TPTP Problem File: GRP446-1.p
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% File : GRP446-1 : TPTP v9.0.0. Released v2.6.0.
% Domain : Group Theory
% Problem : Axiom for group theory, in division, part 2
% Version : [McC93] (equality) axioms.
% English :
% Refs : [HN52] Higman & Neumann (1952), Groups as Groupoids with One
% : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr
% Source : [TPTP]
% Names :
% Status : Unsatisfiable
% Rating : 0.09 v8.2.0, 0.08 v8.1.0, 0.10 v7.5.0, 0.12 v7.4.0, 0.22 v7.3.0, 0.21 v7.1.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.12 v6.0.0, 0.29 v5.5.0, 0.26 v5.4.0, 0.07 v5.3.0, 0.08 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.00 v2.6.0
% Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR)
% Number of literals : 4 ( 4 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments : A UEQ part of GRP063-1
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cnf(single_axiom,axiom,
divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C))) = B ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)) ).
cnf(inverse,axiom,
inverse(A) = divide(divide(B,B),A) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
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