TPTP Problem File: GRP122-1.p
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% File : GRP122-1 : TPTP v8.2.0. Released v1.2.0.
% Domain : Group Theory
% Problem : Derive associativity from a single axiom for groups order 4
% Version : [Wos96] (equality) axioms.
% English :
% Refs : [Wos96] Wos (1996), The Automation of Reasoning: An Experiment
% Source : [OTTER]
% Names : groups.exp4.in part 4 [OTTER]
% Status : Unsatisfiable
% Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.30 v7.5.0, 0.25 v7.4.0, 0.30 v7.3.0, 0.26 v7.1.0, 0.17 v7.0.0, 0.21 v6.4.0, 0.26 v6.3.0, 0.24 v6.2.0, 0.21 v6.1.0, 0.38 v6.0.0, 0.52 v5.5.0, 0.47 v5.4.0, 0.33 v5.3.0, 0.25 v5.2.0, 0.29 v5.1.0, 0.20 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.2.0, 0.07 v3.1.0, 0.22 v2.7.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 0.43 v2.0.0
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 2 RR)
% Number of literals : 3 ( 3 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; 4 con; 0-2 aty)
% Number of variables : 3 ( 0 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments :
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cnf(single_axiom,axiom,
multiply(Y,multiply(multiply(Y,multiply(multiply(Y,Y),multiply(X,Z))),multiply(Z,multiply(Z,Z)))) = X ).
cnf(single_axiom2,axiom,
multiply(identity,identity) = identity ).
cnf(prove_order3,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)) ).
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