%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 10:11:18 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 3 RR)
% Number of literals : 91 ( 90 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c3,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(multiply(X2,X),X3) = multiply(inverse(double_divide(X,X2)),X3),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
double_divide(multiply(multiply(X3,X2),X),inverse(X)) = double_divide(multiply(inverse(double_divide(X2,X3)),X),inverse(X)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(multiply(X3,multiply(inverse(X2),double_divide(X,X3))),X) = inverse(double_divide(X,multiply(X3,multiply(inverse(X2),double_divide(X,X3))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
multiply(inverse(X),double_divide(X3,X2)) = inverse(double_divide(double_divide(X3,X2),inverse(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
multiply(X2,multiply(inverse(X),double_divide(X3,X2))) = multiply(X2,inverse(double_divide(double_divide(X3,X2),inverse(X)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
double_divide(X3,multiply(X2,multiply(inverse(X),double_divide(X3,X2)))) = double_divide(X3,multiply(X2,inverse(double_divide(double_divide(X3,X2),inverse(X))))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X2,inverse(double_divide(double_divide(X3,X2),inverse(X)))) = inverse(double_divide(inverse(double_divide(double_divide(X3,X2),inverse(X))),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
double_divide(X3,multiply(X2,inverse(double_divide(double_divide(X3,X2),inverse(X))))) = double_divide(X3,inverse(double_divide(inverse(double_divide(double_divide(X3,X2),inverse(X))),X2))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
double_divide(A2,inverse(double_divide(inverse(double_divide(double_divide(A2,B2),inverse(C))),B2))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c13,plain,
double_divide(X3,inverse(double_divide(inverse(double_divide(double_divide(X3,X2),inverse(X))),X2))) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
double_divide(X3,multiply(X2,inverse(double_divide(double_divide(X3,X2),inverse(X))))) = X,
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
double_divide(X3,multiply(X2,multiply(inverse(X),double_divide(X3,X2)))) = X,
inference(transitivity,[status(thm)],[c9,c14]) ).
cnf(c16,plain,
double_divide(X,multiply(X3,multiply(inverse(X2),double_divide(X,X3)))) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
inverse(double_divide(X,multiply(X3,multiply(inverse(X2),double_divide(X,X3))))) = inverse(X2),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(multiply(X3,multiply(inverse(X2),double_divide(X,X3))),X) = inverse(X2),
inference(transitivity,[status(thm)],[c6,c17]) ).
cnf(c19,plain,
multiply(multiply(X,multiply(inverse(X2),double_divide(multiply(inverse(X3),X2),X))),multiply(inverse(X3),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(X2) = multiply(multiply(X,multiply(inverse(X2),double_divide(multiply(inverse(X3),X2),X))),multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
double_divide(multiply(inverse(X3),X2),inverse(X2)) = double_divide(multiply(inverse(X3),X2),multiply(multiply(X,multiply(inverse(X2),double_divide(multiply(inverse(X3),X2),X))),multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
X = double_divide(X3,multiply(X2,multiply(inverse(X),double_divide(X3,X2)))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c23,plain,
multiply(inverse(X4),X) = multiply(inverse(X4),double_divide(X3,multiply(X2,multiply(inverse(X),double_divide(X3,X2))))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(X3,multiply(inverse(X2),double_divide(X4,X3))),multiply(inverse(X),X2)) = multiply(multiply(X3,multiply(inverse(X2),double_divide(X4,X3))),multiply(inverse(X),double_divide(X4,multiply(X3,multiply(inverse(X2),double_divide(X4,X3)))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
double_divide(X4,multiply(multiply(X3,multiply(inverse(X2),double_divide(X4,X3))),multiply(inverse(X),X2))) = double_divide(X4,multiply(multiply(X3,multiply(inverse(X2),double_divide(X4,X3))),multiply(inverse(X),double_divide(X4,multiply(X3,multiply(inverse(X2),double_divide(X4,X3))))))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
double_divide(X4,multiply(multiply(X3,multiply(inverse(X2),double_divide(X4,X3))),multiply(inverse(X),double_divide(X4,multiply(X3,multiply(inverse(X2),double_divide(X4,X3))))))) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c27,plain,
double_divide(X4,multiply(multiply(X3,multiply(inverse(X2),double_divide(X4,X3))),multiply(inverse(X),X2))) = X,
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
double_divide(multiply(inverse(X3),X2),multiply(multiply(X,multiply(inverse(X2),double_divide(multiply(inverse(X3),X2),X))),multiply(inverse(X3),X2))) = X3,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
double_divide(multiply(inverse(X2),X),inverse(X)) = X2,
inference(transitivity,[status(thm)],[c21,c28]) ).
cnf(c30,plain,
double_divide(multiply(inverse(double_divide(X2,X3)),X),inverse(X)) = double_divide(X2,X3),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
double_divide(multiply(multiply(X3,X2),X),inverse(X)) = double_divide(X2,X3),
inference(transitivity,[status(thm)],[c5,c30]) ).
cnf(c32,plain,
double_divide(multiply(multiply(X,multiply(multiply(inverse(X3),X3),double_divide(X2,X))),X2),inverse(X2)) = double_divide(multiply(multiply(inverse(X3),X3),double_divide(X2,X)),X),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
double_divide(multiply(multiply(inverse(X3),X3),double_divide(X2,X)),X) = double_divide(multiply(multiply(X,multiply(multiply(inverse(X3),X3),double_divide(X2,X))),X2),inverse(X2)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(multiply(X4,multiply(multiply(X3,X2),double_divide(X,X4))),X) = inverse(double_divide(X,multiply(X4,multiply(multiply(X3,X2),double_divide(X,X4))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
multiply(multiply(X2,X),double_divide(X4,X3)) = multiply(inverse(double_divide(X,X2)),double_divide(X4,X3)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(X3,multiply(multiply(X2,X),double_divide(X4,X3))) = multiply(X3,multiply(inverse(double_divide(X,X2)),double_divide(X4,X3))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
double_divide(X4,multiply(X3,multiply(multiply(X2,X),double_divide(X4,X3)))) = double_divide(X4,multiply(X3,multiply(inverse(double_divide(X,X2)),double_divide(X4,X3)))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
double_divide(X4,multiply(X3,multiply(inverse(double_divide(X,X2)),double_divide(X4,X3)))) = double_divide(X,X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c40,plain,
double_divide(X4,multiply(X3,multiply(multiply(X2,X),double_divide(X4,X3)))) = double_divide(X,X2),
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
double_divide(X,multiply(X4,multiply(multiply(X3,X2),double_divide(X,X4)))) = double_divide(X2,X3),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
inverse(double_divide(X,multiply(X4,multiply(multiply(X3,X2),double_divide(X,X4))))) = inverse(double_divide(X2,X3)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
inverse(double_divide(X,multiply(X4,multiply(multiply(X3,X2),double_divide(X,X4))))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
multiply(multiply(X4,multiply(multiply(X3,X2),double_divide(X,X4))),X) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c34,c45]) ).
cnf(c47,plain,
multiply(multiply(X,multiply(multiply(inverse(X3),X3),double_divide(X2,X))),X2) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
double_divide(multiply(multiply(X,multiply(multiply(inverse(X3),X3),double_divide(X2,X))),X2),inverse(X2)) = double_divide(multiply(inverse(X3),X3),inverse(X2)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(inverse(X2),multiply(inverse(X),X2)) = inverse(double_divide(multiply(inverse(X),X2),inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
double_divide(multiply(inverse(X),X2),inverse(X2)) = X,
inference(substitution,[status(thm)],[c29]) ).
cnf(c51,plain,
inverse(double_divide(multiply(inverse(X),X2),inverse(X2))) = inverse(X),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(inverse(X2),multiply(inverse(X),X2)) = inverse(X),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
inverse(X) = multiply(inverse(X2),multiply(inverse(X),X2)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
double_divide(multiply(inverse(X2),X2),inverse(X)) = double_divide(multiply(inverse(X2),X2),multiply(inverse(X2),multiply(inverse(X),X2))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
X2 = double_divide(multiply(inverse(X2),X),inverse(X)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c56,plain,
multiply(inverse(X),X3) = multiply(inverse(X),double_divide(multiply(inverse(X3),X2),inverse(X2))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(X2),multiply(inverse(X),X3)) = multiply(inverse(X2),multiply(inverse(X),double_divide(multiply(inverse(X3),X2),inverse(X2)))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
double_divide(multiply(inverse(X3),X2),multiply(inverse(X2),multiply(inverse(X),X3))) = double_divide(multiply(inverse(X3),X2),multiply(inverse(X2),multiply(inverse(X),double_divide(multiply(inverse(X3),X2),inverse(X2))))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
double_divide(multiply(inverse(X3),X2),multiply(inverse(X2),multiply(inverse(X),double_divide(multiply(inverse(X3),X2),inverse(X2))))) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c60,plain,
double_divide(multiply(inverse(X3),X2),multiply(inverse(X2),multiply(inverse(X),X3))) = X,
inference(transitivity,[status(thm)],[c58,c59]) ).
cnf(c61,plain,
double_divide(multiply(inverse(X2),X2),multiply(inverse(X2),multiply(inverse(X),X2))) = X,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
double_divide(multiply(inverse(X2),X2),inverse(X)) = X,
inference(transitivity,[status(thm)],[c54,c61]) ).
cnf(c63,plain,
double_divide(multiply(multiply(X,multiply(multiply(inverse(X3),X3),double_divide(X2,X))),X2),inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c48,c62]) ).
cnf(c64,plain,
double_divide(multiply(multiply(inverse(X3),X3),double_divide(X2,X)),X) = X2,
inference(transitivity,[status(thm)],[c33,c63]) ).
cnf(c65,plain,
double_divide(multiply(multiply(inverse(X),X),double_divide(multiply(inverse(X2),X2),multiply(inverse(X2),multiply(inverse(X3),X2)))),multiply(inverse(X2),multiply(inverse(X3),X2))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(inverse(X2),X2) = double_divide(multiply(multiply(inverse(X),X),double_divide(multiply(inverse(X2),X2),multiply(inverse(X2),multiply(inverse(X3),X2)))),multiply(inverse(X2),multiply(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
double_divide(multiply(inverse(X),X),multiply(inverse(X),multiply(inverse(X2),X))) = X2,
inference(substitution,[status(thm)],[c60]) ).
cnf(c68,plain,
multiply(multiply(inverse(X),X),double_divide(multiply(inverse(X2),X2),multiply(inverse(X2),multiply(inverse(X3),X2)))) = multiply(multiply(inverse(X),X),X3),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
double_divide(multiply(multiply(inverse(X),X),double_divide(multiply(inverse(X2),X2),multiply(inverse(X2),multiply(inverse(X3),X2)))),multiply(inverse(X2),multiply(inverse(X3),X2))) = double_divide(multiply(multiply(inverse(X),X),X3),multiply(inverse(X2),multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(inverse(X),multiply(inverse(X2),X)) = inverse(X2),
inference(substitution,[status(thm)],[c52]) ).
cnf(c71,plain,
double_divide(multiply(multiply(inverse(X),X),X3),multiply(inverse(X2),multiply(inverse(X3),X2))) = double_divide(multiply(multiply(inverse(X),X),X3),inverse(X3)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
double_divide(multiply(multiply(inverse(X),multiply(multiply(inverse(X3),X3),X2)),multiply(inverse(X2),X)),inverse(multiply(inverse(X2),X))) = double_divide(multiply(multiply(inverse(X3),X3),X2),inverse(X)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c73,plain,
double_divide(multiply(multiply(inverse(X3),X3),X2),inverse(X)) = double_divide(multiply(multiply(inverse(X),multiply(multiply(inverse(X3),X3),X2)),multiply(inverse(X2),X)),inverse(multiply(inverse(X2),X))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
double_divide(multiply(inverse(X),X2),inverse(X2)) = X,
inference(substitution,[status(thm)],[c29]) ).
cnf(c75,plain,
X = double_divide(multiply(inverse(X),X2),inverse(X2)),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(multiply(X3,X2),X) = multiply(multiply(X3,X2),double_divide(multiply(inverse(X),X4),inverse(X4))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(inverse(X4),multiply(multiply(X3,X2),X)) = multiply(inverse(X4),multiply(multiply(X3,X2),double_divide(multiply(inverse(X),X4),inverse(X4)))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(multiply(inverse(X4),multiply(multiply(X3,X2),X)),multiply(inverse(X),X4)) = multiply(multiply(inverse(X4),multiply(multiply(X3,X2),double_divide(multiply(inverse(X),X4),inverse(X4)))),multiply(inverse(X),X4)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(multiply(inverse(X4),multiply(multiply(X3,X2),double_divide(multiply(inverse(X),X4),inverse(X4)))),multiply(inverse(X),X4)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c80,plain,
multiply(multiply(inverse(X4),multiply(multiply(X3,X2),X)),multiply(inverse(X),X4)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
multiply(multiply(inverse(X),multiply(multiply(inverse(X3),X3),X2)),multiply(inverse(X2),X)) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
double_divide(multiply(multiply(inverse(X),multiply(multiply(inverse(X3),X3),X2)),multiply(inverse(X2),X)),inverse(multiply(inverse(X2),X))) = double_divide(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),X))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
double_divide(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),X))) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c62]) ).
cnf(c84,plain,
double_divide(multiply(multiply(inverse(X),multiply(multiply(inverse(X3),X3),X2)),multiply(inverse(X2),X)),inverse(multiply(inverse(X2),X))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
double_divide(multiply(multiply(inverse(X3),X3),X2),inverse(X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c73,c84]) ).
cnf(c86,plain,
double_divide(multiply(multiply(inverse(X),X),X2),inverse(X2)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
double_divide(multiply(multiply(inverse(X),X),X3),multiply(inverse(X2),multiply(inverse(X3),X2))) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c71,c86]) ).
cnf(c88,plain,
double_divide(multiply(multiply(inverse(X),X),double_divide(multiply(inverse(X2),X2),multiply(inverse(X2),multiply(inverse(X3),X2)))),multiply(inverse(X2),multiply(inverse(X3),X2))) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c69,c87]) ).
cnf(c89,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c66,c88]) ).
cnf(c90,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
$false,
inference(resolution,[status(thm)],[c1,c90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.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 10:07:25 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.46 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
% 0.13/0.46
% 0.13/0.46 % SZS status Unsatisfiable
% 0.13/0.46
% 0.13/0.47 % SZS output start CNFRefutation
% See solution above
% 0.55/0.52
% 0.55/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------