1 include "logic/equality.ma".
3 (* Inclusion of: GRP196-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP196-1 : TPTP v3.7.0. Released v2.2.0. *)
9 (* Domain : Group Theory (Semigroups) *)
11 (* Problem : In semigroups, xyyy=yyyx -> (uy)^9 = u^9v^9. *)
13 (* Version : [MP96] (equality) axioms. *)
17 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
19 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
21 (* : [McC95] McCune (1995), Four Challenge Problems in Equational L *)
23 (* Source : [McC98] *)
25 (* Names : CS-3 [MP96] *)
27 (* : Problem B [McC95] *)
29 (* Status : Unsatisfiable *)
31 (* Rating : 0.89 v3.4.0, 1.00 v3.3.0, 0.93 v3.1.0, 1.00 v2.2.1 *)
33 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
35 (* Number of atoms : 3 ( 3 equality) *)
37 (* Maximal clause size : 1 ( 1 average) *)
39 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
41 (* Number of functors : 3 ( 2 constant; 0-2 arity) *)
43 (* Number of variables : 5 ( 0 singleton) *)
45 (* Maximal term depth : 18 ( 8 average) *)
47 (* Comments : The problem was originally posed for cancellative semigroups, *)
49 (* Otter does this with a nonstandard representation [MP96]. *)
51 (* -------------------------------------------------------------------------- *)
53 (* ----Include semigroups axioms *)
55 (* Inclusion of: Axioms/GRP008-0.ax *)
57 (* -------------------------------------------------------------------------- *)
59 (* File : GRP008-0 : TPTP v3.7.0. Released v2.2.0. *)
61 (* Domain : Group Theory (Semigroups) *)
63 (* Axioms : Semigroups axioms *)
65 (* Version : [MP96] (equality) axioms. *)
69 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
71 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
73 (* Source : [McC98] *)
79 (* Syntax : Number of clauses : 1 ( 0 non-Horn; 1 unit; 0 RR) *)
81 (* Number of atoms : 1 ( 1 equality) *)
83 (* Maximal clause size : 1 ( 1 average) *)
85 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
87 (* Number of functors : 1 ( 0 constant; 2-2 arity) *)
89 (* Number of variables : 3 ( 0 singleton) *)
91 (* Maximal term depth : 3 ( 3 average) *)
95 (* -------------------------------------------------------------------------- *)
97 (* ----Associativity: *)
99 (* -------------------------------------------------------------------------- *)
101 (* -------------------------------------------------------------------------- *)
103 (* ----Hypothesis: *)
105 (* ----Denial of conclusion: *)
107 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
110 ∀multiply:∀_:Univ.∀_:Univ.Univ.
111 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y (multiply Y Y))) (multiply Y (multiply Y (multiply Y X))).
112 ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))))))))))))) (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b b))))))))))))))))))
124 ntry (nassumption) ##;
127 (* -------------------------------------------------------------------------- *)