%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:08:51 AM UTC 2026
% Result : Unsatisfiable 0.54s 0.49s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 8
% Syntax : Number of clauses : 239 ( 239 unt; 0 nHn; 7 RR)
% Number of literals : 239 ( 238 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 470 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
cnf(c2,axiom,
multiply(X,identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(c3,plain,
multiply(commutator(commutator(X3,X2),X2),identity) = commutator(commutator(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
commutator(commutator(X3,X2),X2) = multiply(commutator(commutator(X3,X2),X2),identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,inverse(X2)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(commutator(commutator(X3,X2),X2),identity) = multiply(commutator(commutator(X3,X2),X2),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(multiply(X2,Y),Z) = multiply(X2,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c9,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(multiply(X3,inverse(X3)),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c12,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c13,plain,
multiply(multiply(X3,inverse(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c10,c13]) ).
cnf(c15,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(inverse(X2)) = multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(inverse(X2),inverse(inverse(X2))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c18,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c18,c2]) ).
cnf(c20,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c16,c19]) ).
cnf(c21,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(commutator(X3,X2),X2) = multiply(commutator(X3,X2),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(multiply(inverse(X3),inverse(X2)),X4) = multiply(inverse(X3),multiply(inverse(X2),X4)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c24,plain,
multiply(inverse(X4),multiply(inverse(X3),X2)) = multiply(multiply(inverse(X4),inverse(X3)),X2),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(X3,multiply(inverse(X4),multiply(inverse(X3),X2))) = multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),X2)))) = multiply(X4,multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2) = multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c28,plain,
multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2)) = multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X4,multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2))) = multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(X4,multiply(X3,multiply(inverse(X4),inverse(X3)))),X2) = multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c31,plain,
multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)) = multiply(multiply(X4,multiply(X3,multiply(inverse(X4),inverse(X3)))),X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
commutator(X2,Y2) = multiply(X2,multiply(Y2,multiply(inverse(X2),inverse(Y2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
cnf(c33,plain,
commutator(X3,X2) = multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2)))) = commutator(X3,X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(multiply(X4,multiply(X3,multiply(inverse(X4),inverse(X3)))),X2) = multiply(commutator(X4,X3),X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)) = multiply(commutator(X4,X3),X2),
inference(transitivity,[status(thm)],[c31,c35]) ).
cnf(c37,plain,
multiply(X4,multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2))) = multiply(commutator(X4,X3),X2),
inference(transitivity,[status(thm)],[c29,c36]) ).
cnf(c38,plain,
multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),X2)))) = multiply(commutator(X4,X3),X2),
inference(transitivity,[status(thm)],[c26,c37]) ).
cnf(c39,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X2)))))) = multiply(commutator(X3,X2),inverse(inverse(X2))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(commutator(X3,X2),inverse(inverse(X2))) = multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X2)))))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(inverse(X2),inverse(inverse(X2))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c42,plain,
multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X2)))) = multiply(inverse(X3),identity),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X2))))) = multiply(X2,multiply(inverse(X3),identity)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X2)))))) = multiply(X3,multiply(X2,multiply(inverse(X3),identity))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
multiply(X2,multiply(inverse(X3),identity)) = multiply(X2,inverse(X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),identity))) = multiply(X3,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X2)))))) = multiply(X3,multiply(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c44,c47]) ).
cnf(c49,plain,
multiply(commutator(X3,X2),inverse(inverse(X2))) = multiply(X3,multiply(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c40,c48]) ).
cnf(c50,plain,
multiply(commutator(X3,X2),X2) = multiply(X3,multiply(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c22,c49]) ).
cnf(c51,plain,
multiply(commutator(commutator(X3,X2),X2),X2) = multiply(commutator(X3,X2),multiply(X2,inverse(commutator(X3,X2)))),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
commutator(X3,X2) = multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c53,plain,
inverse(commutator(X3,X2)) = inverse(multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2))))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c55,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c57,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c57,c12]) ).
cnf(c59,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c55,c58]) ).
cnf(c60,plain,
multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = multiply(X3,inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c63,plain,
multiply(X3,inverse(multiply(X2,X3))) = multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,X2))) = multiply(X3,multiply(X2,inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c65,plain,
multiply(X3,multiply(X2,inverse(multiply(X3,X2)))) = multiply(multiply(X3,X2),inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,X2))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c67,plain,
multiply(X3,multiply(X2,inverse(multiply(X3,X2)))) = identity,
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
multiply(X2,multiply(X3,inverse(multiply(X2,X3)))) = identity,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = multiply(inverse(X2),identity),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = inverse(X2),
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
multiply(X3,inverse(multiply(X2,X3))) = inverse(X2),
inference(transitivity,[status(thm)],[c63,c71]) ).
cnf(c73,plain,
multiply(X2,inverse(multiply(X3,X2))) = inverse(X3),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = multiply(inverse(X2),inverse(X3)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),inverse(X3)),
inference(transitivity,[status(thm)],[c61,c74]) ).
cnf(c76,plain,
inverse(multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2))))) = multiply(inverse(multiply(X2,multiply(inverse(X3),inverse(X2)))),inverse(X3)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
inverse(multiply(X2,multiply(inverse(X3),inverse(X2)))) = multiply(inverse(multiply(inverse(X3),inverse(X2))),inverse(X2)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c78,plain,
multiply(inverse(multiply(X2,multiply(inverse(X3),inverse(X2)))),inverse(X3)) = multiply(multiply(inverse(multiply(inverse(X3),inverse(X2))),inverse(X2)),inverse(X3)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(multiply(inverse(multiply(inverse(X3),inverse(X2))),inverse(X2)),inverse(X3)) = multiply(inverse(multiply(inverse(X3),inverse(X2))),multiply(inverse(X2),inverse(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c80,plain,
multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),inverse(X2))))) = inverse(multiply(inverse(X3),inverse(X2))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c81,plain,
inverse(multiply(inverse(X3),inverse(X2))) = multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),inverse(X2))))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(X2,multiply(inverse(X2),multiply(X3,inverse(multiply(inverse(X2),X3))))) = multiply(X3,inverse(multiply(inverse(X2),X3))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c83,plain,
multiply(X3,inverse(multiply(inverse(X2),X3))) = multiply(X2,multiply(inverse(X2),multiply(X3,inverse(multiply(inverse(X2),X3))))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(X2),multiply(X3,inverse(multiply(inverse(X2),X3)))) = identity,
inference(substitution,[status(thm)],[c67]) ).
cnf(c85,plain,
multiply(X2,multiply(inverse(X2),multiply(X3,inverse(multiply(inverse(X2),X3))))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(X2,multiply(inverse(X2),multiply(X3,inverse(multiply(inverse(X2),X3))))) = X2,
inference(transitivity,[status(thm)],[c85,c2]) ).
cnf(c87,plain,
multiply(X3,inverse(multiply(inverse(X2),X3))) = X2,
inference(transitivity,[status(thm)],[c83,c86]) ).
cnf(c88,plain,
multiply(inverse(X2),inverse(multiply(inverse(X3),inverse(X2)))) = X3,
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),inverse(X2))))) = multiply(X2,X3),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
inverse(multiply(inverse(X3),inverse(X2))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c81,c89]) ).
cnf(c91,plain,
multiply(inverse(multiply(inverse(X3),inverse(X2))),multiply(inverse(X2),inverse(X3))) = multiply(multiply(X2,X3),multiply(inverse(X2),inverse(X3))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(multiply(X2,X3),multiply(inverse(X2),inverse(X3))) = multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3)))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c93,plain,
commutator(X2,X3) = multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c94,plain,
multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3)))) = commutator(X2,X3),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(multiply(X2,X3),multiply(inverse(X2),inverse(X3))) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c92,c94]) ).
cnf(c96,plain,
multiply(inverse(multiply(inverse(X3),inverse(X2))),multiply(inverse(X2),inverse(X3))) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c91,c95]) ).
cnf(c97,plain,
multiply(multiply(inverse(multiply(inverse(X3),inverse(X2))),inverse(X2)),inverse(X3)) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c79,c96]) ).
cnf(c98,plain,
multiply(inverse(multiply(X2,multiply(inverse(X3),inverse(X2)))),inverse(X3)) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c78,c97]) ).
cnf(c99,plain,
inverse(multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2))))) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c76,c98]) ).
cnf(c100,plain,
inverse(commutator(X3,X2)) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c53,c99]) ).
cnf(c101,plain,
multiply(X2,inverse(commutator(X3,X2))) = multiply(X2,commutator(X2,X3)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(commutator(X3,X2),multiply(X2,inverse(commutator(X3,X2)))) = multiply(commutator(X3,X2),multiply(X2,commutator(X2,X3))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
inverse(commutator(inverse(X2),X3)) = commutator(X3,inverse(X2)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c104,plain,
commutator(X3,inverse(X2)) = inverse(commutator(inverse(X2),X3)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c106,plain,
multiply(inverse(multiply(X3,X2)),X3) = multiply(inverse(multiply(X3,X2)),inverse(inverse(X3))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(X2,inverse(multiply(X3,X2))) = inverse(X3),
inference(substitution,[status(thm)],[c72]) ).
cnf(c108,plain,
inverse(X3) = multiply(X2,inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
inverse(inverse(X3)) = inverse(multiply(X2,inverse(multiply(X3,X2)))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(inverse(multiply(X3,X2)),inverse(inverse(X3))) = multiply(inverse(multiply(X3,X2)),inverse(multiply(X2,inverse(multiply(X3,X2))))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(inverse(multiply(X3,X2)),inverse(multiply(X2,inverse(multiply(X3,X2))))) = inverse(X2),
inference(substitution,[status(thm)],[c72]) ).
cnf(c112,plain,
multiply(inverse(multiply(X3,X2)),inverse(inverse(X3))) = inverse(X2),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
multiply(inverse(multiply(X3,X2)),X3) = inverse(X2),
inference(transitivity,[status(thm)],[c106,c112]) ).
cnf(c114,plain,
multiply(inverse(multiply(commutator(X2,X3),commutator(inverse(X2),X3))),commutator(X2,X3)) = inverse(commutator(inverse(X2),X3)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
inverse(commutator(inverse(X2),X3)) = multiply(inverse(multiply(commutator(X2,X3),commutator(inverse(X2),X3))),commutator(X2,X3)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),commutator(inverse(X3),X2))))) = multiply(commutator(X3,X2),commutator(inverse(X3),X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c117,plain,
multiply(commutator(X3,X2),commutator(inverse(X3),X2)) = multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),commutator(inverse(X3),X2))))),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
commutator(X2,X3) = multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c119,plain,
multiply(inverse(X3),commutator(X2,X3)) = multiply(inverse(X3),multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3))))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(X2,multiply(inverse(X3),commutator(X2,X3))) = multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3)))))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),commutator(X2,X3)))) = multiply(X3,multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3))))))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(inverse(X2),inverse(X3)) = inverse(multiply(X3,X2)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c123,plain,
multiply(X3,multiply(inverse(X2),inverse(X3))) = multiply(X3,inverse(multiply(X3,X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3)))) = multiply(X2,multiply(X3,inverse(multiply(X3,X2)))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(inverse(X3),multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3))))) = multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2))))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3)))))) = multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3))))))) = multiply(X3,multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2))))))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
X2 = multiply(X3,multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c129,plain,
multiply(X3,X2) = multiply(X3,multiply(X3,multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(X3,multiply(X3,X2)) = multiply(X3,multiply(X3,multiply(X3,multiply(inverse(X3),X2)))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(multiply(X3,X3),X2) = multiply(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c132,plain,
multiply(X3,multiply(X3,X2)) = multiply(multiply(X3,X3),X2),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = multiply(X3,multiply(multiply(X3,X3),X2)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = multiply(X3,multiply(multiply(X3,X3),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c135,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = multiply(multiply(X3,multiply(X3,X3)),X2),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,axiom,
multiply(X2,multiply(X2,X2)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c137,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = X2,
inference(transitivity,[status(thm)],[c137,c12]) ).
cnf(c139,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = X2,
inference(transitivity,[status(thm)],[c135,c138]) ).
cnf(c140,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c133,c139]) ).
cnf(c141,plain,
multiply(X3,multiply(X3,multiply(X3,multiply(inverse(X3),X2)))) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(X3,multiply(X3,X2)) = multiply(inverse(X3),X2),
inference(transitivity,[status(thm)],[c130,c141]) ).
cnf(c143,plain,
multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))) = multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2))))),
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2))))) = multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))) = multiply(X2,multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2))))))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2))))))) = multiply(X3,multiply(X2,multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))) = multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2))))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c148,plain,
multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2))))) = multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))) = multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2))))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(X2,multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2))))))) = multiply(X2,multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))))),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(X3,multiply(X2,multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))))) = multiply(X3,multiply(X2,multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2))))))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))))) = multiply(X3,multiply(X2,multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2))))))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c153,plain,
multiply(X3,multiply(X2,multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2))))))) = multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))))),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(inverse(X2),multiply(X2,multiply(X2,X2))) = multiply(X2,X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c155,plain,
multiply(X2,X2) = multiply(inverse(X2),multiply(X2,multiply(X2,X2))),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(inverse(X2),multiply(X2,multiply(X2,X2))) = multiply(inverse(X2),identity),
inference(congruence,[status(thm)],[c136]) ).
cnf(c157,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c158,plain,
multiply(inverse(X2),multiply(X2,multiply(X2,X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
multiply(X2,X2) = inverse(X2),
inference(transitivity,[status(thm)],[c155,c158]) ).
cnf(c160,plain,
multiply(multiply(X3,X2),multiply(X3,X2)) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
inverse(multiply(X3,X2)) = multiply(multiply(X3,X2),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
multiply(X3,inverse(multiply(X3,X2))) = multiply(X3,multiply(multiply(X3,X2),multiply(X3,X2))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))) = multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,X2)))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2))))) = multiply(X3,multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,X2))))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))))) = multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,X2)))))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c167,plain,
multiply(X4,multiply(X3,X2)) = multiply(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
multiply(X3,multiply(X4,multiply(X3,X2))) = multiply(X3,multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(X3,X2)))) = multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(X3,multiply(X4,multiply(X3,multiply(X4,multiply(X3,X2))))) = multiply(X3,multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2)))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(X3,multiply(X4,multiply(X3,X2)))))) = multiply(X4,multiply(X3,multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2))))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2)) = multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c173,plain,
multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2))) = multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2)),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
multiply(X3,multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2)))) = multiply(X3,multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2))))) = multiply(X4,multiply(X3,multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2)))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2))) = multiply(X4,multiply(X3,multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2)))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c177,plain,
multiply(X4,multiply(X3,multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2)))) = multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2))) = X2,
inference(substitution,[status(thm)],[c140]) ).
cnf(c179,plain,
multiply(X4,multiply(X3,multiply(multiply(X4,X3),multiply(multiply(X4,X3),X2)))) = X2,
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(X3,multiply(multiply(X4,X3),X2))))) = X2,
inference(transitivity,[status(thm)],[c175,c179]) ).
cnf(c181,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(X3,multiply(X4,multiply(X3,X2)))))) = X2,
inference(transitivity,[status(thm)],[c171,c180]) ).
cnf(c182,plain,
multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,X2)))))) = X2,
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
multiply(multiply(X3,X2),multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2)))))) = X2,
inference(transitivity,[status(thm)],[c165,c182]) ).
cnf(c184,plain,
multiply(X3,multiply(X2,multiply(X3,multiply(multiply(X3,X2),multiply(X3,inverse(multiply(X3,X2))))))) = X2,
inference(transitivity,[status(thm)],[c153,c183]) ).
cnf(c185,plain,
multiply(X3,multiply(X2,multiply(X3,multiply(X3,multiply(X2,multiply(X3,inverse(multiply(X3,X2)))))))) = X2,
inference(transitivity,[status(thm)],[c151,c184]) ).
cnf(c186,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,inverse(multiply(X3,X2))))))) = X2,
inference(transitivity,[status(thm)],[c146,c185]) ).
cnf(c187,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(X2,multiply(X3,multiply(inverse(X2),inverse(X3))))))) = X2,
inference(transitivity,[status(thm)],[c127,c186]) ).
cnf(c188,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),commutator(X2,X3)))) = X2,
inference(transitivity,[status(thm)],[c121,c187]) ).
cnf(c189,plain,
multiply(X2,multiply(inverse(X3),multiply(inverse(X2),commutator(inverse(X3),X2)))) = inverse(X3),
inference(substitution,[status(thm)],[c188]) ).
cnf(c190,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),commutator(inverse(X3),X2))))) = multiply(X3,inverse(X3)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),commutator(inverse(X3),X2))))) = identity,
inference(transitivity,[status(thm)],[c190,c5]) ).
cnf(c192,plain,
multiply(commutator(X3,X2),commutator(inverse(X3),X2)) = identity,
inference(transitivity,[status(thm)],[c117,c191]) ).
cnf(c193,plain,
multiply(commutator(X2,X3),commutator(inverse(X2),X3)) = identity,
inference(substitution,[status(thm)],[c192]) ).
cnf(c194,plain,
inverse(multiply(commutator(X2,X3),commutator(inverse(X2),X3))) = inverse(identity),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
multiply(inverse(multiply(commutator(X2,X3),commutator(inverse(X2),X3))),commutator(X2,X3)) = multiply(inverse(identity),commutator(X2,X3)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
multiply(identity,inverse(identity)) = inverse(identity),
inference(substitution,[status(thm)],[c12]) ).
cnf(c197,plain,
inverse(identity) = multiply(identity,inverse(identity)),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(identity,inverse(identity)) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c199,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c197,c198]) ).
cnf(c200,plain,
multiply(inverse(identity),commutator(X2,X3)) = multiply(identity,commutator(X2,X3)),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
multiply(identity,commutator(X2,X3)) = commutator(X2,X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c202,plain,
multiply(inverse(identity),commutator(X2,X3)) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c200,c201]) ).
cnf(c203,plain,
multiply(inverse(multiply(commutator(X2,X3),commutator(inverse(X2),X3))),commutator(X2,X3)) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c195,c202]) ).
cnf(c204,plain,
inverse(commutator(inverse(X2),X3)) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c115,c203]) ).
cnf(c205,plain,
commutator(X3,inverse(X2)) = commutator(X2,X3),
inference(transitivity,[status(thm)],[c104,c204]) ).
cnf(c206,plain,
commutator(X2,X3) = commutator(X3,inverse(X2)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
multiply(X2,commutator(X2,X3)) = multiply(X2,commutator(X3,inverse(X2))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
multiply(commutator(X3,X2),multiply(X2,commutator(X2,X3))) = multiply(commutator(X3,X2),multiply(X2,commutator(X3,inverse(X2)))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
inverse(commutator(X2,X3)) = commutator(X3,X2),
inference(substitution,[status(thm)],[c100]) ).
cnf(c210,plain,
commutator(X3,X2) = inverse(commutator(X2,X3)),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(commutator(X3,X2),multiply(X2,commutator(X3,inverse(X2)))) = multiply(inverse(commutator(X2,X3)),multiply(X2,commutator(X3,inverse(X2)))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c213,plain,
multiply(commutator(X3,X2),X3) = multiply(commutator(X3,X2),inverse(inverse(X3))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X3)))))) = multiply(commutator(X3,X2),inverse(inverse(X3))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c215,plain,
multiply(commutator(X3,X2),inverse(inverse(X3))) = multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X3)))))),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
commutator(X2,inverse(X3)) = multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X3))))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c217,plain,
multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X3))))) = commutator(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(X3,multiply(X2,multiply(inverse(X3),multiply(inverse(X2),inverse(inverse(X3)))))) = multiply(X3,commutator(X2,inverse(X3))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(commutator(X3,X2),inverse(inverse(X3))) = multiply(X3,commutator(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c215,c218]) ).
cnf(c220,plain,
multiply(commutator(X3,X2),X3) = multiply(X3,commutator(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c213,c219]) ).
cnf(c221,plain,
multiply(commutator(X2,X3),X2) = multiply(X2,commutator(X3,inverse(X2))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(X2,commutator(X3,inverse(X2))) = multiply(commutator(X2,X3),X2),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c223,plain,
multiply(inverse(commutator(X2,X3)),multiply(X2,commutator(X3,inverse(X2)))) = multiply(inverse(commutator(X2,X3)),multiply(commutator(X2,X3),X2)),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
multiply(inverse(commutator(X2,X3)),multiply(commutator(X2,X3),X2)) = X2,
inference(substitution,[status(thm)],[c59]) ).
cnf(c225,plain,
multiply(inverse(commutator(X2,X3)),multiply(X2,commutator(X3,inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c223,c224]) ).
cnf(c226,plain,
multiply(commutator(X3,X2),multiply(X2,commutator(X3,inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c211,c225]) ).
cnf(c227,plain,
multiply(commutator(X3,X2),multiply(X2,commutator(X2,X3))) = X2,
inference(transitivity,[status(thm)],[c208,c226]) ).
cnf(c228,plain,
multiply(commutator(X3,X2),multiply(X2,inverse(commutator(X3,X2)))) = X2,
inference(transitivity,[status(thm)],[c102,c227]) ).
cnf(c229,plain,
multiply(commutator(commutator(X3,X2),X2),X2) = X2,
inference(transitivity,[status(thm)],[c51,c228]) ).
cnf(c230,plain,
X2 = multiply(commutator(commutator(X3,X2),X2),X2),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
inverse(X2) = inverse(multiply(commutator(commutator(X3,X2),X2),X2)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(X2,inverse(X2)) = multiply(X2,inverse(multiply(commutator(commutator(X3,X2),X2),X2))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
multiply(commutator(commutator(X3,X2),X2),multiply(X2,inverse(X2))) = multiply(commutator(commutator(X3,X2),X2),multiply(X2,inverse(multiply(commutator(commutator(X3,X2),X2),X2)))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
multiply(commutator(commutator(X3,X2),X2),multiply(X2,inverse(multiply(commutator(commutator(X3,X2),X2),X2)))) = identity,
inference(substitution,[status(thm)],[c67]) ).
cnf(c235,plain,
multiply(commutator(commutator(X3,X2),X2),multiply(X2,inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c233,c234]) ).
cnf(c236,plain,
multiply(commutator(commutator(X3,X2),X2),identity) = identity,
inference(transitivity,[status(thm)],[c7,c235]) ).
cnf(c237,plain,
commutator(commutator(X3,X2),X2) = identity,
inference(transitivity,[status(thm)],[c4,c236]) ).
cnf(c238,plain,
commutator(commutator(a,b),b) = identity,
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
$false,
inference(resolution,[status(thm)],[c1,c238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:13:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.49 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.54/0.49
% 0.54/0.49 % SZS status Unsatisfiable
% 0.54/0.49
% 0.54/0.51 % SZS output start CNFRefutation
% See solution above
% 1.15/0.62
% 1.15/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------