%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 10:09:41 AM UTC 2026
% Result : Unsatisfiable 1.71s 0.67s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 10
% Syntax : Number of clauses : 160 ( 160 unt; 0 nHn; 4 RR)
% Number of literals : 160 ( 159 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 328 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang4) ).
cnf(c2,axiom,
multiply(X,left_division(X,Y)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_left_division) ).
cnf(c3,plain,
multiply(X3,left_division(X3,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = multiply(X3,left_division(X3,X2)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(left_inverse(X3),X2) = multiply(left_inverse(X3),multiply(X3,left_division(X3,X2))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X3,multiply(left_inverse(X3),X2)) = multiply(X3,multiply(left_inverse(X3),multiply(X3,left_division(X3,X2)))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
right_division(multiply(X2,Y2),Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_division_multiply) ).
cnf(c8,plain,
right_division(multiply(right_inverse(X2),X2),X2) = right_inverse(X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
right_inverse(X2) = right_division(multiply(right_inverse(X2),X2),X2),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
left_division(X2,multiply(X2,Y2)) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_division_multiply) ).
cnf(c11,plain,
left_division(X2,multiply(X2,multiply(right_inverse(X2),X2))) = multiply(right_inverse(X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(right_inverse(X2),X2) = left_division(X2,multiply(X2,multiply(right_inverse(X2),X2))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
multiply(X2,identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(c14,plain,
multiply(multiply(multiply(X3,X2),X3),identity) = multiply(multiply(X3,X2),X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(X3,X2),X3) = multiply(multiply(multiply(X3,X2),X3),identity),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,axiom,
multiply(multiply(multiply(X2,Y2),X2),Z) = multiply(X2,multiply(Y2,multiply(X2,Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',moufang3) ).
cnf(c17,plain,
multiply(multiply(multiply(X3,X2),X3),identity) = multiply(X3,multiply(X2,multiply(X3,identity))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X2,multiply(X3,identity)) = multiply(X2,X3),
inference(congruence,[status(thm)],[c13]) ).
cnf(c19,plain,
multiply(X3,multiply(X2,multiply(X3,identity))) = multiply(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(multiply(multiply(X3,X2),X3),identity) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
multiply(multiply(X3,X2),X3) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c15,c20]) ).
cnf(c22,plain,
multiply(multiply(X2,right_inverse(X2)),X2) = multiply(X2,multiply(right_inverse(X2),X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X2,multiply(right_inverse(X2),X2)) = multiply(multiply(X2,right_inverse(X2)),X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,axiom,
multiply(X2,right_inverse(X2)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c25,plain,
multiply(multiply(X2,right_inverse(X2)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
multiply(multiply(X2,right_inverse(X2)),X2) = X2,
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
multiply(X2,multiply(right_inverse(X2),X2)) = X2,
inference(transitivity,[status(thm)],[c23,c27]) ).
cnf(c29,plain,
left_division(X2,multiply(X2,multiply(right_inverse(X2),X2))) = left_division(X2,X2),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c31,plain,
left_division(X2,X2) = left_division(X2,multiply(X2,identity)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
left_division(X2,multiply(X2,identity)) = identity,
inference(substitution,[status(thm)],[c10]) ).
cnf(c33,plain,
left_division(X2,X2) = identity,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
left_division(X2,multiply(X2,multiply(right_inverse(X2),X2))) = identity,
inference(transitivity,[status(thm)],[c29,c33]) ).
cnf(c35,plain,
multiply(right_inverse(X2),X2) = identity,
inference(transitivity,[status(thm)],[c12,c34]) ).
cnf(c36,plain,
right_division(multiply(right_inverse(X2),X2),X2) = right_division(identity,X2),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
multiply(left_inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c38,plain,
identity = multiply(left_inverse(X2),X2),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
right_division(identity,X2) = right_division(multiply(left_inverse(X2),X2),X2),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
right_division(multiply(left_inverse(X2),X2),X2) = left_inverse(X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c41,plain,
right_division(identity,X2) = left_inverse(X2),
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
right_division(multiply(right_inverse(X2),X2),X2) = left_inverse(X2),
inference(transitivity,[status(thm)],[c36,c41]) ).
cnf(c43,plain,
right_inverse(X2) = left_inverse(X2),
inference(transitivity,[status(thm)],[c9,c42]) ).
cnf(c44,plain,
left_inverse(X2) = right_inverse(X2),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(left_inverse(X3),multiply(X3,X2)) = multiply(right_inverse(X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(X3,multiply(left_inverse(X3),multiply(X3,X2))) = multiply(X3,multiply(right_inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(multiply(multiply(X3,right_inverse(X3)),X3),X2) = multiply(X3,multiply(right_inverse(X3),multiply(X3,X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c48,plain,
multiply(X3,multiply(right_inverse(X3),multiply(X3,X2))) = multiply(multiply(multiply(X3,right_inverse(X3)),X3),X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(multiply(X2,right_inverse(X2)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c50,plain,
multiply(multiply(multiply(X3,right_inverse(X3)),X3),X2) = multiply(multiply(identity,X3),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(multiply(identity,X3),X2) = multiply(X3,X2),
inference(congruence,[status(thm)],[c26]) ).
cnf(c52,plain,
multiply(multiply(multiply(X3,right_inverse(X3)),X3),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
multiply(X3,multiply(right_inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c48,c52]) ).
cnf(c54,plain,
multiply(X3,multiply(left_inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c46,c53]) ).
cnf(c55,plain,
multiply(X3,multiply(left_inverse(X3),multiply(X3,left_division(X3,X2)))) = multiply(X3,left_division(X3,X2)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X3,left_division(X3,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c57,plain,
multiply(X3,multiply(left_inverse(X3),multiply(X3,left_division(X3,X2)))) = X2,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
multiply(X3,multiply(left_inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c6,c57]) ).
cnf(c59,plain,
X2 = multiply(X3,multiply(left_inverse(X3),X2)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
left_division(X3,X2) = left_division(X3,multiply(X3,multiply(left_inverse(X3),X2))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
left_division(X3,multiply(X3,multiply(left_inverse(X3),X2))) = multiply(left_inverse(X3),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c62,plain,
left_division(X3,X2) = multiply(left_inverse(X3),X2),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
multiply(left_inverse(X3),X2) = left_division(X3,X2),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(multiply(left_inverse(X3),X2),multiply(X3,X4)) = multiply(left_division(X3,X2),multiply(X3,X4)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(X4,multiply(multiply(left_inverse(X4),X3),multiply(X4,X2))) = multiply(X4,multiply(left_division(X4,X3),multiply(X4,X2))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(multiply(multiply(X4,left_division(X4,X3)),X4),X2) = multiply(X4,multiply(left_division(X4,X3),multiply(X4,X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c67,plain,
multiply(X4,multiply(left_division(X4,X3),multiply(X4,X2))) = multiply(multiply(multiply(X4,left_division(X4,X3)),X4),X2),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(X3,left_division(X3,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
multiply(multiply(X3,left_division(X3,X2)),X3) = multiply(X2,X3),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(multiply(multiply(X4,left_division(X4,X3)),X4),X2) = multiply(multiply(X3,X4),X2),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(X4,multiply(left_division(X4,X3),multiply(X4,X2))) = multiply(multiply(X3,X4),X2),
inference(transitivity,[status(thm)],[c67,c70]) ).
cnf(c72,plain,
multiply(X4,multiply(multiply(left_inverse(X4),X3),multiply(X4,X2))) = multiply(multiply(X3,X4),X2),
inference(transitivity,[status(thm)],[c65,c71]) ).
cnf(c73,plain,
multiply(left_inverse(X2),multiply(multiply(left_inverse(left_inverse(X2)),X3),multiply(left_inverse(X2),X2))) = multiply(multiply(X3,left_inverse(X2)),X2),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(multiply(X3,left_inverse(X2)),X2) = multiply(left_inverse(X2),multiply(multiply(left_inverse(left_inverse(X2)),X3),multiply(left_inverse(X2),X2))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(multiply(left_inverse(left_inverse(X2)),X3),multiply(left_inverse(X2),X2)) = multiply(multiply(left_inverse(left_inverse(X2)),X3),identity),
inference(congruence,[status(thm)],[c37]) ).
cnf(c76,plain,
multiply(left_inverse(X2),multiply(multiply(left_inverse(left_inverse(X2)),X3),multiply(left_inverse(X2),X2))) = multiply(left_inverse(X2),multiply(multiply(left_inverse(left_inverse(X2)),X3),identity)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(multiply(left_inverse(left_inverse(X2)),X3),identity) = multiply(left_inverse(left_inverse(X2)),X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c78,plain,
multiply(left_inverse(X2),multiply(multiply(left_inverse(left_inverse(X2)),X3),identity)) = multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),X3)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),X3)) = X3,
inference(substitution,[status(thm)],[c58]) ).
cnf(c80,plain,
multiply(left_inverse(X2),multiply(multiply(left_inverse(left_inverse(X2)),X3),identity)) = X3,
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
multiply(left_inverse(X2),multiply(multiply(left_inverse(left_inverse(X2)),X3),multiply(left_inverse(X2),X2))) = X3,
inference(transitivity,[status(thm)],[c76,c80]) ).
cnf(c82,plain,
multiply(multiply(X3,left_inverse(X2)),X2) = X3,
inference(transitivity,[status(thm)],[c74,c81]) ).
cnf(c83,plain,
multiply(multiply(right_division(X3,left_inverse(X2)),left_inverse(X2)),X2) = right_division(X3,left_inverse(X2)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
right_division(X3,left_inverse(X2)) = multiply(multiply(right_division(X3,left_inverse(X2)),left_inverse(X2)),X2),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,axiom,
multiply(right_division(X2,Y2),Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_right_division) ).
cnf(c86,plain,
multiply(right_division(X3,left_inverse(X2)),left_inverse(X2)) = X3,
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(multiply(right_division(X3,left_inverse(X2)),left_inverse(X2)),X2) = multiply(X3,X2),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
right_division(X3,left_inverse(X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c84,c87]) ).
cnf(c89,plain,
right_division(multiply(X4,X3),left_inverse(multiply(X2,X4))) = multiply(multiply(X4,X3),multiply(X2,X4)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(multiply(X4,X3),multiply(X2,X4)) = right_division(multiply(X4,X3),left_inverse(multiply(X2,X4))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(X3,multiply(left_inverse(X3),left_division(left_inverse(X3),X2))) = left_division(left_inverse(X3),X2),
inference(substitution,[status(thm)],[c58]) ).
cnf(c92,plain,
left_division(left_inverse(X3),X2) = multiply(X3,multiply(left_inverse(X3),left_division(left_inverse(X3),X2))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(left_inverse(X3),left_division(left_inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
multiply(X3,multiply(left_inverse(X3),left_division(left_inverse(X3),X2))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
left_division(left_inverse(X3),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c92,c94]) ).
cnf(c96,plain,
left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2) = multiply(multiply(X4,multiply(X3,X4)),X2),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(multiply(X4,multiply(X3,X4)),X2) = left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(X3,multiply(X2,X3)) = multiply(multiply(X3,X2),X3),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c99,plain,
left_inverse(multiply(X3,multiply(X2,X3))) = left_inverse(multiply(multiply(X3,X2),X3)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
multiply(left_inverse(multiply(X4,multiply(X3,X4))),X2) = multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),X2)) = multiply(X4,multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(X3,multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),X2))) = multiply(X3,multiply(X4,multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),X2)))) = multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2)))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
left_division(multiply(multiply(X4,X3),X4),X2) = multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2),
inference(substitution,[status(thm)],[c62]) ).
cnf(c105,plain,
multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2) = left_division(multiply(multiply(X4,X3),X4),X2),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(X4,multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2)) = multiply(X4,left_division(multiply(multiply(X4,X3),X4),X2)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(X3,multiply(X4,multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2))) = multiply(X3,multiply(X4,left_division(multiply(multiply(X4,X3),X4),X2))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2)))) = multiply(X4,multiply(X3,multiply(X4,left_division(multiply(multiply(X4,X3),X4),X2)))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(multiply(multiply(X4,X3),X4),left_division(multiply(multiply(X4,X3),X4),X2)) = multiply(X4,multiply(X3,multiply(X4,left_division(multiply(multiply(X4,X3),X4),X2)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c110,plain,
multiply(X4,multiply(X3,multiply(X4,left_division(multiply(multiply(X4,X3),X4),X2)))) = multiply(multiply(multiply(X4,X3),X4),left_division(multiply(multiply(X4,X3),X4),X2)),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(multiply(multiply(X4,X3),X4),left_division(multiply(multiply(X4,X3),X4),X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
multiply(X4,multiply(X3,multiply(X4,left_division(multiply(multiply(X4,X3),X4),X2)))) = X2,
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(multiply(X4,X3),X4)),X2)))) = X2,
inference(transitivity,[status(thm)],[c108,c112]) ).
cnf(c114,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),X2)))) = X2,
inference(transitivity,[status(thm)],[c103,c113]) ).
cnf(c115,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2))))) = left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2),
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2) = multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2))))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(left_inverse(multiply(X4,multiply(X3,X4))),left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c118,plain,
multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2))) = multiply(X4,X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
multiply(X3,multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2)))) = multiply(X3,multiply(X4,X2)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(X4,multiply(X3,multiply(X4,multiply(left_inverse(multiply(X4,multiply(X3,X4))),left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2))))) = multiply(X4,multiply(X3,multiply(X4,X2))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
left_division(left_inverse(multiply(X4,multiply(X3,X4))),X2) = multiply(X4,multiply(X3,multiply(X4,X2))),
inference(transitivity,[status(thm)],[c116,c120]) ).
cnf(c122,plain,
multiply(multiply(X4,multiply(X3,X4)),X2) = multiply(X4,multiply(X3,multiply(X4,X2))),
inference(transitivity,[status(thm)],[c97,c121]) ).
cnf(c123,plain,
multiply(multiply(X4,multiply(multiply(X3,X2),X4)),left_inverse(multiply(X2,X4))) = multiply(X4,multiply(multiply(X3,X2),multiply(X4,left_inverse(multiply(X2,X4))))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
left_division(X3,multiply(X3,multiply(left_inverse(X3),multiply(X3,X2)))) = multiply(left_inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c125,plain,
multiply(left_inverse(X3),multiply(X3,X2)) = left_division(X3,multiply(X3,multiply(left_inverse(X3),multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
left_division(X3,multiply(X3,multiply(left_inverse(X3),multiply(X3,X2)))) = left_division(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c127,plain,
left_division(X3,multiply(X3,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c128,plain,
left_division(X3,multiply(X3,multiply(left_inverse(X3),multiply(X3,X2)))) = X2,
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
multiply(left_inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c125,c128]) ).
cnf(c130,plain,
multiply(left_inverse(X2),multiply(X2,X3)) = X3,
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
X3 = multiply(left_inverse(X2),multiply(X2,X3)),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
multiply(X3,left_inverse(multiply(X2,X3))) = multiply(multiply(left_inverse(X2),multiply(X2,X3)),left_inverse(multiply(X2,X3))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
left_inverse(X2) = right_inverse(X2),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c134,plain,
multiply(multiply(X3,X2),left_inverse(X2)) = multiply(multiply(X3,X2),right_inverse(X2)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(X2,multiply(multiply(left_inverse(X2),X3),multiply(X2,right_inverse(X2)))) = multiply(multiply(X3,X2),right_inverse(X2)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c136,plain,
multiply(multiply(X3,X2),right_inverse(X2)) = multiply(X2,multiply(multiply(left_inverse(X2),X3),multiply(X2,right_inverse(X2)))),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(multiply(left_inverse(X2),X3),multiply(X2,right_inverse(X2))) = multiply(multiply(left_inverse(X2),X3),identity),
inference(congruence,[status(thm)],[c24]) ).
cnf(c138,plain,
multiply(X2,multiply(multiply(left_inverse(X2),X3),multiply(X2,right_inverse(X2)))) = multiply(X2,multiply(multiply(left_inverse(X2),X3),identity)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(multiply(left_inverse(X2),X3),identity) = multiply(left_inverse(X2),X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c140,plain,
multiply(X2,multiply(multiply(left_inverse(X2),X3),identity)) = multiply(X2,multiply(left_inverse(X2),X3)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(X2,multiply(left_inverse(X2),X3)) = X3,
inference(substitution,[status(thm)],[c58]) ).
cnf(c142,plain,
multiply(X2,multiply(multiply(left_inverse(X2),X3),identity)) = X3,
inference(transitivity,[status(thm)],[c140,c141]) ).
cnf(c143,plain,
multiply(X2,multiply(multiply(left_inverse(X2),X3),multiply(X2,right_inverse(X2)))) = X3,
inference(transitivity,[status(thm)],[c138,c142]) ).
cnf(c144,plain,
multiply(multiply(X3,X2),right_inverse(X2)) = X3,
inference(transitivity,[status(thm)],[c136,c143]) ).
cnf(c145,plain,
multiply(multiply(X3,X2),left_inverse(X2)) = X3,
inference(transitivity,[status(thm)],[c134,c144]) ).
cnf(c146,plain,
multiply(multiply(left_inverse(X2),multiply(X2,X3)),left_inverse(multiply(X2,X3))) = left_inverse(X2),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(X3,left_inverse(multiply(X2,X3))) = left_inverse(X2),
inference(transitivity,[status(thm)],[c132,c146]) ).
cnf(c148,plain,
multiply(multiply(X3,X2),multiply(X4,left_inverse(multiply(X2,X4)))) = multiply(multiply(X3,X2),left_inverse(X2)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(X4,multiply(multiply(X3,X2),multiply(X4,left_inverse(multiply(X2,X4))))) = multiply(X4,multiply(multiply(X3,X2),left_inverse(X2))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(X4,multiply(multiply(X3,X2),left_inverse(X2))) = multiply(X4,X3),
inference(congruence,[status(thm)],[c145]) ).
cnf(c151,plain,
multiply(X4,multiply(multiply(X3,X2),multiply(X4,left_inverse(multiply(X2,X4))))) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
multiply(multiply(X4,multiply(multiply(X3,X2),X4)),left_inverse(multiply(X2,X4))) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c123,c151]) ).
cnf(c153,plain,
multiply(X4,X3) = multiply(multiply(X4,multiply(multiply(X3,X2),X4)),left_inverse(multiply(X2,X4))),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
right_division(multiply(X4,X3),left_inverse(multiply(X2,X4))) = right_division(multiply(multiply(X4,multiply(multiply(X3,X2),X4)),left_inverse(multiply(X2,X4))),left_inverse(multiply(X2,X4))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
right_division(multiply(multiply(X4,multiply(multiply(X3,X2),X4)),left_inverse(multiply(X2,X4))),left_inverse(multiply(X2,X4))) = multiply(X4,multiply(multiply(X3,X2),X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c156,plain,
right_division(multiply(X4,X3),left_inverse(multiply(X2,X4))) = multiply(X4,multiply(multiply(X3,X2),X4)),
inference(transitivity,[status(thm)],[c154,c155]) ).
cnf(c157,plain,
multiply(multiply(X4,X3),multiply(X2,X4)) = multiply(X4,multiply(multiply(X3,X2),X4)),
inference(transitivity,[status(thm)],[c90,c156]) ).
cnf(c158,plain,
multiply(multiply(x,y),multiply(z,x)) = multiply(x,multiply(multiply(y,z),x)),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(x,multiply(multiply(y,z),x)) = multiply(multiply(x,y),multiply(z,x)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
$false,
inference(resolution,[status(thm)],[c1,c159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:37:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.71/0.67 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
% 1.71/0.67
% 1.71/0.67 % SZS status Unsatisfiable
% 1.71/0.67
% 1.71/0.68 % SZS output start CNFRefutation
% See solution above
% 2.09/0.75
% 2.09/0.75 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------