%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP512-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:11:07 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 2
% Syntax : Number of clauses : 90 ( 90 unt; 0 nHn; 7 RR)
% Number of literals : 90 ( 89 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 222 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
cnf(c2,axiom,
multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(multiply(multiply(X3,inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X2))))),X),inverse(multiply(X3,X))) = inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X2)))) = multiply(multiply(multiply(X3,inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X2))))),X),inverse(multiply(X3,X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(multiply(multiply(X2,X3),X),inverse(multiply(X2,X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
X3 = multiply(multiply(multiply(X2,X3),X),inverse(multiply(X2,X))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X3,inverse(multiply(multiply(X2,X3),inverse(multiply(X2,X))))) = multiply(multiply(multiply(multiply(X2,X3),X),inverse(multiply(X2,X))),inverse(multiply(multiply(X2,X3),inverse(multiply(X2,X))))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(multiply(multiply(multiply(X2,X3),X),inverse(multiply(X2,X))),inverse(multiply(multiply(X2,X3),inverse(multiply(X2,X))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
multiply(X3,inverse(multiply(multiply(X2,X3),inverse(multiply(X2,X))))) = X,
inference(transitivity,[status(thm)],[c7,c8]) ).
cnf(c10,plain,
multiply(X2,inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X))))) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(multiply(X3,inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X2))))),X) = multiply(X2,X),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(multiply(X3,inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X2))))),X),inverse(multiply(X3,X))) = multiply(multiply(X2,X),inverse(multiply(X3,X))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X2)))) = multiply(multiply(X2,X),inverse(multiply(X3,X))),
inference(transitivity,[status(thm)],[c4,c12]) ).
cnf(c14,plain,
inverse(multiply(multiply(X,X3),inverse(multiply(X,X3)))) = multiply(multiply(X3,X2),inverse(multiply(X3,X2))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,X2))) = inverse(multiply(multiply(X,X3),inverse(multiply(X,X3)))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X4,multiply(multiply(X3,X2),inverse(multiply(X3,X2)))) = multiply(X4,inverse(multiply(multiply(X,X3),inverse(multiply(X,X3))))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(X,inverse(multiply(multiply(X3,X),inverse(multiply(X3,X2))))) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c18,plain,
X3 = multiply(X2,inverse(multiply(multiply(X,X2),inverse(multiply(X,X3))))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X4,X2) = multiply(multiply(X3,inverse(multiply(multiply(X,X3),inverse(multiply(X,X4))))),X2),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(multiply(X4,X2),inverse(multiply(X3,X2))) = multiply(multiply(multiply(X3,inverse(multiply(multiply(X,X3),inverse(multiply(X,X4))))),X2),inverse(multiply(X3,X2))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(multiply(X3,inverse(multiply(multiply(X,X3),inverse(multiply(X,X4))))),X2),inverse(multiply(X3,X2))) = inverse(multiply(multiply(X,X3),inverse(multiply(X,X4)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
multiply(multiply(multiply(X2,inverse(multiply(multiply(X,X2),inverse(multiply(X,X4))))),X3),inverse(multiply(X2,X3))) = inverse(multiply(multiply(X,X2),inverse(multiply(X,X4)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
inverse(multiply(multiply(X,X2),inverse(multiply(X,X4)))) = multiply(multiply(multiply(X2,inverse(multiply(multiply(X,X2),inverse(multiply(X,X4))))),X3),inverse(multiply(X2,X3))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X2,inverse(multiply(multiply(X,X2),inverse(multiply(X,X3))))) = X3,
inference(substitution,[status(thm)],[c9]) ).
cnf(c25,plain,
multiply(multiply(X2,inverse(multiply(multiply(X,X2),inverse(multiply(X,X4))))),X3) = multiply(X4,X3),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(multiply(multiply(X2,inverse(multiply(multiply(X,X2),inverse(multiply(X,X4))))),X3),inverse(multiply(X2,X3))) = multiply(multiply(X4,X3),inverse(multiply(X2,X3))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
inverse(multiply(multiply(X,X2),inverse(multiply(X,X4)))) = multiply(multiply(X4,X3),inverse(multiply(X2,X3))),
inference(transitivity,[status(thm)],[c23,c26]) ).
cnf(c28,plain,
multiply(multiply(multiply(X3,inverse(multiply(multiply(X,X3),inverse(multiply(X,X5))))),X2),inverse(multiply(X3,X2))) = multiply(multiply(X5,X4),inverse(multiply(X3,X4))),
inference(transitivity,[status(thm)],[c21,c27]) ).
cnf(c29,plain,
multiply(multiply(X4,X),inverse(multiply(X2,X))) = multiply(multiply(X4,X3),inverse(multiply(X2,X3))),
inference(transitivity,[status(thm)],[c20,c28]) ).
cnf(c30,plain,
multiply(multiply(X,X2),inverse(multiply(X,X2))) = multiply(multiply(X,X3),inverse(multiply(X,X3))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(multiply(multiply(X,X2),inverse(multiply(X,X2)))) = inverse(multiply(multiply(X,X3),inverse(multiply(X,X3)))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X3,inverse(multiply(multiply(X,X2),inverse(multiply(X,X2))))) = multiply(X3,inverse(multiply(multiply(X,X3),inverse(multiply(X,X3))))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X2,inverse(multiply(multiply(X,X2),inverse(multiply(X,X2))))) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c34,plain,
multiply(X3,inverse(multiply(multiply(X,X2),inverse(multiply(X,X2))))) = X3,
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
multiply(X3,multiply(multiply(X2,X),inverse(multiply(X2,X)))) = X3,
inference(transitivity,[status(thm)],[c16,c34]) ).
cnf(c36,plain,
X3 = multiply(X3,multiply(multiply(X2,X),inverse(multiply(X2,X)))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(X3) = inverse(multiply(X3,multiply(multiply(X2,X),inverse(multiply(X2,X))))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(multiply(X4,X3),inverse(X4)) = multiply(multiply(X4,X3),inverse(multiply(X4,multiply(multiply(X2,X),inverse(multiply(X2,X)))))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(multiply(X4,X3),multiply(multiply(X2,X),inverse(multiply(X2,X)))) = multiply(X4,X3),
inference(substitution,[status(thm)],[c35]) ).
cnf(c40,plain,
multiply(X4,X3) = multiply(multiply(X4,X3),multiply(multiply(X2,X),inverse(multiply(X2,X)))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(multiply(X4,X3),inverse(multiply(X4,multiply(multiply(X2,X),inverse(multiply(X2,X)))))) = multiply(multiply(multiply(X4,X3),multiply(multiply(X2,X),inverse(multiply(X2,X)))),inverse(multiply(X4,multiply(multiply(X2,X),inverse(multiply(X2,X)))))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(multiply(multiply(X4,X3),multiply(multiply(X2,X),inverse(multiply(X2,X)))),inverse(multiply(X4,multiply(multiply(X2,X),inverse(multiply(X2,X)))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,plain,
multiply(multiply(X4,X3),inverse(multiply(X4,multiply(multiply(X2,X),inverse(multiply(X2,X)))))) = X3,
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
multiply(multiply(X2,X),inverse(X2)) = X,
inference(transitivity,[status(thm)],[c38,c43]) ).
cnf(c45,plain,
multiply(multiply(X,X2),inverse(X)) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
X2 = multiply(multiply(X,X2),inverse(X)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(X2,inverse(multiply(X,X2))) = multiply(multiply(multiply(X,X2),inverse(X)),inverse(multiply(X,X2))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(multiply(multiply(X,X2),inverse(X)),inverse(multiply(X,X2))) = inverse(X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c49,plain,
multiply(X2,inverse(multiply(X,X2))) = inverse(X),
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
multiply(multiply(X2,X),inverse(multiply(X2,multiply(X2,X)))) = inverse(X2),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
inverse(X2) = multiply(multiply(X2,X),inverse(multiply(X2,multiply(X2,X)))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
inverse(inverse(X2)) = inverse(multiply(multiply(X2,X),inverse(multiply(X2,multiply(X2,X))))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(X,inverse(inverse(X2))) = multiply(X,inverse(multiply(multiply(X2,X),inverse(multiply(X2,multiply(X2,X)))))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(X,inverse(multiply(multiply(X2,X),inverse(multiply(X2,multiply(X2,X)))))) = multiply(X2,X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c55,plain,
multiply(X,inverse(inverse(X2))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
multiply(X,inverse(inverse(inverse(X2)))) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(X2,multiply(X,inverse(inverse(inverse(X2))))) = multiply(X2,multiply(inverse(X2),X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(multiply(inverse(X2),X),inverse(inverse(X2))) = multiply(X2,multiply(inverse(X2),X)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c59,plain,
multiply(X2,multiply(inverse(X2),X)) = multiply(multiply(inverse(X2),X),inverse(inverse(X2))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(multiply(inverse(X2),X),inverse(inverse(X2))) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c61,plain,
multiply(X2,multiply(inverse(X2),X)) = X,
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
multiply(X2,multiply(X,inverse(inverse(inverse(X2))))) = X,
inference(transitivity,[status(thm)],[c57,c61]) ).
cnf(c63,plain,
multiply(X,multiply(inverse(inverse(X)),inverse(inverse(inverse(X))))) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(inverse(X)) = multiply(X,multiply(inverse(inverse(X)),inverse(inverse(inverse(X))))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(X),inverse(inverse(X))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c66,plain,
multiply(X,inverse(X)) = multiply(inverse(X),inverse(inverse(X))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(X2,multiply(X,inverse(X))) = multiply(X2,multiply(inverse(X),inverse(inverse(X)))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(multiply(X,inverse(multiply(X2,X))),inverse(X)) = inverse(multiply(X2,X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c69,plain,
inverse(multiply(X2,X)) = multiply(multiply(X,inverse(multiply(X2,X))),inverse(X)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(X,inverse(multiply(X2,X))) = inverse(X2),
inference(substitution,[status(thm)],[c49]) ).
cnf(c71,plain,
multiply(multiply(X,inverse(multiply(X2,X))),inverse(X)) = multiply(inverse(X2),inverse(X)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
inverse(multiply(X2,X)) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c69,c71]) ).
cnf(c73,plain,
inverse(multiply(X,inverse(X))) = multiply(inverse(X),inverse(inverse(X))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(inverse(X),inverse(inverse(X))) = inverse(multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(X2,multiply(inverse(X),inverse(inverse(X)))) = multiply(X2,inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(multiply(X,X2),inverse(X)) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c77,plain,
X2 = multiply(multiply(X,X2),inverse(X)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(X2,inverse(multiply(X,inverse(X)))) = multiply(multiply(multiply(X,X2),inverse(X)),inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(multiply(multiply(X,X2),inverse(X)),inverse(multiply(X,inverse(X)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c80,plain,
multiply(X2,inverse(multiply(X,inverse(X)))) = X2,
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
multiply(X2,multiply(inverse(X),inverse(inverse(X)))) = X2,
inference(transitivity,[status(thm)],[c75,c80]) ).
cnf(c82,plain,
multiply(X2,multiply(X,inverse(X))) = X2,
inference(transitivity,[status(thm)],[c67,c81]) ).
cnf(c83,plain,
multiply(X,multiply(inverse(inverse(X)),inverse(inverse(inverse(X))))) = X,
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c64,c83]) ).
cnf(c85,plain,
inverse(inverse(b)) = b,
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
b = inverse(inverse(b)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(a,b) = multiply(a,inverse(inverse(b))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(a,inverse(inverse(b))) = multiply(b,a),
inference(substitution,[status(thm)],[c55]) ).
cnf(c89,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
$false,
inference(resolution,[status(thm)],[c1,c89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP512-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:04:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 Command-line arguments: --no-flatten-goal
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.19/0.47
% 0.19/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------