1 include "logic/equality.ma".
3 (* Inclusion of: ROB013-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : ROB013-1 : TPTP v3.7.0. Released v1.0.0. *)
9 (* Domain : Robbins Algebra *)
11 (* Problem : If -(a + b) = c then -(c + -(-b + a)) = a *)
13 (* Version : [Win90] (equality) axioms. *)
17 (* Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
19 (* Source : [Win90] *)
21 (* Names : Lemma 3.5 [Win90] *)
23 (* Status : Unsatisfiable *)
25 (* Rating : 0.00 v2.0.0 *)
27 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR) *)
29 (* Number of atoms : 5 ( 5 equality) *)
31 (* Maximal clause size : 1 ( 1 average) *)
33 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
35 (* Number of functors : 5 ( 3 constant; 0-2 arity) *)
37 (* Number of variables : 7 ( 0 singleton) *)
39 (* Maximal term depth : 6 ( 3 average) *)
43 (* -------------------------------------------------------------------------- *)
45 (* ----Include axioms for Robbins algebra *)
47 (* Inclusion of: Axioms/ROB001-0.ax *)
49 (* -------------------------------------------------------------------------- *)
51 (* File : ROB001-0 : TPTP v3.7.0. Released v1.0.0. *)
53 (* Domain : Robbins algebra *)
55 (* Axioms : Robbins algebra axioms *)
57 (* Version : [Win90] (equality) axioms. *)
61 (* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
63 (* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
65 (* Source : [OTTER] *)
67 (* Names : Lemma 2.2 [Win90] *)
71 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
73 (* Number of atoms : 3 ( 3 equality) *)
75 (* Maximal clause size : 1 ( 1 average) *)
77 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
79 (* Number of functors : 2 ( 0 constant; 1-2 arity) *)
81 (* Number of variables : 7 ( 0 singleton) *)
83 (* Maximal term depth : 6 ( 3 average) *)
87 (* -------------------------------------------------------------------------- *)
89 (* -------------------------------------------------------------------------- *)
91 (* -------------------------------------------------------------------------- *)
92 ntheorem prove_result:
93 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
95 ∀add:∀_:Univ.∀_:Univ.Univ.
99 ∀H0:eq Univ (negate (add a b)) c.
100 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
101 ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
102 ∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add (negate b) a)))) a)
117 nauto by H0,H1,H2,H3 ##;
118 ntry (nassumption) ##;
121 (* -------------------------------------------------------------------------- *)