TPTP Problem File: GRP001-2.p
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%------------------------------------------------------------------------------
% File : GRP001-2 : TPTP v9.0.0. Released v1.0.0.
% Domain : Group Theory
% Problem : X^2 = identity => commutativity
% Version : [MOW76] (equality) axioms : Augmented.
% English : If the square of every element is the identity, the system
% is commutative.
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% : [LO85] Lusk & Overbeek (1985), Reasoning about Equality
% : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit
% Source : [ANL]
% Names : GP1 [MOW76]
% : Problem 1 [LO85]
% : GT1 [LW92]
% : xsquared.ver2.in [ANL]
% Status : Unsatisfiable
% Rating : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v7.0.0, 0.05 v6.4.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.14 v5.5.0, 0.11 v5.4.0, 0.00 v5.1.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 2 RR)
% Number of literals : 8 ( 8 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments :
%------------------------------------------------------------------------------
%----Include equality group theory axioms
include('Axioms/GRP004-0.ax').
%------------------------------------------------------------------------------
%----Redundant two axioms
cnf(right_identity,axiom,
multiply(X,identity) = X ).
cnf(right_inverse,axiom,
multiply(X,inverse(X)) = identity ).
cnf(squareness,hypothesis,
multiply(X,X) = identity ).
cnf(a_times_b_is_c,hypothesis,
multiply(a,b) = c ).
cnf(prove_b_times_a_is_c,negated_conjecture,
multiply(b,a) != c ).
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