%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP515-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 10:11:08 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 2
% Syntax : Number of clauses : 83 ( 83 unt; 0 nHn; 7 RR)
% Number of literals : 83 ( 82 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 218 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c2,axiom,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(X3,multiply(multiply(X2,X),inverse(multiply(X3,X)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = multiply(X3,multiply(multiply(X2,X),inverse(multiply(X3,X)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
inverse(X2) = inverse(multiply(X3,multiply(multiply(X2,X),inverse(multiply(X3,X))))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X2,inverse(X2)) = multiply(X2,inverse(multiply(X3,multiply(multiply(X2,X),inverse(multiply(X3,X)))))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X3,multiply(X2,inverse(X2))) = multiply(X3,multiply(X2,inverse(multiply(X3,multiply(multiply(X2,X),inverse(multiply(X3,X))))))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(X3,multiply(multiply(X2,X),inverse(multiply(X3,X)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
X3 = multiply(X,multiply(multiply(X3,X2),inverse(multiply(X,X2)))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X3,inverse(multiply(X4,multiply(multiply(X3,X2),inverse(multiply(X,X2)))))) = multiply(multiply(X,multiply(multiply(X3,X2),inverse(multiply(X,X2)))),inverse(multiply(X4,multiply(multiply(X3,X2),inverse(multiply(X,X2)))))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(X4,multiply(X3,inverse(multiply(X4,multiply(multiply(X3,X2),inverse(multiply(X,X2))))))) = multiply(X4,multiply(multiply(X,multiply(multiply(X3,X2),inverse(multiply(X,X2)))),inverse(multiply(X4,multiply(multiply(X3,X2),inverse(multiply(X,X2))))))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X4,multiply(multiply(X,multiply(multiply(X3,X2),inverse(multiply(X,X2)))),inverse(multiply(X4,multiply(multiply(X3,X2),inverse(multiply(X,X2))))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
multiply(X4,multiply(X3,inverse(multiply(X4,multiply(multiply(X3,X2),inverse(multiply(X,X2))))))) = X,
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
multiply(X3,multiply(X2,inverse(multiply(X3,multiply(multiply(X2,X),inverse(multiply(X3,X))))))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X2,multiply(X,inverse(X))) = X2,
inference(transitivity,[status(thm)],[c7,c14]) ).
cnf(c16,plain,
X2 = multiply(X2,multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
inverse(X2) = inverse(multiply(X2,multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X2,inverse(X3)) = multiply(X2,inverse(multiply(X3,multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X3,multiply(X2,inverse(X3))) = multiply(X3,multiply(X2,inverse(multiply(X3,multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
X2 = multiply(X2,multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c21,plain,
multiply(X2,inverse(multiply(X3,multiply(X,inverse(X))))) = multiply(multiply(X2,multiply(X,inverse(X))),inverse(multiply(X3,multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X3,multiply(X2,inverse(multiply(X3,multiply(X,inverse(X)))))) = multiply(X3,multiply(multiply(X2,multiply(X,inverse(X))),inverse(multiply(X3,multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X3,multiply(multiply(X2,multiply(X,inverse(X))),inverse(multiply(X3,multiply(X,inverse(X)))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
multiply(X3,multiply(X2,inverse(multiply(X3,multiply(X,inverse(X)))))) = X2,
inference(transitivity,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
multiply(X2,multiply(X,inverse(X2))) = X,
inference(transitivity,[status(thm)],[c19,c24]) ).
cnf(c26,plain,
multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(X3,X2)))) = multiply(X,X2),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X,X2) = multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
inverse(multiply(X,X2)) = inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(X3,X2))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X,inverse(multiply(X,X2))) = multiply(X,inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(X3,X2)))))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(X3,X2),multiply(X,inverse(multiply(X,X2)))) = multiply(multiply(X3,X2),multiply(X,inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(X3,X2))))))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(multiply(X3,X2),multiply(X,inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(X3,X2))))))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c32,plain,
multiply(multiply(X3,X2),multiply(X,inverse(multiply(X,X2)))) = X3,
inference(transitivity,[status(thm)],[c30,c31]) ).
cnf(c33,plain,
multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(multiply(X,X2),X2)))) = X3,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
X3 = multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(multiply(X,X2),X2)))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(X3) = inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(multiply(X,X2),X2))))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X,inverse(X3)) = multiply(X,inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(multiply(X,X2),X2)))))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(multiply(X3,X2),multiply(X,inverse(X3))) = multiply(multiply(X3,X2),multiply(X,inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(multiply(X,X2),X2))))))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(multiply(X3,X2),multiply(X,inverse(multiply(multiply(X3,X2),multiply(multiply(X,X2),inverse(multiply(multiply(X,X2),X2))))))) = multiply(X,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c39,plain,
multiply(multiply(X3,X2),multiply(X,inverse(X3))) = multiply(X,X2),
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
multiply(multiply(X3,X),multiply(multiply(X3,X2),inverse(X3))) = multiply(multiply(X3,X2),X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(multiply(X3,X2),X) = multiply(multiply(X3,X),multiply(multiply(X3,X2),inverse(X3))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(multiply(X,multiply(X2,inverse(X))),multiply(X3,inverse(X))) = multiply(X3,multiply(X2,inverse(X))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c43,plain,
multiply(X3,multiply(X2,inverse(X))) = multiply(multiply(X,multiply(X2,inverse(X))),multiply(X3,inverse(X))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(X,multiply(X2,inverse(X))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c45,plain,
multiply(multiply(X,multiply(X2,inverse(X))),multiply(X3,inverse(X))) = multiply(X2,multiply(X3,inverse(X))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(X3,multiply(X2,inverse(X))) = multiply(X2,multiply(X3,inverse(X))),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
multiply(multiply(X2,X),multiply(X3,inverse(X2))) = multiply(X3,multiply(multiply(X2,X),inverse(X2))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(X3,multiply(multiply(X2,X),inverse(X2))) = multiply(multiply(X2,X),multiply(X3,inverse(X2))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(multiply(X2,X),multiply(X3,inverse(X2))) = multiply(X3,X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c50,plain,
multiply(X3,multiply(multiply(X2,X),inverse(X2))) = multiply(X3,X),
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
multiply(multiply(X3,X),multiply(multiply(X3,X2),inverse(X3))) = multiply(multiply(X3,X),X2),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(multiply(X3,X2),X) = multiply(multiply(X3,X),X2),
inference(transitivity,[status(thm)],[c41,c51]) ).
cnf(c53,plain,
multiply(multiply(X2,X),inverse(X3)) = multiply(multiply(X2,inverse(X3)),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(multiply(X2,inverse(X3)),X) = multiply(multiply(X2,X),inverse(X3)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(X3,multiply(multiply(X2,inverse(X3)),X)) = multiply(X3,multiply(multiply(X2,X),inverse(X3))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X3,multiply(multiply(X2,X),inverse(X3))) = multiply(X2,X),
inference(substitution,[status(thm)],[c25]) ).
cnf(c57,plain,
multiply(X3,multiply(multiply(X2,inverse(X3)),X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
multiply(X,multiply(multiply(X2,inverse(X)),inverse(multiply(X,inverse(X))))) = multiply(X2,inverse(multiply(X,inverse(X)))),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X2,inverse(multiply(X,inverse(X)))) = multiply(X,multiply(multiply(X2,inverse(X)),inverse(multiply(X,inverse(X))))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(X,multiply(multiply(X2,inverse(X)),inverse(multiply(X,inverse(X))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c61,plain,
multiply(X2,inverse(multiply(X,inverse(X)))) = X2,
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
X2 = multiply(X2,inverse(multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X2,X3) = multiply(X2,multiply(X3,inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X2,multiply(X3,inverse(multiply(X,inverse(X))))) = multiply(X3,multiply(X2,inverse(multiply(X,inverse(X))))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c65,plain,
multiply(X3,multiply(X2,inverse(multiply(X,inverse(X))))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c61]) ).
cnf(c66,plain,
multiply(X2,multiply(X3,inverse(multiply(X,inverse(X))))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
multiply(X,X2) = multiply(X2,X),
inference(transitivity,[status(thm)],[c63,c66]) ).
cnf(c68,plain,
multiply(c3,multiply(a3,b3)) = multiply(multiply(a3,b3),c3),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(multiply(a3,b3),c3) = multiply(c3,multiply(a3,b3)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(X3,multiply(X2,X)) = multiply(multiply(X2,X),X3),
inference(substitution,[status(thm)],[c67]) ).
cnf(c71,plain,
multiply(multiply(X2,X),X3) = multiply(multiply(X2,X3),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c72,plain,
multiply(X,multiply(X2,X3)) = multiply(multiply(X2,X3),X),
inference(substitution,[status(thm)],[c67]) ).
cnf(c73,plain,
multiply(multiply(X2,X3),X) = multiply(X,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(X2,X) = multiply(X,X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c75,plain,
multiply(X,X2) = multiply(X2,X),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(X,multiply(X2,X3)) = multiply(X,multiply(X3,X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(multiply(X2,X3),X) = multiply(X,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c73,c76]) ).
cnf(c78,plain,
multiply(multiply(X2,X),X3) = multiply(X,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c71,c77]) ).
cnf(c79,plain,
multiply(X3,multiply(X2,X)) = multiply(X,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c70,c78]) ).
cnf(c80,plain,
multiply(a3,multiply(b3,c3)) = multiply(c3,multiply(a3,b3)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(transitivity,[status(thm)],[c69,c81]) ).
cnf(c83,plain,
$false,
inference(resolution,[status(thm)],[c1,c82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP515-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 10:08:10 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 Command-line arguments: --no-flatten-goal
% 0.13/0.45
% 0.13/0.45 % SZS status Unsatisfiable
% 0.13/0.45
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
% 0.13/0.50
% 0.13/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------