1 set "baseuri" "cic:/matita/TPTP/ROB014-1".
2 include "logic/equality.ma".
4 (* Inclusion of: ROB014-1.p *)
6 (* -------------------------------------------------------------------------- *)
8 (* File : ROB014-1 : TPTP v3.2.0. Released v1.0.0. *)
10 (* Domain : Robbins Algebra *)
12 (* Problem : If -(-e + -(d + -e)) = d then -(e + k(d + -(d + -e))) = -e, k=1 *)
14 (* Version : [Win90] (equality) axioms. *)
16 (* English : This is the base step of an induction proof. *)
18 (* Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
20 (* Source : [Win90] *)
22 (* Names : Lemma 3.6 [Win90] *)
24 (* Status : Unsatisfiable *)
26 (* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.86 v2.5.0, 1.00 v2.0.0 *)
28 (* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 4 RR) *)
30 (* Number of atoms : 11 ( 7 equality) *)
32 (* Maximal clause size : 2 ( 1 average) *)
34 (* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
36 (* Number of functors : 7 ( 3 constant; 0-2 arity) *)
38 (* Number of variables : 11 ( 0 singleton) *)
40 (* Maximal term depth : 8 ( 3 average) *)
44 (* -------------------------------------------------------------------------- *)
46 (* ----Include axioms for Robbins algebra *)
48 (* Inclusion of: Axioms/ROB001-0.ax *)
50 (* -------------------------------------------------------------------------- *)
52 (* File : ROB001-0 : TPTP v3.2.0. Released v1.0.0. *)
54 (* Domain : Robbins algebra *)
56 (* Axioms : Robbins algebra axioms *)
58 (* Version : [Win90] (equality) axioms. *)
62 (* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
64 (* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
66 (* Source : [OTTER] *)
68 (* Names : Lemma 2.2 [Win90] *)
72 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
74 (* Number of literals : 3 ( 3 equality) *)
76 (* Maximal clause size : 1 ( 1 average) *)
78 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
80 (* Number of functors : 2 ( 0 constant; 1-2 arity) *)
82 (* Number of variables : 7 ( 0 singleton) *)
84 (* Maximal term depth : 6 ( 3 average) *)
88 (* -------------------------------------------------------------------------- *)
90 (* -------------------------------------------------------------------------- *)
92 (* ----Include axioms for numbers in Robbins algebras *)
94 (* Inclusion of: Axioms/ROB001-1.ax *)
96 (* -------------------------------------------------------------------------- *)
98 (* File : ROB001-1 : TPTP v3.2.0. Released v1.0.0. *)
100 (* Domain : Robbins Algebra *)
102 (* Axioms : Robbins algebra numbers axioms *)
104 (* Version : [Win90] (equality) axioms. *)
108 (* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
110 (* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
112 (* Source : [Win90] *)
118 (* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
120 (* Number of literals : 6 ( 2 equality) *)
122 (* Maximal clause size : 2 ( 2 average) *)
124 (* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
126 (* Number of functors : 4 ( 1 constant; 0-2 arity) *)
128 (* Number of variables : 4 ( 0 singleton) *)
130 (* Maximal term depth : 3 ( 2 average) *)
132 (* Comments : Requires ROB001-0.ax *)
134 (* -------------------------------------------------------------------------- *)
136 (* -------------------------------------------------------------------------- *)
138 (* -------------------------------------------------------------------------- *)
139 theorem prove_base_step:
140 ∀Univ:Set.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀d:Univ.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (negate (add (negate e) (negate (add d (negate e))))) d.∀H1:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H2:positive_integer one.∀H3:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H4:∀X:Univ.eq Univ (multiply one X) X.∀H5:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add e (multiply one (add d (negate (add d (negate e))))))) (negate e)
143 autobatch depth=5 width=5 size=20 timeout=10;
148 (* -------------------------------------------------------------------------- *)