Oabs (c_times (v_a v_x) (v_b v_x) t_b) t_b) (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) t_b
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_inverse_is_an_involution:
- ∀Univ:Set.∀U:Univ.∀V:Univ.∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀additive_identity:Univ.∀inverse:∀_:Univ.Univ.∀multiplicative_identity:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀product:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀sum:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀x:Univ.∀H0:∀X:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀_:product X Y X_times_Y.∀_:product Y Z Y_times_Z.∀_:product X_times_Y Z X_times_Y_times_Z.product X Y_times_Z X_times_Y_times_Z.∀H1:∀X:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀_:product X Y X_times_Y.∀_:product Y Z Y_times_Z.∀_:product X Y_times_Z X_times_Y_times_Z.product X_times_Y Z X_times_Y_times_Z.∀H2:∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Z:Univ.∀_:sum X Y X_plus_Y.∀_:sum Y Z Y_plus_Z.∀_:sum X_plus_Y Z X_plus_Y_plus_Z.sum X Y_plus_Z X_plus_Y_plus_Z.∀H3:∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Z:Univ.∀_:sum X Y X_plus_Y.∀_:sum Y Z Y_plus_Z.∀_:sum X Y_plus_Z X_plus_Y_plus_Z.sum X_plus_Y Z X_plus_Y_plus_Z.∀H4:∀X:Univ.∀Y:Univ.product X (add X Y) X.∀H5:∀X:Univ.∀Y:Univ.sum X (multiply X Y) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y Z.product X Z X.∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y Z.sum X Z X.∀H8:∀X:Univ.product X additive_identity additive_identity.∀H9:∀X:Univ.sum X multiplicative_identity multiplicative_identity.∀H10:∀X:Univ.product X X X.∀H11:∀X:Univ.sum X X X.∀H12:∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀_:product X Y U.∀_:product X Y V.eq Univ U V.∀H13:∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀_:sum X Y U.∀_:sum X Y V.eq Univ U V.∀H14:∀X:Univ.product X (inverse X) additive_identity.∀H15:∀X:Univ.product (inverse X) X additive_identity.∀H16:∀X:Univ.sum X (inverse X) multiplicative_identity.∀H17:∀X:Univ.sum (inverse X) X multiplicative_identity.∀H18:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum Y X V1.∀_:sum Z X V2.∀_:product Y Z V3.∀_:product V1 V2 V4.sum V3 X V4.∀H19:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum Y X V1.∀_:sum Z X V2.∀_:product Y Z V3.∀_:sum V3 X V4.product V1 V2 V4.∀H20:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y V1.∀_:sum X Z V2.∀_:product Y Z V3.∀_:product V1 V2 V4.sum X V3 V4.∀H21:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y V1.∀_:sum X Z V2.∀_:product Y Z V3.∀_:sum X V3 V4.product V1 V2 V4.∀H22:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product Y X V1.∀_:product Z X V2.∀_:sum Y Z V3.∀_:sum V1 V2 V4.product V3 X V4.∀H23:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product Y X V1.∀_:product Z X V2.∀_:sum Y Z V3.∀_:product V3 X V4.sum V1 V2 V4.∀H24:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y V1.∀_:product X Z V2.∀_:sum Y Z V3.∀_:sum V1 V2 V4.product X V3 V4.∀H25:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y V1.∀_:product X Z V2.∀_:sum Y Z V3.∀_:product X V3 V4.sum V1 V2 V4.∀H26:∀X:Univ.product X multiplicative_identity X.∀H27:∀X:Univ.product multiplicative_identity X X.∀H28:∀X:Univ.sum X additive_identity X.∀H29:∀X:Univ.sum additive_identity X X.∀H30:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y Z.product Y X Z.∀H31:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y Z.sum Y X Z.∀H32:∀X:Univ.∀Y:Univ.product X Y (multiply X Y).∀H33:∀X:Univ.∀Y:Univ.sum X Y (add X Y).eq Univ (inverse (inverse x)) x
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀additive_identity:Univ.∀inverse:∀_:Univ.Univ.∀multiplicative_identity:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀product:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀sum:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀x:Univ.∀H0:∀X:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀_:product X Y_times_Z X_times_Y_times_Z.∀_:product Y Z Y_times_Z.∀_:product X Y X_times_Y.product X_times_Y Z X_times_Y_times_Z.∀H1:∀X:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀_:product X Y_times_Z X_times_Y_times_Z.∀_:product Y Z Y_times_Z.∀_:product X Y X_times_Y.product X_times_Y Z X_times_Y_times_Z.∀H2:∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Z:Univ.∀_:sum X Y_plus_Z X_plus_Y_plus_Z.∀_:sum Y Z Y_plus_Z.∀_:sum X Y X_plus_Y.sum X_plus_Y Z X_plus_Y_plus_Z.∀H3:∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Z:Univ.∀_:sum X Y_plus_Z X_plus_Y_plus_Z.∀_:sum Y Z Y_plus_Z.∀_:sum X Y X_plus_Y.sum X_plus_Y Z X_plus_Y_plus_Z.∀H4:∀X:Univ.∀Y:Univ.product X (add X Y) X.∀H5:∀X:Univ.∀Y:Univ.sum X (multiply X Y) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y Z.product X Z X.∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y Z.sum X Z X.∀H8:∀X:Univ.product X additive_identity additive_identity.∀H9:∀X:Univ.sum X multiplicative_identity multiplicative_identity.∀H10:∀X:Univ.product X X X.∀H11:∀X:Univ.sum X X X.∀H12:∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀_:product X Y V.∀_:product X Y U.eq Univ U V.∀H13:∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀_:sum X Y V.∀_:sum X Y U.eq Univ U V.∀H14:∀X:Univ.product X (inverse X) additive_identity.∀H15:∀X:Univ.product (inverse X) X additive_identity.∀H16:∀X:Univ.sum X (inverse X) multiplicative_identity.∀H17:∀X:Univ.sum (inverse X) X multiplicative_identity.∀H18:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product V1 V2 V4.∀_:product Y Z V3.∀_:sum Z X V2.∀_:sum Y X V1.sum V3 X V4.∀H19:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum V3 X V4.∀_:product Y Z V3.∀_:sum Z X V2.∀_:sum Y X V1.product V1 V2 V4.∀H20:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product V1 V2 V4.∀_:product Y Z V3.∀_:sum X Z V2.∀_:sum X Y V1.sum X V3 V4.∀H21:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X V3 V4.∀_:product Y Z V3.∀_:sum X Z V2.∀_:sum X Y V1.product V1 V2 V4.∀H22:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum V1 V2 V4.∀_:sum Y Z V3.∀_:product Z X V2.∀_:product Y X V1.product V3 X V4.∀H23:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product V3 X V4.∀_:sum Y Z V3.∀_:product Z X V2.∀_:product Y X V1.sum V1 V2 V4.∀H24:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum V1 V2 V4.∀_:sum Y Z V3.∀_:product X Z V2.∀_:product X Y V1.product X V3 V4.∀H25:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X V3 V4.∀_:sum Y Z V3.∀_:product X Z V2.∀_:product X Y V1.sum V1 V2 V4.∀H26:∀X:Univ.product X multiplicative_identity X.∀H27:∀X:Univ.product multiplicative_identity X X.∀H28:∀X:Univ.sum X additive_identity X.∀H29:∀X:Univ.sum additive_identity X X.∀H30:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y Z.product Y X Z.∀H31:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y Z.sum Y X Z.∀H32:∀X:Univ.∀Y:Univ.product X Y (multiply X Y).∀H33:∀X:Univ.∀Y:Univ.sum X Y (add X Y).eq Univ (inverse (inverse x)) x
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_a_bc_exists:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀codomain:∀_:Univ.Univ.∀compose:∀_:Univ.∀_:Univ.Univ.∀domain:∀_:Univ.Univ.∀equivalent:∀_:Univ.∀_:Univ.Prop.∀there_exists:∀_:Univ.Prop.∀H0:there_exists (compose b c).∀H1:there_exists (compose a b).∀H2:∀X:Univ.eq Univ (compose (codomain X) X) X.∀H3:∀X:Univ.eq Univ (compose X (domain X)) X.∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (compose X (compose Y Z)) (compose (compose X Y) Z).∀H5:∀X:Univ.∀Y:Univ.∀_:there_exists (domain X).∀_:eq Univ (domain X) (codomain Y).there_exists (compose X Y).∀H6:∀X:Univ.∀Y:Univ.∀_:there_exists (compose X Y).eq Univ (domain X) (codomain Y).∀H7:∀X:Univ.∀Y:Univ.∀_:there_exists (compose X Y).there_exists (domain X).∀H8:∀X:Univ.∀_:there_exists (codomain X).there_exists X.∀H9:∀X:Univ.∀_:there_exists (domain X).there_exists X.∀H10:∀X:Univ.∀Y:Univ.∀_:there_exists X.∀_:eq Univ X Y.equivalent X Y.∀H11:∀X:Univ.∀Y:Univ.∀_:equivalent X Y.eq Univ X Y.∀H12:∀X:Univ.∀Y:Univ.∀_:equivalent X Y.there_exists X.there_exists (compose a (compose b c))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀codomain:∀_:Univ.Univ.∀compose:∀_:Univ.∀_:Univ.Univ.∀domain:∀_:Univ.Univ.∀equivalent:∀_:Univ.∀_:Univ.Prop.∀there_exists:∀_:Univ.Prop.∀H0:there_exists (compose b c).∀H1:there_exists (compose a b).∀H2:∀X:Univ.eq Univ (compose (codomain X) X) X.∀H3:∀X:Univ.eq Univ (compose X (domain X)) X.∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (compose X (compose Y Z)) (compose (compose X Y) Z).∀H5:∀X:Univ.∀Y:Univ.∀_:there_exists (domain X).∀_:there_exists (compose X Y).eq Univ (domain X) (codomain Y).∀H6:∀X:Univ.∀Y:Univ.∀_:there_exists (compose X Y).eq Univ (domain X) (codomain Y).∀H7:∀X:Univ.∀Y:Univ.∀_:there_exists (compose X Y).there_exists (domain X).∀H8:∀X:Univ.∀_:there_exists (codomain X).there_exists X.∀H9:∀X:Univ.∀_:there_exists (domain X).there_exists X.∀H10:∀X:Univ.∀Y:Univ.∀_:there_exists X.∀_:equivalent X Y.eq Univ X Y.∀H11:∀X:Univ.∀Y:Univ.∀_:equivalent X Y.eq Univ X Y.∀H12:∀X:Univ.∀Y:Univ.∀_:equivalent X Y.there_exists X.there_exists (compose a (compose b c))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b (apply b w)) (apply (apply b b) b)))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b (apply b w)) (apply (apply b b) b)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b (apply (apply b w) b)) b))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b (apply (apply b w) b)) b))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply (apply b w) b))) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply (apply b w) b))) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) w)) (apply (apply b b) b))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) w)) (apply (apply b b) b))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w w)) w)) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w w)) w)) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply b w))) (apply (apply b b) b))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply b w))) (apply (apply b b) b))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply k (apply (apply s s) (apply s k)))) (apply (apply s (apply k s)) k)))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply k (apply (apply s s) (apply s k)))) (apply (apply s (apply k s)) k)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply (apply s (apply k s)) k)) (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply (apply s (apply k s)) k)) (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply (apply s s) (apply (apply s k) k)) (apply (apply s s) (apply s k))))) (apply (apply s (apply k s)) k))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply (apply s s) (apply (apply s k) k)) (apply (apply s s) (apply s k))))) (apply (apply s (apply k s)) k))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) (apply (apply b b) b))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) (apply (apply b b) b))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) b))) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) b))) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) (apply (apply b b) b)))
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) (apply (apply b b) b)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀h:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀h:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply (apply b b) n)) n))) n)) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply (apply b b) n)) n))) n)) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply n (apply b b))) n))) n)) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply n (apply b b))) n))) n)) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply (apply b b) n))))) n)) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply (apply b b) n))))) n)) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_strong_fixed_point:
- ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply n (apply b b)))))) n)) b)) b)
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:fixed_point Strong_fixed_point.eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply n (apply b b)))))) n)) b)) b)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_commutativity:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀divide:∀_:Univ.∀_:Univ.Univ.∀e:Univ.∀g:Univ.∀identity:Univ.∀less_equal:∀_:Univ.∀_:Univ.Prop.∀zero:Univ.∀H0:eq Univ (divide identity d) g.∀H1:eq Univ (divide identity c) e.∀H2:eq Univ (divide identity b) d.∀H3:eq Univ (divide identity a) c.∀H4:eq Univ (divide (divide identity a) (divide identity (divide identity b))) (divide (divide identity b) (divide identity (divide identity a))).∀H5:∀X:Univ.less_equal X identity.∀H6:∀X:Univ.∀Y:Univ.∀_:less_equal X Y.∀_:less_equal Y X.eq Univ X Y.∀H7:∀X:Univ.less_equal zero X.∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.less_equal (divide (divide X Z) (divide Y Z)) (divide (divide X Y) Z).∀H9:∀X:Univ.∀Y:Univ.less_equal (divide X Y) X.∀H10:∀X:Univ.∀Y:Univ.∀_:eq Univ (divide X Y) zero.less_equal X Y.∀H11:∀X:Univ.∀Y:Univ.∀_:less_equal X Y.eq Univ (divide X Y) zero.eq Univ (divide c g) (divide d e)
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀divide:∀_:Univ.∀_:Univ.Univ.∀e:Univ.∀g:Univ.∀identity:Univ.∀less_equal:∀_:Univ.∀_:Univ.Prop.∀zero:Univ.∀H0:eq Univ (divide identity d) g.∀H1:eq Univ (divide identity c) e.∀H2:eq Univ (divide identity b) d.∀H3:eq Univ (divide identity a) c.∀H4:eq Univ (divide (divide identity a) (divide identity (divide identity b))) (divide (divide identity b) (divide identity (divide identity a))).∀H5:∀X:Univ.less_equal X identity.∀H6:∀X:Univ.∀Y:Univ.∀_:less_equal Y X.∀_:less_equal X Y.eq Univ X Y.∀H7:∀X:Univ.less_equal zero X.∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.less_equal (divide (divide X Z) (divide Y Z)) (divide (divide X Y) Z).∀H9:∀X:Univ.∀Y:Univ.less_equal (divide X Y) X.∀H10:∀X:Univ.∀Y:Univ.∀_:less_equal X Y.eq Univ (divide X Y) zero.∀H11:∀X:Univ.∀Y:Univ.∀_:less_equal X Y.eq Univ (divide X Y) zero.eq Univ (divide c g) (divide d e)
.
intros.
autobatch paramodulation timeout=600;
(* ----Problem axioms *)
theorem prove_cannot_construct_this:
- ∀Univ:Set.∀V:Univ.∀X:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X1:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xname:Univ.∀Xrevlist:Univ.∀Y:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀Z:Univ.∀add_inverter:∀_:Univ.∀_:Univ.Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀end:Univ.∀inverter_table:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀list:∀_:Univ.∀_:Univ.Univ.∀list_reversion:∀_:Univ.∀_:Univ.Univ.∀make_reverse_list:∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀not_reversion:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀possible_reversion:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀r00m:Univ.∀r01m:Univ.∀r0m0:Univ.∀r0m1:Univ.∀r10m:Univ.∀r11m:Univ.∀r1m0:Univ.∀r1m1:Univ.∀rm00:Univ.∀rm01:Univ.∀rm10:Univ.∀rm11:Univ.∀test:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀H0:∀X:Univ.output n0 n1 n0 n1 n0 n1 n0 n1 X.∀H1:∀X:Univ.output n0 n0 n1 n1 n0 n0 n1 n1 X.∀H2:∀X:Univ.output n0 n0 n0 n0 n1 n1 n1 n1 X.∀H3:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xrevlist:Univ.∀_:test X1 X2 X3 X4 X5 X6 X7 X8 V Xrevlist.output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H4:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.test (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8) (add_inverter V (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8))) (make_reverse_list (list (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8)) V)).∀H5:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.output (or X1 Y1) (or X2 Y2) (or X3 Y3) (or X4 Y4) (or X5 Y5) (or X6 Y6) (or X7 Y7) (or X8 Y8) V.∀H6:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.output (myand X1 Y1) (myand X2 Y2) (myand X3 Y3) (myand X4 Y4) (myand X5 Y5) (myand X6 Y6) (myand X7 Y7) (myand X8 Y8) V.∀H7:∀X:Univ.∀Y:Univ.eq Univ (list_reversion X (list_reversion X Y)) (list_reversion X Y).∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (list_reversion X (list_reversion Y Z)) (list_reversion Y (list_reversion X Z)).∀H9:∀X:Univ.eq Univ (list_reversion not_reversion X) X.∀H10:∀X:Univ.∀Xname:Univ.eq Univ (possible_reversion Xname X X) not_reversion.∀H11:∀Xname:Univ.eq Univ (possible_reversion Xname n0 n1) not_reversion.∀H12:∀Xname:Univ.eq Univ (possible_reversion Xname n1 n0) Xname.∀H13:∀V:Univ.eq Univ (make_reverse_list V) end.∀H14:∀V:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.eq Univ (make_reverse_list (list (inverter_table X000 X001 X010 X011 X100 X101 X110 X111) V)) (list_reversion (possible_reversion r00m X000 X001) (list_reversion (possible_reversion r01m X010 X011) (list_reversion (possible_reversion r10m X100 X101) (list_reversion (possible_reversion r11m X110 X111) (list_reversion (possible_reversion r0m0 X000 X010) (list_reversion (possible_reversion r0m1 X001 X011) (list_reversion (possible_reversion r1m0 X100 X110) (list_reversion (possible_reversion r1m1 X101 X111) (list_reversion (possible_reversion rm00 X000 X100) (list_reversion (possible_reversion rm01 X001 X101) (list_reversion (possible_reversion rm10 X010 X110) (list_reversion (possible_reversion rm11 X011 X111) (make_reverse_list V))))))))))))).∀H15:∀X:Univ.∀Y:Univ.eq Univ (add_inverter X Y) (list Y X).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add_inverter (list X Y) Z) (list X (add_inverter Y Z)).∀H17:eq Univ (not n1) n0.∀H18:eq Univ (not n0) n1.∀H19:∀X:Univ.eq Univ (or X n1) n1.∀H20:∀X:Univ.eq Univ (or X n0) X.∀H21:∀X:Univ.eq Univ (myand X n1) X.∀H22:∀X:Univ.eq Univ (myand X n0) n0.∃V:Univ.And (output n1 n1 n1 n1 n0 n0 n0 n0 V) (And (output n1 n1 n0 n0 n1 n1 n0 n0 V) (output n1 n0 n1 n0 n1 n0 n1 n0 V))
+ ∀Univ:Set.∀V:Univ.∀X:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X1:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xname:Univ.∀Xrevlist:Univ.∀Y:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀Z:Univ.∀add_inverter:∀_:Univ.∀_:Univ.Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀end:Univ.∀inverter_table:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀list:∀_:Univ.∀_:Univ.Univ.∀list_reversion:∀_:Univ.∀_:Univ.Univ.∀make_reverse_list:∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀not_reversion:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀possible_reversion:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀r00m:Univ.∀r01m:Univ.∀r0m0:Univ.∀r0m1:Univ.∀r10m:Univ.∀r11m:Univ.∀r1m0:Univ.∀r1m1:Univ.∀rm00:Univ.∀rm01:Univ.∀rm10:Univ.∀rm11:Univ.∀test:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀H0:∀X:Univ.output n0 n1 n0 n1 n0 n1 n0 n1 X.∀H1:∀X:Univ.output n0 n0 n1 n1 n0 n0 n1 n1 X.∀H2:∀X:Univ.output n0 n0 n0 n0 n1 n1 n1 n1 X.∀H3:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xrevlist:Univ.∀_:test X1 X2 X3 X4 X5 X6 X7 X8 V Xrevlist.output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H4:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.test (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8) (add_inverter V (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8))) (make_reverse_list (list (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8)) V)).∀H5:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.output (or X1 Y1) (or X2 Y2) (or X3 Y3) (or X4 Y4) (or X5 Y5) (or X6 Y6) (or X7 Y7) (or X8 Y8) V.∀H6:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.output (myand X1 Y1) (myand X2 Y2) (myand X3 Y3) (myand X4 Y4) (myand X5 Y5) (myand X6 Y6) (myand X7 Y7) (myand X8 Y8) V.∀H7:∀X:Univ.∀Y:Univ.eq Univ (list_reversion X (list_reversion X Y)) (list_reversion X Y).∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (list_reversion X (list_reversion Y Z)) (list_reversion Y (list_reversion X Z)).∀H9:∀X:Univ.eq Univ (list_reversion not_reversion X) X.∀H10:∀X:Univ.∀Xname:Univ.eq Univ (possible_reversion Xname X X) not_reversion.∀H11:∀Xname:Univ.eq Univ (possible_reversion Xname n0 n1) not_reversion.∀H12:∀Xname:Univ.eq Univ (possible_reversion Xname n1 n0) Xname.∀H13:∀V:Univ.eq Univ (make_reverse_list V) end.∀H14:∀V:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.eq Univ (make_reverse_list (list (inverter_table X000 X001 X010 X011 X100 X101 X110 X111) V)) (list_reversion (possible_reversion r00m X000 X001) (list_reversion (possible_reversion r01m X010 X011) (list_reversion (possible_reversion r10m X100 X101) (list_reversion (possible_reversion r11m X110 X111) (list_reversion (possible_reversion r0m0 X000 X010) (list_reversion (possible_reversion r0m1 X001 X011) (list_reversion (possible_reversion r1m0 X100 X110) (list_reversion (possible_reversion r1m1 X101 X111) (list_reversion (possible_reversion rm00 X000 X100) (list_reversion (possible_reversion rm01 X001 X101) (list_reversion (possible_reversion rm10 X010 X110) (list_reversion (possible_reversion rm11 X011 X111) (make_reverse_list V))))))))))))).∀H15:∀X:Univ.∀Y:Univ.eq Univ (add_inverter X Y) (list Y X).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add_inverter (list X Y) Z) (list X (add_inverter Y Z)).∀H17:eq Univ (not n1) n0.∀H18:eq Univ (not n0) n1.∀H19:∀X:Univ.eq Univ (or X n1) n1.∀H20:∀X:Univ.eq Univ (or X n0) X.∀H21:∀X:Univ.eq Univ (myand X n1) X.∀H22:∀X:Univ.eq Univ (myand X n0) n0.∃V:Univ.And (output n1 n0 n1 n0 n1 n0 n1 n0 V) (And (output n1 n1 n0 n0 n1 n1 n0 n0 V) (output n1 n1 n1 n1 n0 n0 n0 n0 V))
.
intros.
exists[
(* ----Problem axioms *)
theorem prove_cannot_construct_this:
- ∀Univ:Set.∀V:Univ.∀X:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X1:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xname:Univ.∀Xrevlist:Univ.∀Y:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀Z:Univ.∀add_inverter:∀_:Univ.∀_:Univ.Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀basic_output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀end:Univ.∀inverter_table:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀list:∀_:Univ.∀_:Univ.Univ.∀list_reversion:∀_:Univ.∀_:Univ.Univ.∀make_reverse_list:∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀not_reversion:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀possible_reversion:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀r00m:Univ.∀r01m:Univ.∀r0m0:Univ.∀r0m1:Univ.∀r10m:Univ.∀r11m:Univ.∀r1m0:Univ.∀r1m1:Univ.∀rm00:Univ.∀rm01:Univ.∀rm10:Univ.∀rm11:Univ.∀test:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀H0:∀X:Univ.output n0 n1 n0 n1 n0 n1 n0 n1 X.∀H1:∀X:Univ.output n0 n0 n1 n1 n0 n0 n1 n1 X.∀H2:∀X:Univ.output n0 n0 n0 n0 n1 n1 n1 n1 X.∀H3:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xrevlist:Univ.∀_:test X1 X2 X3 X4 X5 X6 X7 X8 V Xrevlist.basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H4:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H5:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.test (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8) (add_inverter V (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8))) (make_reverse_list (list (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8)) V)).∀H6:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.output (or X1 Y1) (or X2 Y2) (or X3 Y3) (or X4 Y4) (or X5 Y5) (or X6 Y6) (or X7 Y7) (or X8 Y8) V.∀H7:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:basic_output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.basic_output (myand X1 Y1) (myand X2 Y2) (myand X3 Y3) (myand X4 Y4) (myand X5 Y5) (myand X6 Y6) (myand X7 Y7) (myand X8 Y8) V.∀H8:∀X:Univ.∀Y:Univ.eq Univ (list_reversion X (list_reversion X Y)) (list_reversion X Y).∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (list_reversion X (list_reversion Y Z)) (list_reversion Y (list_reversion X Z)).∀H10:∀X:Univ.eq Univ (list_reversion not_reversion X) X.∀H11:∀X:Univ.∀Xname:Univ.eq Univ (possible_reversion Xname X X) not_reversion.∀H12:∀Xname:Univ.eq Univ (possible_reversion Xname n0 n1) not_reversion.∀H13:∀Xname:Univ.eq Univ (possible_reversion Xname n1 n0) Xname.∀H14:∀V:Univ.eq Univ (make_reverse_list V) end.∀H15:∀V:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.eq Univ (make_reverse_list (list (inverter_table X000 X001 X010 X011 X100 X101 X110 X111) V)) (list_reversion (possible_reversion r00m X000 X001) (list_reversion (possible_reversion r01m X010 X011) (list_reversion (possible_reversion r10m X100 X101) (list_reversion (possible_reversion r11m X110 X111) (list_reversion (possible_reversion r0m0 X000 X010) (list_reversion (possible_reversion r0m1 X001 X011) (list_reversion (possible_reversion r1m0 X100 X110) (list_reversion (possible_reversion r1m1 X101 X111) (list_reversion (possible_reversion rm00 X000 X100) (list_reversion (possible_reversion rm01 X001 X101) (list_reversion (possible_reversion rm10 X010 X110) (list_reversion (possible_reversion rm11 X011 X111) (make_reverse_list V))))))))))))).∀H16:∀X:Univ.∀Y:Univ.eq Univ (add_inverter X Y) (list Y X).∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add_inverter (list X Y) Z) (list X (add_inverter Y Z)).∀H18:eq Univ (not n1) n0.∀H19:eq Univ (not n0) n1.∀H20:∀X:Univ.eq Univ (or X n1) n1.∀H21:∀X:Univ.eq Univ (or X n0) X.∀H22:∀X:Univ.eq Univ (myand X n1) X.∀H23:∀X:Univ.eq Univ (myand X n0) n0.∃V:Univ.And (output n1 n1 n1 n1 n0 n0 n0 n0 V) (And (output n1 n1 n0 n0 n1 n1 n0 n0 V) (output n1 n0 n1 n0 n1 n0 n1 n0 V))
+ ∀Univ:Set.∀V:Univ.∀X:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X1:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xname:Univ.∀Xrevlist:Univ.∀Y:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀Z:Univ.∀add_inverter:∀_:Univ.∀_:Univ.Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀basic_output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀end:Univ.∀inverter_table:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀list:∀_:Univ.∀_:Univ.Univ.∀list_reversion:∀_:Univ.∀_:Univ.Univ.∀make_reverse_list:∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀not_reversion:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀possible_reversion:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀r00m:Univ.∀r01m:Univ.∀r0m0:Univ.∀r0m1:Univ.∀r10m:Univ.∀r11m:Univ.∀r1m0:Univ.∀r1m1:Univ.∀rm00:Univ.∀rm01:Univ.∀rm10:Univ.∀rm11:Univ.∀test:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀H0:∀X:Univ.output n0 n1 n0 n1 n0 n1 n0 n1 X.∀H1:∀X:Univ.output n0 n0 n1 n1 n0 n0 n1 n1 X.∀H2:∀X:Univ.output n0 n0 n0 n0 n1 n1 n1 n1 X.∀H3:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xrevlist:Univ.∀_:test X1 X2 X3 X4 X5 X6 X7 X8 V Xrevlist.basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H4:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H5:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.test (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8) (add_inverter V (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8))) (make_reverse_list (list (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8)) V)).∀H6:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.output (or X1 Y1) (or X2 Y2) (or X3 Y3) (or X4 Y4) (or X5 Y5) (or X6 Y6) (or X7 Y7) (or X8 Y8) V.∀H7:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:basic_output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.basic_output (myand X1 Y1) (myand X2 Y2) (myand X3 Y3) (myand X4 Y4) (myand X5 Y5) (myand X6 Y6) (myand X7 Y7) (myand X8 Y8) V.∀H8:∀X:Univ.∀Y:Univ.eq Univ (list_reversion X (list_reversion X Y)) (list_reversion X Y).∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (list_reversion X (list_reversion Y Z)) (list_reversion Y (list_reversion X Z)).∀H10:∀X:Univ.eq Univ (list_reversion not_reversion X) X.∀H11:∀X:Univ.∀Xname:Univ.eq Univ (possible_reversion Xname X X) not_reversion.∀H12:∀Xname:Univ.eq Univ (possible_reversion Xname n0 n1) not_reversion.∀H13:∀Xname:Univ.eq Univ (possible_reversion Xname n1 n0) Xname.∀H14:∀V:Univ.eq Univ (make_reverse_list V) end.∀H15:∀V:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.eq Univ (make_reverse_list (list (inverter_table X000 X001 X010 X011 X100 X101 X110 X111) V)) (list_reversion (possible_reversion r00m X000 X001) (list_reversion (possible_reversion r01m X010 X011) (list_reversion (possible_reversion r10m X100 X101) (list_reversion (possible_reversion r11m X110 X111) (list_reversion (possible_reversion r0m0 X000 X010) (list_reversion (possible_reversion r0m1 X001 X011) (list_reversion (possible_reversion r1m0 X100 X110) (list_reversion (possible_reversion r1m1 X101 X111) (list_reversion (possible_reversion rm00 X000 X100) (list_reversion (possible_reversion rm01 X001 X101) (list_reversion (possible_reversion rm10 X010 X110) (list_reversion (possible_reversion rm11 X011 X111) (make_reverse_list V))))))))))))).∀H16:∀X:Univ.∀Y:Univ.eq Univ (add_inverter X Y) (list Y X).∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add_inverter (list X Y) Z) (list X (add_inverter Y Z)).∀H18:eq Univ (not n1) n0.∀H19:eq Univ (not n0) n1.∀H20:∀X:Univ.eq Univ (or X n1) n1.∀H21:∀X:Univ.eq Univ (or X n0) X.∀H22:∀X:Univ.eq Univ (myand X n1) X.∀H23:∀X:Univ.eq Univ (myand X n0) n0.∃V:Univ.And (output n1 n0 n1 n0 n1 n0 n1 n0 V) (And (output n1 n1 n0 n0 n1 n1 n0 n0 V) (output n1 n1 n1 n1 n0 n0 n0 n0 V))
.
intros.
exists[
(* ----Problem clauses *)
theorem prove_inversion:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a1:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀circuit:∀_:Univ.Prop.∀i1:Univ.∀i2:Univ.∀i3:Univ.∀inv1:Univ.∀inv2:Univ.∀n0:Univ.∀n1:Univ.∀n10:Univ.∀n11:Univ.∀n12:Univ.∀n13:Univ.∀n14:Univ.∀n15:Univ.∀n16:Univ.∀n17:Univ.∀n18:Univ.∀n19:Univ.∀n2:Univ.∀n20:Univ.∀n21:Univ.∀n22:Univ.∀n23:Univ.∀n24:Univ.∀n25:Univ.∀n3:Univ.∀n4:Univ.∀n5:Univ.∀n6:Univ.∀n7:Univ.∀n8:Univ.∀n9:Univ.∀not:∀_:Univ.Univ.∀o1:Univ.∀o2:Univ.∀o3:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀xor:∀_:Univ.∀_:Univ.Univ.∀H0:circuit o3.∀H1:circuit o2.∀H2:circuit o1.∀H3:eq Univ inv2 (not n9).∀H4:eq Univ inv1 (not n20).∀H5:eq Univ n25 (or n2 n24).∀H6:eq Univ n24 (myand i1 inv1).∀H7:eq Univ n23 (myand i1 i3).∀H8:eq Univ n22 (or n23 n6).∀H9:eq Univ n21 (myand inv1 inv2).∀H10:eq Univ n20 (or n22 n14).∀H11:eq Univ n19 (myand n23 inv2).∀H12:eq Univ n18 (or n19 n25).∀H13:eq Univ n17 (or n18 n21).∀H14:eq Univ n16 (myand n14 inv2).∀H15:eq Univ n15 (myand inv2 n6).∀H16:eq Univ n14 (myand i2 i3).∀H17:eq Univ n13 (or n12 n21).∀H18:eq Univ n12 (or n11 n16).∀H19:eq Univ n11 (or a1 n2).∀H20:eq Univ n10 (or n24 n7).∀H21:eq Univ n9 (or n8 n2).∀H22:eq Univ n8 (or a1 n10).∀H23:eq Univ n7 (myand n6 i3).∀H24:eq Univ n6 (myand i1 i2).∀H25:eq Univ n5 (or n4 n21).∀H26:eq Univ n4 (or n15 n3).∀H27:eq Univ n3 (or a1 n24).∀H28:eq Univ n2 (myand inv1 i3).∀H29:eq Univ a1 (myand inv1 i2).∀H30:eq Univ o3 n5.∀H31:eq Univ o2 n17.∀H32:eq Univ o1 n13.∀H33:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand Y (myand X Z)) (myand X (myand Y Z)).∀H34:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (myand Y X).∀H35:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (xor Y (xor X Z)) (xor X (xor Y Z)).∀H36:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (xor Y X).∀H37:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (xor (myand X Y) (xor X Y)).∀H38:∀X:Univ.eq Univ (not X) (xor n1 X).∀H39:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand X (xor Y Z)) (xor (myand X Y) (myand X Z)).∀H40:∀X:Univ.∀Y:Univ.eq Univ (myand X (myand X Y)) (myand X Y).∀H41:∀X:Univ.eq Univ (myand X X) X.∀H42:∀X:Univ.eq Univ (myand X n1) X.∀H43:∀X:Univ.eq Univ (myand n1 X) X.∀H44:∀X:Univ.eq Univ (myand X n0) n0.∀H45:∀X:Univ.eq Univ (myand n0 X) n0.∀H46:∀X:Univ.∀Y:Univ.eq Univ (xor X (xor X Y)) Y.∀H47:∀X:Univ.eq Univ (xor X X) n0.∀H48:∀X:Univ.eq Univ (xor X n0) X.∀H49:∀X:Univ.eq Univ (xor n0 X) X.∀_:circuit (not i1).∀_:circuit (not i2).circuit (not i3)
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a1:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀circuit:∀_:Univ.Prop.∀i1:Univ.∀i2:Univ.∀i3:Univ.∀inv1:Univ.∀inv2:Univ.∀n0:Univ.∀n1:Univ.∀n10:Univ.∀n11:Univ.∀n12:Univ.∀n13:Univ.∀n14:Univ.∀n15:Univ.∀n16:Univ.∀n17:Univ.∀n18:Univ.∀n19:Univ.∀n2:Univ.∀n20:Univ.∀n21:Univ.∀n22:Univ.∀n23:Univ.∀n24:Univ.∀n25:Univ.∀n3:Univ.∀n4:Univ.∀n5:Univ.∀n6:Univ.∀n7:Univ.∀n8:Univ.∀n9:Univ.∀not:∀_:Univ.Univ.∀o1:Univ.∀o2:Univ.∀o3:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀xor:∀_:Univ.∀_:Univ.Univ.∀H0:circuit o3.∀H1:circuit o2.∀H2:circuit o1.∀H3:eq Univ inv2 (not n9).∀H4:eq Univ inv1 (not n20).∀H5:eq Univ n25 (or n2 n24).∀H6:eq Univ n24 (myand i1 inv1).∀H7:eq Univ n23 (myand i1 i3).∀H8:eq Univ n22 (or n23 n6).∀H9:eq Univ n21 (myand inv1 inv2).∀H10:eq Univ n20 (or n22 n14).∀H11:eq Univ n19 (myand n23 inv2).∀H12:eq Univ n18 (or n19 n25).∀H13:eq Univ n17 (or n18 n21).∀H14:eq Univ n16 (myand n14 inv2).∀H15:eq Univ n15 (myand inv2 n6).∀H16:eq Univ n14 (myand i2 i3).∀H17:eq Univ n13 (or n12 n21).∀H18:eq Univ n12 (or n11 n16).∀H19:eq Univ n11 (or a1 n2).∀H20:eq Univ n10 (or n24 n7).∀H21:eq Univ n9 (or n8 n2).∀H22:eq Univ n8 (or a1 n10).∀H23:eq Univ n7 (myand n6 i3).∀H24:eq Univ n6 (myand i1 i2).∀H25:eq Univ n5 (or n4 n21).∀H26:eq Univ n4 (or n15 n3).∀H27:eq Univ n3 (or a1 n24).∀H28:eq Univ n2 (myand inv1 i3).∀H29:eq Univ a1 (myand inv1 i2).∀H30:eq Univ o3 n5.∀H31:eq Univ o2 n17.∀H32:eq Univ o1 n13.∀H33:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand Y (myand X Z)) (myand X (myand Y Z)).∀H34:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (myand Y X).∀H35:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (xor Y (xor X Z)) (xor X (xor Y Z)).∀H36:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (xor Y X).∀H37:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (xor (myand X Y) (xor X Y)).∀H38:∀X:Univ.eq Univ (not X) (xor n1 X).∀H39:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand X (xor Y Z)) (xor (myand X Y) (myand X Z)).∀H40:∀X:Univ.∀Y:Univ.eq Univ (myand X (myand X Y)) (myand X Y).∀H41:∀X:Univ.eq Univ (myand X X) X.∀H42:∀X:Univ.eq Univ (myand X n1) X.∀H43:∀X:Univ.eq Univ (myand n1 X) X.∀H44:∀X:Univ.eq Univ (myand X n0) n0.∀H45:∀X:Univ.eq Univ (myand n0 X) n0.∀H46:∀X:Univ.∀Y:Univ.eq Univ (xor X (xor X Y)) Y.∀H47:∀X:Univ.eq Univ (xor X X) n0.∀H48:∀X:Univ.eq Univ (xor X n0) X.∀H49:∀X:Univ.eq Univ (xor n0 X) X.∀_:circuit (not i3).∀_:circuit (not i2).circuit (not i1)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_complememt:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (meet X Y) n0.∀_:eq Univ (join X Y) n1.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.complement a (join r1 (meet r2 b))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:complement X Y.∀_:eq Univ (join X Y) n1.eq Univ (meet X Y) n0.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet Z (join X Y)) (join X (meet Y Z)).eq Univ (meet X Z) X.∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.complement a (join r1 (meet r2 b))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_complememt_exists:
- ∀Univ:Set.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (meet X Y) n0.∀_:eq Univ (join X Y) n1.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.∃W:Univ.complement a W
+ ∀Univ:Set.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:complement X Y.∀_:eq Univ (join X Y) n1.eq Univ (meet X Y) n0.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet Z (join X Y)) (join X (meet Y Z)).eq Univ (meet X Z) X.∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.∃W:Univ.complement a W
.
intros.
exists[
(* -------------------------------------------------------------------------- *)
theorem prove_lemma:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (meet X Y) n0.∀_:eq Univ (join X Y) n1.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.eq Univ r1 (meet (join r1 (meet r2 b)) (join r1 (meet r2 a)))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:complement X Y.∀_:eq Univ (join X Y) n1.eq Univ (meet X Y) n0.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet Z (join X Y)) (join X (meet Y Z)).eq Univ (meet X Z) X.∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.eq Univ r1 (meet (join r1 (meet r2 b)) (join r1 (meet r2 a)))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_q4:
- ∀Univ:Set.∀V:Univ.∀W:Univ.∀W1:Univ.∀W2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀big_p:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀big_t:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c:Univ.∀d:Univ.∀e:Univ.∀plus:∀_:Univ.∀_:Univ.Univ.∀term:∀_:Univ.Prop.∀term1:Univ.∀term2:Univ.∀term3:Univ.∀term4:Univ.∀term5:Univ.∀term6:Univ.∀times:∀_:Univ.∀_:Univ.Univ.∀H0:∀W1:Univ.∀W2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W1.∀_:term W2.eq Univ (big_t W1 (big_p W2 (big_t W1 X Y) Z) (big_p W2 Y Z)) (big_p W2 (big_t W1 X Y) Z).∀H1:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W.eq Univ (big_p W (big_p W X Y) (big_p W Z V)) (big_p W (big_p W X Z) (big_p W Y V)).∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W.eq Univ (big_p W (big_p W X Y) Z) (big_p W X (big_p W Y Z)).∀H3:term term6.∀H4:term term5.∀H5:term term4.∀H6:term term3.∀H7:term term2.∀H8:term term1.∀H9:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (big_t W X Y) (big_p W X Y).∀H10:∀X:Univ.∀Y:Univ.eq Univ (big_p term6 X Y) (plus Y X).∀H11:∀X:Univ.∀Y:Univ.eq Univ (big_p term5 X Y) (plus X Y).∀H12:∀X:Univ.∀Y:Univ.eq Univ (big_p term4 X Y) (times Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (big_p term3 X Y) (times X Y).∀H14:∀X:Univ.∀Y:Univ.eq Univ (big_p term2 X Y) Y.∀H15:∀X:Univ.∀Y:Univ.eq Univ (big_p term1 X Y) X.eq Univ (times a (plus b (times d (times c e)))) (times a (plus b (times (plus b c) (times d (times c e)))))
+ ∀Univ:Set.∀V:Univ.∀W:Univ.∀W1:Univ.∀W2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀big_p:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀big_t:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c:Univ.∀d:Univ.∀e:Univ.∀plus:∀_:Univ.∀_:Univ.Univ.∀term:∀_:Univ.Prop.∀term1:Univ.∀term2:Univ.∀term3:Univ.∀term4:Univ.∀term5:Univ.∀term6:Univ.∀times:∀_:Univ.∀_:Univ.Univ.∀H0:∀W1:Univ.∀W2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W2.∀_:term W1.eq Univ (big_t W1 (big_p W2 (big_t W1 X Y) Z) (big_p W2 Y Z)) (big_p W2 (big_t W1 X Y) Z).∀H1:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W.eq Univ (big_p W (big_p W X Y) (big_p W Z V)) (big_p W (big_p W X Z) (big_p W Y V)).∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W.eq Univ (big_p W (big_p W X Y) Z) (big_p W X (big_p W Y Z)).∀H3:term term6.∀H4:term term5.∀H5:term term4.∀H6:term term3.∀H7:term term2.∀H8:term term1.∀H9:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (big_t W X Y) (big_p W X Y).∀H10:∀X:Univ.∀Y:Univ.eq Univ (big_p term6 X Y) (plus Y X).∀H11:∀X:Univ.∀Y:Univ.eq Univ (big_p term5 X Y) (plus X Y).∀H12:∀X:Univ.∀Y:Univ.eq Univ (big_p term4 X Y) (times Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (big_p term3 X Y) (times X Y).∀H14:∀X:Univ.∀Y:Univ.eq Univ (big_p term2 X Y) Y.∀H15:∀X:Univ.∀Y:Univ.eq Univ (big_p term1 X Y) X.eq Univ (times a (plus b (times d (times c e)))) (times a (plus b (times (plus b c) (times d (times c e)))))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_mv_4:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (big_V (implies x y) (implies y x)) truth
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (big_V (implies x y) (implies y x)) truth
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_wajsberg_theorem:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_V x y) z) (big_hat (implies x z) (implies y z))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_V x y) z) (big_hat (implies x z) (implies y z))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_wajsberg_theorem:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (big_hat y z)) (big_hat (implies x y) (implies x z))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (big_hat y z)) (big_hat (implies x y) (implies x z))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_wajsberg_theorem:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (big_V y z)) (big_V (implies x y) (implies x z))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (big_V y z)) (big_V (implies x y) (implies x z))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_wajsberg_theorem:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_hat x y) z) (big_V (implies x z) (implies y z))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_hat x y) z) (big_V (implies x z) (implies y z))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_wajsberg_theorem:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (big_V (big_hat x y) z) (big_hat (big_V x z) (big_V y z))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (big_V (big_hat x y) z) (big_hat (big_V x z) (big_V y z))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_wajsberg_theorem:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_hat x y) z) (implies (implies x y) (implies x z))
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_hat x y) z) (implies (implies x y) (implies x z))
.
intros.
autobatch paramodulation timeout=600;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (implies q r) (implies p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (implies q r) (implies p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (not p) q) (implies (not q) p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (not p) q) (implies (not q) p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (not q) (not p)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (not q) (not p)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (not q) (not p)) (implies p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (not q) (not p)) (implies p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p (or q r)) (or (or p q) r))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p (or q r)) (or (or p q) r))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or (or p q) r) (or p (or q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or (or p q) r) (or p (or q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (or p q) (or r p)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (or p q) (or r p)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (or q p) (or p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (or q p) (or p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (or q p) (or r p)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (or q p) (or r p)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or (not p) (implies p q)) (implies p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or (not p) (implies p q)) (implies p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (not (or p q)) (or (not p) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (not (or p q)) (or (not p) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (not (implies p q)) (implies (not p) (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (not (implies p q)) (implies (not p) (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (not p) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (not p) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (implies (not p) q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (implies (not p) q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (implies p q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (implies p q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (or p q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (or p q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or p (not q)) p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or p (not q)) p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (implies p (not q)) (not p)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (implies p (not q)) (not p)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (or p q) q) (implies p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (or p q) q) (implies p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (implies p q) q) (or p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (implies p q) q) (or p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (implies p q) q) (implies (implies q p) p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (implies p q) q) (implies (implies q p) p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (or (or p q) r) (or q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (or (or p q) r) (or q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q p) (implies (or (or p q) r) (or p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q p) (implies (or (or p q) r) (or p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or p (implies q r)) (or p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or p (implies q r)) (or p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p (implies q r)) (implies (or p q) (or p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p (implies q r)) (implies (or p q) (or p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p (implies q r)) (implies (implies p q) (implies p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p (implies q r)) (implies (implies p q) (implies p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or q r) (implies (or (not r) s) (or q s)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or q r) (implies (or (not r) s) (or q s)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q (implies r s)) (implies (or p q) (implies (or p r) (or p s))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q (implies r s)) (implies (or p q) (implies (or p r) (or p s))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p (implies q r)) (implies (implies p (implies r s)) (implies p (implies q s))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p (implies q r)) (implies (implies p (implies r s)) (implies p (implies q s))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (or p q) (or p r)) (or p (implies q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (or p q) (or p r)) (or p (implies q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (implies p q) (implies p r)) (implies p (implies q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (implies p q) (implies p r)) (implies p (implies q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies p (implies q (myand p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies p (implies q (myand p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies q (implies p (myand p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies q (implies p (myand p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (myand p q) r) (implies p (implies q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (myand p q) r) (implies p (implies q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p (implies q r)) (implies (myand p q) r))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p (implies q r)) (implies (myand p q) r))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies q r) (implies p q)) (implies p r))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies q r) (implies p q)) (implies p r))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand p (implies p q)) q)
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand p (implies p q)) q)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (myand p q) r) (implies (myand p (not r)) (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (myand p q) r) (implies (myand p (not r)) (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p r) (implies (myand p q) r))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p r) (implies (myand p q) r))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (myand p q) r))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (myand p q) r))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p q) (implies p r)) (implies p (myand q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p q) (implies p r)) (implies p (myand q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies q p) (implies r p)) (implies (or q r) p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies q p) (implies r p)) (implies (or q r) p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (myand p r) (myand q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (myand p r) (myand q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p r) (implies q s)) (implies (myand p q) (myand r s)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p r) (implies q s)) (implies (myand p q) (myand r s)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p r) (implies q s)) (implies (or p q) (or r s)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p r) (implies q s)) (implies (or p q) (or r s)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or (not p) q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or (not p) q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (not p) (or (not q) (myand p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (not p) (or (not q) (myand p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (implies (not q) (not p)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (implies (not q) (not p)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (equivalent (not p) (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (equivalent (not p) (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (equivalent (not p) (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (equivalent (not p) (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (not (not p)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (not (not p)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (implies q r)) (myand p (implies (not r) (not q))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (implies q r)) (myand p (implies (not r) (not q))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (equivalent q p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (equivalent q p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (equivalent p q) (equivalent q r)) (equivalent p r))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (equivalent p q) (equivalent q r)) (equivalent p r))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (myand p p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (myand p p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (or p p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (or p p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p q) (myand q p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p q) (myand q p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p q) (or q p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p q) (or q p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand r (myand p q)) (myand p (myand q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand r (myand p q)) (myand p (myand q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or r (or p q)) (or p (or q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or r (or p q)) (or p (or q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (myand p r) (myand q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (myand p r) (myand q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (or p r) (or q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (or p r) (or q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (or q r)) (or (myand p q) (myand p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (or q r)) (or (myand p q) (myand p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p (myand q r)) (myand (or p q) (or p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p (myand q r)) (myand (or p q) (or p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (or (myand p q) (myand p (not q))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (or (myand p q) (myand p (not q))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (myand (or p q) (or p (not q))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (myand (or p q) (or p (not q))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (or p (myand p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (or p (myand p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (myand p (or p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (myand p (or p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (myand p (not q))) (or (not p) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (myand p (not q))) (or (not p) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (myand (not p) (not q))) (or p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (myand (not p) (not q))) (or p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (implies p q)) (myand p (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (implies p q)) (myand p (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (myand p q)) (or (not p) (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (myand p q)) (or (not p) (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (implies (not p) q)) (myand (not p) (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (implies (not p) q)) (myand (not p) (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (not p) (not q)) (or p (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (not p) (not q)) (or p (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (implies p (myand p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (implies p (myand p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (equivalent q (or p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (equivalent q (or p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (equivalent q (or p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p q) (equivalent q (or p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies q (equivalent p (myand p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies q (equivalent p (myand p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (not p) (equivalent q (or p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (not p) (equivalent q (or p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies p q) (implies p r)) (implies p (myand q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies p q) (implies p r)) (implies p (myand q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies q p) (implies r p)) (implies (or q r) p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies q p) (implies r p)) (implies (or q r) p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or (implies p q) (implies p r)) (implies p (or q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or (implies p q) (implies p r)) (implies p (or q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or (implies q p) (implies r p)) (implies (myand q r) p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or (implies q p) (implies r p)) (implies (myand q r) p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p (not p)) (not p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p (not p)) (not p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (not p) p) p)
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (not p) p) p)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies p q) (implies p (not q))) (not p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies p q) (implies p (not q))) (not p))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies p q) (implies (not p) q)) q)
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (implies p q) (implies (not p) q)) q)
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (implies p r) (implies q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (implies p r) (implies q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (implies r p) (implies r q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent p q) (equivalent (implies r p) (implies r q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand p q) (equivalent p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand p q) (equivalent p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (implies p q) (implies (not p) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (implies p q) (implies (not p) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (not (myand (equivalent p q) (equivalent p (not q))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (not (myand (equivalent p q) (equivalent p (not q))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (or p q) (not (myand p q))) (equivalent p (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (or p q) (not (myand p q))) (equivalent p (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (not (equivalent p (not p)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (not (equivalent p (not p)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (not p) (not q)) (equivalent p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (not p) (not q)) (equivalent p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (or (myand p q) (myand (not p) (not q))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (equivalent p q) (or (myand p q) (myand (not p) (not q))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (or (myand p q) (myand (not p) (not q)))) (or (myand p (not q)) (myand q (not p))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (not (or (myand p q) (myand (not p) (not q)))) (or (myand p (not q)) (myand q (not p))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p q) (implies (implies p q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p q) (implies (implies p q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (myand p q) r) (implies (myand p q) (myand p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (myand p q) r) (implies (myand p q) (myand p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand r (implies p q)) (implies p (myand q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H2:∀X:Univ.∀_:axiomP X.theoremP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand r (implies p q)) (implies p (myand q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (implies q r)) (myand p (implies (myand p q) r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (implies q r)) (myand p (implies (myand p q) r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p q) (implies q r)) (implies p (equivalent q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p q) (implies q r)) (implies p (equivalent q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (equivalent p q)) (myand q (equivalent p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand p (equivalent p q)) (myand q (equivalent p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p (implies p q)) (implies p q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p (implies p q)) (implies p q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p (implies q r)) (implies p (implies q (myand p r))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies p (implies q r)) (implies p (implies q (myand p r))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (equivalent (implies p r) (implies p (myand q r))))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (equivalent (implies p r) (implies p (myand q r))))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies p (equivalent (implies p q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies p (equivalent (implies p q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies p (equivalent q (equivalent p q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies p (equivalent q (equivalent p q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (equivalent (myand p q) p) (equivalent (myand p q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (equivalent (myand p q) p) (equivalent (myand p q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (equivalent (or p q) p) (equivalent (or p q) q))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (equivalent (or p q) p) (equivalent (or p q) q))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (myand p (not q)) r) (implies p (or q r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (implies (myand p (not q)) r) (implies p (or q r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (or p q) (not q)) (myand p (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (myand (or p q) (not q)) (myand p (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or (myand p q) (not q)) (or p (not q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or (myand p q) (not q)) (or p (not q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p q) (or p (myand (not p) q)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p q) (or p (myand (not p) q)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q (not r)) (equivalent (myand (or p q) r) (myand p r)))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q (not r)) (equivalent (myand (or p q) r) (myand p r)))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem prove_this:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent (myand (implies r (not q)) p) (or q r)) (equivalent (myand p (not q)) r))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (equivalent (myand (implies r (not q)) p) (or q r)) (equivalent (myand p (not q)) r))
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* ----3*2*U2 is a left segment of U1*U3 *)
theorem prove_equation:
- ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀f:∀_:Univ.∀_:Univ.Univ.∀left:∀_:Univ.∀_:Univ.Prop.∀n1:Univ.∀n2:Univ.∀n3:Univ.∀u:Univ.∀u1:Univ.∀u2:Univ.∀u3:Univ.∀H0:eq Univ b (f u1 u3).∀H1:eq Univ a (f (f n3 n2) u2).∀H2:eq Univ u3 (f u n3).∀H3:eq Univ u2 (f u n2).∀H4:eq Univ u1 (f u n1).∀H5:eq Univ u (f n2 n2).∀H6:eq Univ n3 (f n2 n1).∀H7:eq Univ n2 (f n1 n1).∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:left X Y.∀_:left Y Z.left X Z.∀H9:∀X:Univ.∀Y:Univ.left X (f X Y).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).left a b
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀f:∀_:Univ.∀_:Univ.Univ.∀left:∀_:Univ.∀_:Univ.Prop.∀n1:Univ.∀n2:Univ.∀n3:Univ.∀u:Univ.∀u1:Univ.∀u2:Univ.∀u3:Univ.∀H0:eq Univ b (f u1 u3).∀H1:eq Univ a (f (f n3 n2) u2).∀H2:eq Univ u3 (f u n3).∀H3:eq Univ u2 (f u n2).∀H4:eq Univ u1 (f u n1).∀H5:eq Univ u (f n2 n2).∀H6:eq Univ n3 (f n2 n1).∀H7:eq Univ n2 (f n1 n1).∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:left Y Z.∀_:left X Y.left X Z.∀H9:∀X:Univ.∀Y:Univ.left X (f X Y).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).left a b
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
(* -------------------------------------------------------------------------- *)
theorem clause95:
- ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X10:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀X9:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀X9:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:accessible_world U V.∀_:think_believe_consider U W.∀_:present U W.∀_:event U W.∀_:theme U W V.∀_:vincent_forename U X.∀_:forename U X.∀_:agent U W Y.∀_:man U Y.∀_:of U X Y.∀_:state U Z.∀_:man U X1.∀_:be U Z X1 X1.∀_:forename U X2.∀_:jules_forename U X2.∀_:of U X2 X1.∀_:accessible_world U X3.∀_:proposition U X3.∀_:jules_forename U X4.∀_:forename U X4.∀_:smoke X3 X5.∀_:present X3 X5.∀_:agent X3 X5 X6.∀_:event X3 X5.∀_:man U X6.∀_:of U X4 X6.∀_:vincent_forename U X7.∀_:forename U X7.∀_:agent U X8 X9.∀_:man U X9.∀_:of U X7 X9.∀_:theme U X8 X3.∀_:event U X8.∀_:present U X8.∀_:think_believe_consider U X8.∀_:actual_world U.man V (skf4 V).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X10:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃X9:Univ.∃Y:Univ.∃Z:Univ.And (proposition U V) (And (accessible_world U V) (And (smoke V W) (And (present V W) (And (agent V W (skf4 V)) (And (event V W) (And (think_believe_consider U X) (And (present U X) (And (event U X) (And (theme U X V) (And (vincent_forename U Y) (And (forename U Y) (And (agent U X Z) (And (man U Z) (And (of U Y Z) (And (state U X1) (And (man U X2) (And (be U X1 X2 X2) (And (forename U X3) (And (jules_forename U X3) (And (of U X3 X2) (And (accessible_world U X4) (And (proposition U X4) (And (jules_forename U X5) (And (forename U X5) (And (smoke X4 X6) (And (present X4 X6) (And (agent X4 X6 X7) (And (event X4 X6) (And (man U X7) (And (of U X5 X7) (And (vincent_forename U X8) (And (forename U X8) (And (agent U X9 X10) (And (man U X10) (And (of U X8 X10) (And (theme U X9 X4) (And (event U X9) (And (present U X9) (And (think_believe_consider U X9) (actual_world U))))))))))))))))))))))))))))))))))))))))
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X10:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀X9:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀X9:Univ.∀Y:Univ.∀Z:Univ.∀_:actual_world U.∀_:think_believe_consider U X8.∀_:present U X8.∀_:event U X8.∀_:theme U X8 X3.∀_:of U X7 X9.∀_:man U X9.∀_:agent U X8 X9.∀_:forename U X7.∀_:vincent_forename U X7.∀_:of U X4 X6.∀_:man U X6.∀_:event X3 X5.∀_:agent X3 X5 X6.∀_:present X3 X5.∀_:smoke X3 X5.∀_:forename U X4.∀_:jules_forename U X4.∀_:proposition U X3.∀_:accessible_world U X3.∀_:of U X2 X1.∀_:jules_forename U X2.∀_:forename U X2.∀_:be U Z X1 X1.∀_:man U X1.∀_:state U Z.∀_:of U X Y.∀_:man U Y.∀_:agent U W Y.∀_:forename U X.∀_:vincent_forename U X.∀_:theme U W V.∀_:event U W.∀_:present U W.∀_:think_believe_consider U W.∀_:accessible_world U V.∀_:proposition U V.man V (skf4 V).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:agent U X Z.∀_:agent U Y Z.∀_:theme U Y W.∀_:think_believe_consider U Y.∀_:think_believe_consider U X.∀_:theme U X V.∀_:proposition U W.∀_:proposition U V.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:entity U X.∀_:of U V X.∀_:forename U W.∀_:of U W X.∀_:forename U V.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:be U W X Y.∀_:accessible_world U V.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:of U W X.∀_:accessible_world U V.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:theme U W X.∀_:accessible_world U V.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:agent U W X.∀_:accessible_world U V.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:jules_forename U W.∀_:accessible_world U V.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:vincent_forename U W.∀_:accessible_world U V.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relname U W.∀_:accessible_world U V.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:forename U W.∀_:accessible_world U V.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:male U W.∀_:accessible_world U V.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:animate U W.∀_:accessible_world U V.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human U W.∀_:accessible_world U V.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:living U W.∀_:accessible_world U V.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:impartial U W.∀_:accessible_world U V.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:existent U W.∀_:accessible_world U V.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:entity U W.∀_:accessible_world U V.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:organism U W.∀_:accessible_world U V.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human_person U W.∀_:accessible_world U V.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:man U W.∀_:accessible_world U V.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:state U W.∀_:accessible_world U V.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:general U W.∀_:accessible_world U V.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonhuman U W.∀_:accessible_world U V.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:abstraction U W.∀_:accessible_world U V.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relation U W.∀_:accessible_world U V.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:proposition U W.∀_:accessible_world U V.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:think_believe_consider U W.∀_:accessible_world U V.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:present U W.∀_:accessible_world U V.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:unisex U W.∀_:accessible_world U V.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonexistent U W.∀_:accessible_world U V.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:specific U W.∀_:accessible_world U V.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:singleton U W.∀_:accessible_world U V.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:thing U W.∀_:accessible_world U V.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:eventuality U W.∀_:accessible_world U V.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:event U W.∀_:accessible_world U V.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:smoke U W.∀_:accessible_world U V.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:existent U V.nonexistent U V.∀H61:∀U:Univ.∀V:Univ.∀_:nonhuman U V.human U V.∀H62:∀U:Univ.∀V:Univ.∀_:specific U V.general U V.∀H63:∀U:Univ.∀V:Univ.∀_:unisex U V.male U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X10:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃X9:Univ.∃Y:Univ.∃Z:Univ.And (actual_world U) (And (think_believe_consider U X9) (And (present U X9) (And (event U X9) (And (theme U X9 X4) (And (of U X8 X10) (And (man U X10) (And (agent U X9 X10) (And (forename U X8) (And (vincent_forename U X8) (And (of U X5 X7) (And (man U X7) (And (event X4 X6) (And (agent X4 X6 X7) (And (present X4 X6) (And (smoke X4 X6) (And (forename U X5) (And (jules_forename U X5) (And (proposition U X4) (And (accessible_world U X4) (And (of U X3 X2) (And (jules_forename U X3) (And (forename U X3) (And (be U X1 X2 X2) (And (man U X2) (And (state U X1) (And (of U Y Z) (And (man U Z) (And (agent U X Z) (And (forename U Y) (And (vincent_forename U Y) (And (theme U X V) (And (event U X) (And (present U X) (And (think_believe_consider U X) (And (event V W) (And (agent V W (skf4 V)) (And (present V W) (And (smoke V W) (And (accessible_world U V) (proposition U V))))))))))))))))))))))))))))))))))))))))
.
intros.
exists[
(* -------------------------------------------------------------------------- *)
theorem clause95:
- ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀Y:Univ.∀Z:Univ.∀_:accessible_world U V.∀_:proposition U V.∀_:theme U W V.∀_:event U W.∀_:present U W.∀_:think_believe_consider U W.∀_:forename U X.∀_:vincent_forename U X.∀_:of U X Y.∀_:man U Y.∀_:agent U W Y.∀_:state U Z.∀_:smoke X1 X2.∀_:present X1 X2.∀_:agent X1 X2 X3.∀_:event X1 X2.∀_:be U Z X3 X3.∀_:man U X3.∀_:of U X4 X3.∀_:jules_forename U X4.∀_:forename U X4.∀_:proposition U X1.∀_:accessible_world U X1.∀_:think_believe_consider U X5.∀_:present U X5.∀_:event U X5.∀_:theme U X5 X1.∀_:vincent_forename U X6.∀_:forename U X6.∀_:agent U X5 X7.∀_:man U X7.∀_:of U X6 X7.∀_:actual_world U.man V (skf4 V).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃Y:Univ.∃Z:Univ.And (smoke U V) (And (present U V) (And (agent U V (skf4 U)) (And (event U V) (And (accessible_world W U) (And (proposition W U) (And (theme W X U) (And (event W X) (And (present W X) (And (think_believe_consider W X) (And (forename W Y) (And (vincent_forename W Y) (And (of W Y Z) (And (man W Z) (And (agent W X Z) (And (state W X1) (And (smoke X2 X3) (And (present X2 X3) (And (agent X2 X3 X4) (And (event X2 X3) (And (be W X1 X4 X4) (And (man W X4) (And (of W X5 X4) (And (jules_forename W X5) (And (forename W X5) (And (proposition W X2) (And (accessible_world W X2) (And (think_believe_consider W X6) (And (present W X6) (And (event W X6) (And (theme W X6 X2) (And (vincent_forename W X7) (And (forename W X7) (And (agent W X6 X8) (And (man W X8) (And (of W X7 X8) (actual_world W))))))))))))))))))))))))))))))))))))
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀Y:Univ.∀Z:Univ.∀_:actual_world U.∀_:of U X6 X7.∀_:man U X7.∀_:agent U X5 X7.∀_:forename U X6.∀_:vincent_forename U X6.∀_:theme U X5 X1.∀_:event U X5.∀_:present U X5.∀_:think_believe_consider U X5.∀_:accessible_world U X1.∀_:proposition U X1.∀_:forename U X4.∀_:jules_forename U X4.∀_:of U X4 X3.∀_:man U X3.∀_:be U Z X3 X3.∀_:event X1 X2.∀_:agent X1 X2 X3.∀_:present X1 X2.∀_:smoke X1 X2.∀_:state U Z.∀_:agent U W Y.∀_:man U Y.∀_:of U X Y.∀_:vincent_forename U X.∀_:forename U X.∀_:think_believe_consider U W.∀_:present U W.∀_:event U W.∀_:theme U W V.∀_:proposition U V.∀_:accessible_world U V.man V (skf4 V).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:agent U X Z.∀_:agent U Y Z.∀_:theme U Y W.∀_:think_believe_consider U Y.∀_:think_believe_consider U X.∀_:theme U X V.∀_:proposition U W.∀_:proposition U V.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:entity U X.∀_:of U V X.∀_:forename U W.∀_:of U W X.∀_:forename U V.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:be U W X Y.∀_:accessible_world U V.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:of U W X.∀_:accessible_world U V.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:theme U W X.∀_:accessible_world U V.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:agent U W X.∀_:accessible_world U V.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:jules_forename U W.∀_:accessible_world U V.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:vincent_forename U W.∀_:accessible_world U V.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relname U W.∀_:accessible_world U V.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:forename U W.∀_:accessible_world U V.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:male U W.∀_:accessible_world U V.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:animate U W.∀_:accessible_world U V.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human U W.∀_:accessible_world U V.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:living U W.∀_:accessible_world U V.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:impartial U W.∀_:accessible_world U V.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:existent U W.∀_:accessible_world U V.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:entity U W.∀_:accessible_world U V.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:organism U W.∀_:accessible_world U V.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human_person U W.∀_:accessible_world U V.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:man U W.∀_:accessible_world U V.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:state U W.∀_:accessible_world U V.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:general U W.∀_:accessible_world U V.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonhuman U W.∀_:accessible_world U V.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:abstraction U W.∀_:accessible_world U V.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relation U W.∀_:accessible_world U V.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:proposition U W.∀_:accessible_world U V.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:think_believe_consider U W.∀_:accessible_world U V.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:present U W.∀_:accessible_world U V.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:unisex U W.∀_:accessible_world U V.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonexistent U W.∀_:accessible_world U V.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:specific U W.∀_:accessible_world U V.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:singleton U W.∀_:accessible_world U V.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:thing U W.∀_:accessible_world U V.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:eventuality U W.∀_:accessible_world U V.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:event U W.∀_:accessible_world U V.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:smoke U W.∀_:accessible_world U V.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:existent U V.nonexistent U V.∀H61:∀U:Univ.∀V:Univ.∀_:nonhuman U V.human U V.∀H62:∀U:Univ.∀V:Univ.∀_:specific U V.general U V.∀H63:∀U:Univ.∀V:Univ.∀_:unisex U V.male U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃Y:Univ.∃Z:Univ.And (actual_world W) (And (of W X7 X8) (And (man W X8) (And (agent W X6 X8) (And (forename W X7) (And (vincent_forename W X7) (And (theme W X6 X2) (And (event W X6) (And (present W X6) (And (think_believe_consider W X6) (And (accessible_world W X2) (And (proposition W X2) (And (forename W X5) (And (jules_forename W X5) (And (of W X5 X4) (And (man W X4) (And (be W X1 X4 X4) (And (event X2 X3) (And (agent X2 X3 X4) (And (present X2 X3) (And (smoke X2 X3) (And (state W X1) (And (agent W X Z) (And (man W Z) (And (of W Y Z) (And (vincent_forename W Y) (And (forename W Y) (And (think_believe_consider W X) (And (present W X) (And (event W X) (And (theme W X U) (And (proposition W U) (And (accessible_world W U) (And (event U V) (And (agent U V (skf4 U)) (And (present U V) (smoke U V))))))))))))))))))))))))))))))))))))
.
intros.
exists[
(* -------------------------------------------------------------------------- *)
theorem clause95:
- ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀Y:Univ.∀Z:Univ.∀_:state U V.∀_:be U V W W.∀_:man U W.∀_:of U X W.∀_:jules_forename U X.∀_:forename U X.∀_:jules_forename U Y.∀_:forename U Y.∀_:smoke Z X1.∀_:present Z X1.∀_:agent Z X1 X2.∀_:event Z X1.∀_:man U X2.∀_:of U Y X2.∀_:proposition U Z.∀_:accessible_world U Z.∀_:accessible_world U X3.∀_:proposition U X3.∀_:theme U X4 X3.∀_:event U X4.∀_:present U X4.∀_:think_believe_consider U X4.∀_:man U X5.∀_:agent U X4 X5.∀_:agent U X6 X5.∀_:forename U X7.∀_:vincent_forename U X7.∀_:of U X7 X5.∀_:think_believe_consider U X6.∀_:present U X6.∀_:event U X6.∀_:theme U X6 Z.∀_:actual_world U.man X3 (skf4 X3).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃Y:Univ.∃Z:Univ.And (state U V) (And (be U V W W) (And (man U W) (And (of U X W) (And (jules_forename U X) (And (forename U X) (And (jules_forename U Y) (And (forename U Y) (And (smoke Z X1) (And (present Z X1) (And (agent Z X1 X2) (And (event Z X1) (And (man U X2) (And (of U Y X2) (And (proposition U Z) (And (accessible_world U Z) (And (smoke X3 X4) (And (present X3 X4) (And (agent X3 X4 (skf4 X3)) (And (event X3 X4) (And (accessible_world U X3) (And (proposition U X3) (And (theme U X5 X3) (And (event U X5) (And (present U X5) (And (think_believe_consider U X5) (And (man U X6) (And (agent U X5 X6) (And (agent U X7 X6) (And (forename U X8) (And (vincent_forename U X8) (And (of U X8 X6) (And (think_believe_consider U X7) (And (present U X7) (And (event U X7) (And (theme U X7 Z) (actual_world U))))))))))))))))))))))))))))))))))))
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀Y:Univ.∀Z:Univ.∀_:actual_world U.∀_:theme U X6 Z.∀_:event U X6.∀_:present U X6.∀_:think_believe_consider U X6.∀_:of U X7 X5.∀_:vincent_forename U X7.∀_:forename U X7.∀_:agent U X6 X5.∀_:agent U X4 X5.∀_:man U X5.∀_:think_believe_consider U X4.∀_:present U X4.∀_:event U X4.∀_:theme U X4 X3.∀_:proposition U X3.∀_:accessible_world U X3.∀_:accessible_world U Z.∀_:proposition U Z.∀_:of U Y X2.∀_:man U X2.∀_:event Z X1.∀_:agent Z X1 X2.∀_:present Z X1.∀_:smoke Z X1.∀_:forename U Y.∀_:jules_forename U Y.∀_:forename U X.∀_:jules_forename U X.∀_:of U X W.∀_:man U W.∀_:be U V W W.∀_:state U V.man X3 (skf4 X3).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:agent U X Z.∀_:agent U Y Z.∀_:theme U Y W.∀_:think_believe_consider U Y.∀_:think_believe_consider U X.∀_:theme U X V.∀_:proposition U W.∀_:proposition U V.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:entity U X.∀_:of U V X.∀_:forename U W.∀_:of U W X.∀_:forename U V.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:be U W X Y.∀_:accessible_world U V.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:of U W X.∀_:accessible_world U V.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:theme U W X.∀_:accessible_world U V.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:agent U W X.∀_:accessible_world U V.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:jules_forename U W.∀_:accessible_world U V.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:vincent_forename U W.∀_:accessible_world U V.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relname U W.∀_:accessible_world U V.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:forename U W.∀_:accessible_world U V.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:male U W.∀_:accessible_world U V.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:animate U W.∀_:accessible_world U V.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human U W.∀_:accessible_world U V.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:living U W.∀_:accessible_world U V.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:impartial U W.∀_:accessible_world U V.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:existent U W.∀_:accessible_world U V.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:entity U W.∀_:accessible_world U V.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:organism U W.∀_:accessible_world U V.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human_person U W.∀_:accessible_world U V.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:man U W.∀_:accessible_world U V.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:state U W.∀_:accessible_world U V.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:general U W.∀_:accessible_world U V.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonhuman U W.∀_:accessible_world U V.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:abstraction U W.∀_:accessible_world U V.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relation U W.∀_:accessible_world U V.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:proposition U W.∀_:accessible_world U V.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:think_believe_consider U W.∀_:accessible_world U V.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:present U W.∀_:accessible_world U V.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:unisex U W.∀_:accessible_world U V.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonexistent U W.∀_:accessible_world U V.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:specific U W.∀_:accessible_world U V.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:singleton U W.∀_:accessible_world U V.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:thing U W.∀_:accessible_world U V.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:eventuality U W.∀_:accessible_world U V.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:event U W.∀_:accessible_world U V.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:smoke U W.∀_:accessible_world U V.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:existent U V.nonexistent U V.∀H61:∀U:Univ.∀V:Univ.∀_:nonhuman U V.human U V.∀H62:∀U:Univ.∀V:Univ.∀_:specific U V.general U V.∀H63:∀U:Univ.∀V:Univ.∀_:unisex U V.male U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃Y:Univ.∃Z:Univ.And (actual_world U) (And (theme U X7 Z) (And (event U X7) (And (present U X7) (And (think_believe_consider U X7) (And (of U X8 X6) (And (vincent_forename U X8) (And (forename U X8) (And (agent U X7 X6) (And (agent U X5 X6) (And (man U X6) (And (think_believe_consider U X5) (And (present U X5) (And (event U X5) (And (theme U X5 X3) (And (proposition U X3) (And (accessible_world U X3) (And (event X3 X4) (And (agent X3 X4 (skf4 X3)) (And (present X3 X4) (And (smoke X3 X4) (And (accessible_world U Z) (And (proposition U Z) (And (of U Y X2) (And (man U X2) (And (event Z X1) (And (agent Z X1 X2) (And (present Z X1) (And (smoke Z X1) (And (forename U Y) (And (jules_forename U Y) (And (forename U X) (And (jules_forename U X) (And (of U X W) (And (man U W) (And (be U V W W) (state U V))))))))))))))))))))))))))))))))))))
.
intros.
exists[
(* -------------------------------------------------------------------------- *)
theorem clause95:
- ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀Y:Univ.∀Z:Univ.∀_:state U V.∀_:man U W.∀_:be U V W W.∀_:smoke X Y.∀_:present X Y.∀_:agent X Y W.∀_:event X Y.∀_:forename U Z.∀_:jules_forename U Z.∀_:of U Z W.∀_:accessible_world U X.∀_:proposition U X.∀_:proposition U X1.∀_:accessible_world U X1.∀_:think_believe_consider U X2.∀_:present U X2.∀_:event U X2.∀_:theme U X2 X1.∀_:agent U X3 X4.∀_:agent U X2 X4.∀_:man U X4.∀_:of U X5 X4.∀_:vincent_forename U X5.∀_:forename U X5.∀_:theme U X3 X.∀_:event U X3.∀_:present U X3.∀_:think_believe_consider U X3.∀_:actual_world U.man X1 (skf4 X1).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃Y:Univ.∃Z:Univ.And (state U V) (And (man U W) (And (be U V W W) (And (smoke X Y) (And (present X Y) (And (agent X Y W) (And (event X Y) (And (forename U Z) (And (jules_forename U Z) (And (of U Z W) (And (accessible_world U X) (And (proposition U X) (And (proposition U X1) (And (accessible_world U X1) (And (smoke X1 X2) (And (present X1 X2) (And (agent X1 X2 (skf4 X1)) (And (event X1 X2) (And (think_believe_consider U X3) (And (present U X3) (And (event U X3) (And (theme U X3 X1) (And (agent U X4 X5) (And (agent U X3 X5) (And (man U X5) (And (of U X6 X5) (And (vincent_forename U X6) (And (forename U X6) (And (theme U X4 X) (And (event U X4) (And (present U X4) (And (think_believe_consider U X4) (actual_world U))))))))))))))))))))))))))))))))
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀Y:Univ.∀Z:Univ.∀_:actual_world U.∀_:think_believe_consider U X3.∀_:present U X3.∀_:event U X3.∀_:theme U X3 X.∀_:forename U X5.∀_:vincent_forename U X5.∀_:of U X5 X4.∀_:man U X4.∀_:agent U X2 X4.∀_:agent U X3 X4.∀_:theme U X2 X1.∀_:event U X2.∀_:present U X2.∀_:think_believe_consider U X2.∀_:accessible_world U X1.∀_:proposition U X1.∀_:proposition U X.∀_:accessible_world U X.∀_:of U Z W.∀_:jules_forename U Z.∀_:forename U Z.∀_:event X Y.∀_:agent X Y W.∀_:present X Y.∀_:smoke X Y.∀_:be U V W W.∀_:man U W.∀_:state U V.man X1 (skf4 X1).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:agent U X Z.∀_:agent U Y Z.∀_:theme U Y W.∀_:think_believe_consider U Y.∀_:think_believe_consider U X.∀_:theme U X V.∀_:proposition U W.∀_:proposition U V.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:entity U X.∀_:of U V X.∀_:forename U W.∀_:of U W X.∀_:forename U V.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:be U W X Y.∀_:accessible_world U V.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:of U W X.∀_:accessible_world U V.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:theme U W X.∀_:accessible_world U V.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:agent U W X.∀_:accessible_world U V.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:jules_forename U W.∀_:accessible_world U V.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:vincent_forename U W.∀_:accessible_world U V.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relname U W.∀_:accessible_world U V.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:forename U W.∀_:accessible_world U V.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:male U W.∀_:accessible_world U V.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:animate U W.∀_:accessible_world U V.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human U W.∀_:accessible_world U V.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:living U W.∀_:accessible_world U V.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:impartial U W.∀_:accessible_world U V.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:existent U W.∀_:accessible_world U V.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:entity U W.∀_:accessible_world U V.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:organism U W.∀_:accessible_world U V.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:human_person U W.∀_:accessible_world U V.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:man U W.∀_:accessible_world U V.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:state U W.∀_:accessible_world U V.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:general U W.∀_:accessible_world U V.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonhuman U W.∀_:accessible_world U V.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:abstraction U W.∀_:accessible_world U V.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:relation U W.∀_:accessible_world U V.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:proposition U W.∀_:accessible_world U V.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:think_believe_consider U W.∀_:accessible_world U V.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:present U W.∀_:accessible_world U V.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:unisex U W.∀_:accessible_world U V.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:nonexistent U W.∀_:accessible_world U V.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:specific U W.∀_:accessible_world U V.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:singleton U W.∀_:accessible_world U V.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:thing U W.∀_:accessible_world U V.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:eventuality U W.∀_:accessible_world U V.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:event U W.∀_:accessible_world U V.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:smoke U W.∀_:accessible_world U V.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:existent U V.nonexistent U V.∀H61:∀U:Univ.∀V:Univ.∀_:nonhuman U V.human U V.∀H62:∀U:Univ.∀V:Univ.∀_:specific U V.general U V.∀H63:∀U:Univ.∀V:Univ.∀_:unisex U V.male U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃Y:Univ.∃Z:Univ.And (actual_world U) (And (think_believe_consider U X4) (And (present U X4) (And (event U X4) (And (theme U X4 X) (And (forename U X6) (And (vincent_forename U X6) (And (of U X6 X5) (And (man U X5) (And (agent U X3 X5) (And (agent U X4 X5) (And (theme U X3 X1) (And (event U X3) (And (present U X3) (And (think_believe_consider U X3) (And (event X1 X2) (And (agent X1 X2 (skf4 X1)) (And (present X1 X2) (And (smoke X1 X2) (And (accessible_world U X1) (And (proposition U X1) (And (proposition U X) (And (accessible_world U X) (And (of U Z W) (And (jules_forename U Z) (And (forename U Z) (And (event X Y) (And (agent X Y W) (And (present X Y) (And (smoke X Y) (And (be U V W W) (And (man U W) (state U V))))))))))))))))))))))))))))))))
.
intros.
exists[
(* -------------------------------------------------------------------------- *)
theorem prove_there_is_no_common_divisor:
- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀divides:∀_:Univ.∀_:Univ.Prop.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀prime:∀_:Univ.Prop.∀product:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀second_divided_by_1st:∀_:Univ.∀_:Univ.Univ.∀H0:product a e d.∀H1:product c c e.∀H2:product b b d.∀H3:prime a.∀H4:∀A:Univ.∀B:Univ.∀C:Univ.∀_:divides A B.∀_:product C C B.∀_:prime A.divides A C.∀H5:∀A:Univ.∀B:Univ.∀C:Univ.∀_:product A B C.divides A C.∀H6:∀A:Univ.∀B:Univ.∀_:divides A B.product A (second_divided_by_1st A B) B.∀H7:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀_:product A B C.∀_:product A B D.eq Univ D C.∀H8:∀A:Univ.∀B:Univ.∀C:Univ.∀_:divides A B.∀_:divides C A.divides C B.∀H9:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀_:product A B C.∀_:product A D C.eq Univ B D.∀H10:∀A:Univ.∀B:Univ.∀C:Univ.∀_:product A B C.product B A C.∀H11:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀_:product A B C.∀_:product D B E.∀_:product F D A.product F E C.∀H12:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀_:product A B C.∀_:product D E B.∀_:product A D F.product F E C.∀H13:∀A:Univ.∀B:Univ.product A B (multiply A B).∃A:Univ.And (divides A c) (divides A b)
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀divides:∀_:Univ.∀_:Univ.Prop.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀prime:∀_:Univ.Prop.∀product:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀second_divided_by_1st:∀_:Univ.∀_:Univ.Univ.∀H0:product a e d.∀H1:product c c e.∀H2:product b b d.∀H3:prime a.∀H4:∀A:Univ.∀B:Univ.∀C:Univ.∀_:prime A.∀_:product C C B.∀_:divides A B.divides A C.∀H5:∀A:Univ.∀B:Univ.∀C:Univ.∀_:product A B C.divides A C.∀H6:∀A:Univ.∀B:Univ.∀_:divides A B.product A (second_divided_by_1st A B) B.∀H7:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀_:product A B D.∀_:product A B C.eq Univ D C.∀H8:∀A:Univ.∀B:Univ.∀C:Univ.∀_:divides C A.∀_:divides A B.divides C B.∀H9:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀_:product A D C.∀_:product A B C.eq Univ B D.∀H10:∀A:Univ.∀B:Univ.∀C:Univ.∀_:product A B C.product B A C.∀H11:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀_:product F D A.∀_:product D B E.∀_:product A B C.product F E C.∀H12:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀_:product A D F.∀_:product D E B.∀_:product A B C.product F E C.∀H13:∀A:Univ.∀B:Univ.product A B (multiply A B).∃A:Univ.And (divides A b) (divides A c)
.
intros.
exists[
(* ----Hypothesis of the theorem *)
theorem prove_huntingtons_axiom:
- ∀Univ:Set.∀V:Univ.∀V2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (add c d) d.∀H1:∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add (negate Y) (negate (add X (negate Y))))) X.eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add X (negate Y))) (negate Y).eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).∀H3:∀V2:Univ.∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add X Y)) (negate Y).∀_:positive_integer V2.eq Univ (negate (add Y (multiply V2 (add X (negate (add X (negate Y))))))) (negate Y).∀H4:∀X:Univ.eq Univ (add X X) X.∀H5:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H6:positive_integer one.∀H7:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H8:∀X:Univ.eq Univ (multiply one X) X.∀H9:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b
+ ∀Univ:Set.∀V:Univ.∀V2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (add c d) d.∀H1:∀X:Univ.∀Y:Univ.∀_:eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).eq Univ (negate (add (negate Y) (negate (add X (negate Y))))) X.∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).eq Univ (negate (add X (negate Y))) (negate Y).∀H3:∀V2:Univ.∀X:Univ.∀Y:Univ.∀_:positive_integer V2.∀_:eq Univ (negate (add Y (multiply V2 (add X (negate (add X (negate Y))))))) (negate Y).eq Univ (negate (add X Y)) (negate Y).∀H4:∀X:Univ.eq Univ (add X X) X.∀H5:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H6:positive_integer one.∀H7:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H8:∀X:Univ.eq Univ (multiply one X) X.∀H9:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b
.
intros.
autobatch paramodulation timeout=600;
(* ------------------------------------------------------------------------------ *)
theorem cls_conjecture_2:
- ∀Univ:Set.∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀V_G:Univ.∀V_H:Univ.∀V_c:Univ.∀V_x:Univ.∀c_Message_Oanalz:∀_:Univ.Univ.∀c_Message_Osynth:∀_:Univ.Univ.∀c_in:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_insert:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_minus:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c_union:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀tc_Message_Omsg:Univ.∀tc_set:∀_:Univ.Univ.∀v_G:Univ.∀v_H:Univ.∀v_X:Univ.∀v_x:Univ.∀H0:c_in v_x (c_Message_Oanalz (c_insert v_X v_H tc_Message_Omsg)) tc_Message_Omsg.∀H1:c_in v_X (c_Message_Osynth (c_Message_Oanalz v_G)) tc_Message_Omsg.∀H2:∀T_a:Univ.∀V_A:Univ.c_lessequals V_A V_A (tc_set T_a).∀H3:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀_:c_lessequals V_B V_A (tc_set T_a).∀_:c_lessequals V_A V_B (tc_set T_a).eq Univ V_A V_B.∀H4:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_c:Univ.∀_:c_in V_c V_A T_a.∀_:c_lessequals V_A V_B (tc_set T_a).c_in V_c V_B T_a.∀H5:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_x:Univ.∀_:c_in V_x V_B T_a.eq Univ (c_minus (c_insert V_x V_A T_a) V_B (tc_set T_a)) (c_minus V_A V_B (tc_set T_a)).∀H6:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals V_B V_C (tc_set T_a).∀_:c_lessequals V_A V_C (tc_set T_a).c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).∀H7:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).c_lessequals V_B V_C (tc_set T_a).∀H8:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).c_lessequals V_A V_C (tc_set T_a).∀H9:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.eq Univ (c_union V_A (c_minus V_B V_A (tc_set T_a)) T_a) (c_union V_A V_B T_a).∀H10:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.eq Univ (c_union (c_minus V_B V_A (tc_set T_a)) V_A T_a) (c_union V_B V_A T_a).∀H11:∀V_G:Univ.∀V_H:Univ.∀_:c_lessequals V_G V_H (tc_set tc_Message_Omsg).c_lessequals (c_Message_Oanalz V_G) (c_Message_Oanalz V_H) (tc_set tc_Message_Omsg).c_in v_x (c_Message_Oanalz (c_union (c_Message_Osynth (c_Message_Oanalz v_G)) v_H tc_Message_Omsg)) tc_Message_Omsg
+ ∀Univ:Set.∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀V_G:Univ.∀V_H:Univ.∀V_c:Univ.∀V_x:Univ.∀c_Message_Oanalz:∀_:Univ.Univ.∀c_Message_Osynth:∀_:Univ.Univ.∀c_in:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_insert:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_minus:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c_union:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀tc_Message_Omsg:Univ.∀tc_set:∀_:Univ.Univ.∀v_G:Univ.∀v_H:Univ.∀v_X:Univ.∀v_x:Univ.∀H0:c_in v_x (c_Message_Oanalz (c_insert v_X v_H tc_Message_Omsg)) tc_Message_Omsg.∀H1:c_in v_X (c_Message_Osynth (c_Message_Oanalz v_G)) tc_Message_Omsg.∀H2:∀T_a:Univ.∀V_A:Univ.c_lessequals V_A V_A (tc_set T_a).∀H3:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀_:c_lessequals V_A V_B (tc_set T_a).∀_:c_lessequals V_B V_A (tc_set T_a).eq Univ V_A V_B.∀H4:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_c:Univ.∀_:c_lessequals V_A V_B (tc_set T_a).∀_:c_in V_c V_A T_a.c_in V_c V_B T_a.∀H5:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_x:Univ.∀_:c_in V_x V_B T_a.eq Univ (c_minus (c_insert V_x V_A T_a) V_B (tc_set T_a)) (c_minus V_A V_B (tc_set T_a)).∀H6:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals V_A V_C (tc_set T_a).∀_:c_lessequals V_B V_C (tc_set T_a).c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).∀H7:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).c_lessequals V_B V_C (tc_set T_a).∀H8:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).c_lessequals V_A V_C (tc_set T_a).∀H9:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.eq Univ (c_union V_A (c_minus V_B V_A (tc_set T_a)) T_a) (c_union V_A V_B T_a).∀H10:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.eq Univ (c_union (c_minus V_B V_A (tc_set T_a)) V_A T_a) (c_union V_B V_A T_a).∀H11:∀V_G:Univ.∀V_H:Univ.∀_:c_lessequals V_G V_H (tc_set tc_Message_Omsg).c_lessequals (c_Message_Oanalz V_G) (c_Message_Oanalz V_H) (tc_set tc_Message_Omsg).c_in v_x (c_Message_Oanalz (c_union (c_Message_Osynth (c_Message_Oanalz v_G)) v_H tc_Message_Omsg)) tc_Message_Omsg
.
intros.
autobatch depth=5 width=5 size=20 timeout=10;
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