%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP467-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 10:10:33 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of clauses : 78 ( 78 unt; 0 nHn; 3 RR)
% Number of literals : 78 ( 77 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; 2 con; 0-2 aty)
% Number of variables : 254 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c2,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c3,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,plain,
divide(multiply(inverse(X2),X2),divide(X,divide(divide(X4,divide(X3,X)),inverse(X3)))) = divide(divide(inverse(X2),inverse(X2)),divide(X,divide(divide(X4,divide(X3,X)),inverse(X3)))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
divide(divide(A2,A2),divide(B2,divide(divide(C,divide(D,B2)),inverse(D)))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(divide(inverse(X4),inverse(X4)),divide(X3,divide(divide(X2,divide(X,X3)),inverse(X)))) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
divide(multiply(inverse(X4),X4),divide(X3,divide(divide(X2,divide(X,X3)),inverse(X)))) = X2,
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
divide(multiply(inverse(X2),X2),divide(divide(divide(X,multiply(X5,X4)),inverse(X5)),divide(divide(divide(X3,X3),divide(inverse(X4),divide(divide(X,multiply(X5,X4)),inverse(X5)))),inverse(inverse(X4))))) = divide(X3,X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
divide(X5,X5) = divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(divide(divide(X5,X5),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X))))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(X,X2) = divide(X,inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
divide(X2,multiply(X,X3)) = divide(X2,divide(X,inverse(X3))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
divide(divide(X2,multiply(X,X3)),inverse(X)) = divide(divide(X2,divide(X,inverse(X3))),inverse(X)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
divide(inverse(X3),divide(divide(X2,multiply(X,X3)),inverse(X))) = divide(inverse(X3),divide(divide(X2,divide(X,inverse(X3))),inverse(X))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
divide(divide(X4,X4),divide(inverse(X3),divide(divide(X2,multiply(X,X3)),inverse(X)))) = divide(divide(X4,X4),divide(inverse(X3),divide(divide(X2,divide(X,inverse(X3))),inverse(X)))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
divide(divide(X4,X4),divide(inverse(X3),divide(divide(X2,divide(X,inverse(X3))),inverse(X)))) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c17,plain,
divide(divide(X4,X4),divide(inverse(X3),divide(divide(X2,multiply(X,X3)),inverse(X)))) = X2,
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
divide(divide(X4,X4),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))) = X3,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
divide(divide(divide(X4,X4),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X))) = divide(X3,inverse(inverse(X))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(divide(divide(X4,X4),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X)))) = divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(X3,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(divide(divide(X5,X5),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X))))) = divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(X3,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
divide(divide(X4,X4),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))) = X3,
inference(substitution,[status(thm)],[c17]) ).
cnf(c23,plain,
X3 = divide(divide(X4,X4),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
divide(X3,inverse(inverse(X))) = divide(divide(divide(X4,X4),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(X3,inverse(inverse(X)))) = divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(divide(divide(X4,X4),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X)))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(X3,inverse(inverse(X))))) = divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(divide(divide(X5,X5),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X))))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(divide(divide(X5,X5),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X))))) = divide(X5,X5),
inference(substitution,[status(thm)],[c8]) ).
cnf(c28,plain,
divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(X3,inverse(inverse(X))))) = divide(X5,X5),
inference(transitivity,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
divide(multiply(inverse(X4),X4),divide(divide(divide(X3,multiply(X2,X)),inverse(X2)),divide(divide(divide(X5,X5),divide(inverse(X),divide(divide(X3,multiply(X2,X)),inverse(X2)))),inverse(inverse(X))))) = divide(X6,X6),
inference(transitivity,[status(thm)],[c21,c28]) ).
cnf(c30,plain,
divide(X,X) = divide(X2,X2),
inference(transitivity,[status(thm)],[c10,c29]) ).
cnf(c31,plain,
divide(X2,X2) = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
divide(inverse(X),inverse(X)) = divide(X2,X2),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(inverse(X),X) = divide(X2,X2),
inference(transitivity,[status(thm)],[c3,c32]) ).
cnf(c34,plain,
multiply(inverse(X2),X2) = divide(X,X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
divide(multiply(inverse(X5),X5),divide(inverse(X4),divide(multiply(inverse(X3),X3),inverse(X2)))) = divide(divide(X,X),divide(inverse(X4),divide(multiply(inverse(X3),X3),inverse(X2)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(inverse(X2),X2) = divide(multiply(X,X3),multiply(X,X3)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c37,plain,
divide(multiply(inverse(X2),X2),inverse(X)) = divide(divide(multiply(X,X3),multiply(X,X3)),inverse(X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
divide(inverse(X3),divide(multiply(inverse(X2),X2),inverse(X))) = divide(inverse(X3),divide(divide(multiply(X,X3),multiply(X,X3)),inverse(X))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
divide(divide(X,X),divide(inverse(X4),divide(multiply(inverse(X3),X3),inverse(X2)))) = divide(divide(X,X),divide(inverse(X4),divide(divide(multiply(X2,X4),multiply(X2,X4)),inverse(X2)))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
divide(divide(X,X),divide(inverse(X3),divide(divide(multiply(X2,X3),multiply(X2,X3)),inverse(X2)))) = multiply(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c41,plain,
divide(divide(X,X),divide(inverse(X4),divide(multiply(inverse(X3),X3),inverse(X2)))) = multiply(X2,X4),
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
divide(multiply(inverse(X4),X4),divide(inverse(X3),divide(multiply(inverse(X2),X2),inverse(X)))) = multiply(X,X3),
inference(transitivity,[status(thm)],[c35,c41]) ).
cnf(c43,plain,
divide(multiply(inverse(X2),X2),divide(inverse(X3),divide(multiply(inverse(X),X),inverse(multiply(inverse(X4),X4))))) = multiply(multiply(inverse(X4),X4),X3),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(multiply(inverse(X4),X4),X3) = divide(multiply(inverse(X2),X2),divide(inverse(X3),divide(multiply(inverse(X),X),inverse(multiply(inverse(X4),X4))))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(X2),X2) = divide(X,X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c46,plain,
divide(multiply(inverse(X3),X3),divide(inverse(X4),divide(multiply(inverse(X2),X2),inverse(multiply(inverse(X5),X5))))) = divide(divide(X,X),divide(inverse(X4),divide(multiply(inverse(X2),X2),inverse(multiply(inverse(X5),X5))))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(multiply(inverse(X),X),X2) = divide(multiply(inverse(X),X),inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c48,plain,
divide(X2,multiply(multiply(inverse(X),X),X2)) = divide(X2,divide(multiply(inverse(X),X),inverse(X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(inverse(X2),X2) = divide(X,X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c50,plain,
divide(multiply(inverse(X5),X5),divide(X4,divide(multiply(inverse(X3),X3),inverse(X2)))) = divide(divide(X,X),divide(X4,divide(multiply(inverse(X3),X3),inverse(X2)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(inverse(X2),X2) = divide(divide(X,X3),divide(X,X3)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c52,plain,
divide(multiply(inverse(X2),X2),inverse(X)) = divide(divide(divide(X,X3),divide(X,X3)),inverse(X)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
divide(X3,divide(multiply(inverse(X2),X2),inverse(X))) = divide(X3,divide(divide(divide(X,X3),divide(X,X3)),inverse(X))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
divide(divide(X,X),divide(X4,divide(multiply(inverse(X3),X3),inverse(X2)))) = divide(divide(X,X),divide(X4,divide(divide(divide(X2,X4),divide(X2,X4)),inverse(X2)))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
divide(divide(X,X),divide(X3,divide(divide(divide(X2,X3),divide(X2,X3)),inverse(X2)))) = divide(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c56,plain,
divide(divide(X,X),divide(X4,divide(multiply(inverse(X3),X3),inverse(X2)))) = divide(X2,X4),
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
divide(multiply(inverse(X4),X4),divide(X3,divide(multiply(inverse(X2),X2),inverse(X)))) = divide(X,X3),
inference(transitivity,[status(thm)],[c50,c56]) ).
cnf(c58,plain,
divide(multiply(inverse(X),X),divide(divide(multiply(inverse(X2),X2),inverse(X3)),divide(multiply(inverse(X2),X2),inverse(X3)))) = divide(X3,divide(multiply(inverse(X2),X2),inverse(X3))),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
divide(X3,divide(multiply(inverse(X2),X2),inverse(X3))) = divide(multiply(inverse(X),X),divide(divide(multiply(inverse(X2),X2),inverse(X3)),divide(multiply(inverse(X2),X2),inverse(X3)))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(inverse(X),X) = divide(divide(multiply(inverse(X2),X2),inverse(X3)),divide(multiply(inverse(X2),X2),inverse(X3))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c61,plain,
divide(divide(multiply(inverse(X2),X2),inverse(X3)),divide(multiply(inverse(X2),X2),inverse(X3))) = multiply(inverse(X),X),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
divide(multiply(inverse(X),X),divide(divide(multiply(inverse(X2),X2),inverse(X3)),divide(multiply(inverse(X2),X2),inverse(X3)))) = divide(multiply(inverse(X),X),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(inverse(X2),X2) = divide(multiply(inverse(X),X),multiply(inverse(X),X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c64,plain,
divide(multiply(inverse(X),X),multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
divide(multiply(inverse(X),X),divide(divide(multiply(inverse(X3),X3),inverse(X4)),divide(multiply(inverse(X3),X3),inverse(X4)))) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c62,c64]) ).
cnf(c66,plain,
divide(X3,divide(multiply(inverse(X2),X2),inverse(X3))) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
divide(X3,multiply(multiply(inverse(X2),X2),X3)) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c48,c66]) ).
cnf(c68,plain,
divide(X2,multiply(multiply(inverse(X3),X3),X2)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(inverse(X),X) = divide(X2,multiply(multiply(inverse(X3),X3),X2)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
divide(multiply(inverse(X),X),inverse(multiply(inverse(X3),X3))) = divide(divide(X2,multiply(multiply(inverse(X3),X3),X2)),inverse(multiply(inverse(X3),X3))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
divide(inverse(X2),divide(multiply(inverse(X),X),inverse(multiply(inverse(X3),X3)))) = divide(inverse(X2),divide(divide(X2,multiply(multiply(inverse(X3),X3),X2)),inverse(multiply(inverse(X3),X3)))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
divide(divide(X,X),divide(inverse(X3),divide(multiply(inverse(X2),X2),inverse(multiply(inverse(X4),X4))))) = divide(divide(X,X),divide(inverse(X3),divide(divide(X3,multiply(multiply(inverse(X4),X4),X3)),inverse(multiply(inverse(X4),X4))))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
divide(divide(X,X),divide(inverse(X2),divide(divide(X2,multiply(multiply(inverse(X3),X3),X2)),inverse(multiply(inverse(X3),X3))))) = X2,
inference(substitution,[status(thm)],[c17]) ).
cnf(c74,plain,
divide(divide(X,X),divide(inverse(X3),divide(multiply(inverse(X2),X2),inverse(multiply(inverse(X4),X4))))) = X3,
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
divide(multiply(inverse(X2),X2),divide(inverse(X3),divide(multiply(inverse(X),X),inverse(multiply(inverse(X4),X4))))) = X3,
inference(transitivity,[status(thm)],[c46,c74]) ).
cnf(c76,plain,
multiply(multiply(inverse(X2),X2),X) = X,
inference(transitivity,[status(thm)],[c44,c75]) ).
cnf(c77,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
$false,
inference(resolution,[status(thm)],[c1,c77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP467-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 10:06:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.43 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
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation
% See solution above
% 0.09/0.47
% 0.09/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------