%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP558-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:11:14 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 5 RR)
% Number of literals : 64 ( 63 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 153 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c2,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c3,plain,
multiply(X3,divide(divide(X2,X),divide(X3,X))) = divide(X3,inverse(divide(divide(X2,X),divide(X3,X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
divide(A2,inverse(divide(divide(B2,C),divide(A2,C)))) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c5,plain,
divide(X3,inverse(divide(divide(X2,X),divide(X3,X)))) = X2,
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X3,divide(divide(X2,X),divide(X3,X))) = X2,
inference(transitivity,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
X2 = multiply(X3,divide(divide(X2,X),divide(X3,X))),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
divide(X2,X2) = divide(X2,multiply(X3,divide(divide(X2,X),divide(X3,X)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X3,divide(X2,X2)) = multiply(X3,divide(X2,multiply(X3,divide(divide(X2,X),divide(X3,X))))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X3,divide(divide(X2,X),divide(X3,X))) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c11,plain,
X3 = multiply(X,divide(divide(X3,X2),divide(X,X2))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
divide(X3,multiply(X4,divide(divide(X3,X2),divide(X,X2)))) = divide(multiply(X,divide(divide(X3,X2),divide(X,X2))),multiply(X4,divide(divide(X3,X2),divide(X,X2)))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(X4,divide(X3,multiply(X4,divide(divide(X3,X2),divide(X,X2))))) = multiply(X4,divide(multiply(X,divide(divide(X3,X2),divide(X,X2))),multiply(X4,divide(divide(X3,X2),divide(X,X2))))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
divide(multiply(X2,X),multiply(X3,X)) = divide(multiply(X2,X),divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X3,divide(multiply(X2,X),multiply(X3,X))) = multiply(X3,divide(multiply(X2,X),divide(X3,inverse(X)))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
divide(multiply(X2,X),divide(X3,inverse(X))) = divide(divide(X2,inverse(X)),divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X3,divide(multiply(X2,X),divide(X3,inverse(X)))) = multiply(X3,divide(divide(X2,inverse(X)),divide(X3,inverse(X)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X3,divide(divide(X2,inverse(X)),divide(X3,inverse(X)))) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c21,plain,
multiply(X3,divide(multiply(X2,X),divide(X3,inverse(X)))) = X2,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
multiply(X3,divide(multiply(X2,X),multiply(X3,X))) = X2,
inference(transitivity,[status(thm)],[c16,c21]) ).
cnf(c23,plain,
multiply(X4,divide(multiply(X,divide(divide(X3,X2),divide(X,X2))),multiply(X4,divide(divide(X3,X2),divide(X,X2))))) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X4,divide(X3,multiply(X4,divide(divide(X3,X2),divide(X,X2))))) = X,
inference(transitivity,[status(thm)],[c13,c23]) ).
cnf(c25,plain,
multiply(X3,divide(X2,multiply(X3,divide(divide(X2,X),divide(X3,X))))) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X2,divide(X,X)) = X2,
inference(transitivity,[status(thm)],[c9,c25]) ).
cnf(c27,plain,
X2 = multiply(X2,divide(X,X)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
divide(X2,X3) = divide(X2,multiply(X3,divide(X,X))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X3,divide(X2,X3)) = multiply(X3,divide(X2,multiply(X3,divide(X,X)))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
X2 = multiply(X2,divide(X,X)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c31,plain,
divide(X2,multiply(X3,divide(X,X))) = divide(multiply(X2,divide(X,X)),multiply(X3,divide(X,X))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X3,divide(X2,multiply(X3,divide(X,X)))) = multiply(X3,divide(multiply(X2,divide(X,X)),multiply(X3,divide(X,X)))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X3,divide(multiply(X2,divide(X,X)),multiply(X3,divide(X,X)))) = X2,
inference(substitution,[status(thm)],[c22]) ).
cnf(c34,plain,
multiply(X3,divide(X2,multiply(X3,divide(X,X)))) = X2,
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
multiply(X2,divide(X,X2)) = X,
inference(transitivity,[status(thm)],[c29,c34]) ).
cnf(c36,plain,
multiply(X,divide(multiply(X2,X),X)) = multiply(X2,X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(X2,X) = multiply(X,divide(multiply(X2,X),X)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X,divide(X2,X2)) = X,
inference(substitution,[status(thm)],[c26]) ).
cnf(c39,plain,
X = multiply(X,divide(X2,X2)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(inverse(divide(X2,X2)),X) = multiply(inverse(divide(X2,X2)),multiply(X,divide(X2,X2))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(X,X2) = divide(X,inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c42,plain,
multiply(inverse(X2),multiply(X,X2)) = multiply(inverse(X2),divide(X,inverse(X2))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(inverse(X2),divide(X,inverse(X2))) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c44,plain,
multiply(inverse(X2),multiply(X,X2)) = X,
inference(transitivity,[status(thm)],[c42,c43]) ).
cnf(c45,plain,
multiply(inverse(divide(X2,X2)),multiply(X,divide(X2,X2))) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(inverse(divide(X2,X2)),X) = X,
inference(transitivity,[status(thm)],[c40,c45]) ).
cnf(c47,plain,
multiply(inverse(divide(X,X)),X2) = X2,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
X2 = multiply(inverse(divide(X,X)),X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
divide(multiply(X3,X2),X2) = divide(multiply(X3,X2),multiply(inverse(divide(X,X)),X2)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(divide(X,X)),divide(multiply(X3,X2),multiply(inverse(divide(X,X)),X2))) = divide(multiply(X3,X2),multiply(inverse(divide(X,X)),X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c51,plain,
divide(multiply(X3,X2),multiply(inverse(divide(X,X)),X2)) = multiply(inverse(divide(X,X)),divide(multiply(X3,X2),multiply(inverse(divide(X,X)),X2))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(inverse(divide(X,X)),divide(multiply(X3,X2),multiply(inverse(divide(X,X)),X2))) = X3,
inference(substitution,[status(thm)],[c22]) ).
cnf(c53,plain,
divide(multiply(X3,X2),multiply(inverse(divide(X,X)),X2)) = X3,
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
divide(multiply(X2,X),X) = X2,
inference(transitivity,[status(thm)],[c49,c53]) ).
cnf(c55,plain,
multiply(X,divide(multiply(X2,X),X)) = multiply(X,X2),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X2,X) = multiply(X,X2),
inference(transitivity,[status(thm)],[c37,c55]) ).
cnf(c57,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(inverse(b2),b2)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
multiply(X2,multiply(inverse(X),X)) = multiply(X2,divide(inverse(X),inverse(X))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(X2,divide(inverse(X),inverse(X))) = X2,
inference(substitution,[status(thm)],[c26]) ).
cnf(c61,plain,
multiply(X2,multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
multiply(a2,multiply(inverse(b2),b2)) = a2,
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[c57,c62]) ).
cnf(c64,plain,
$false,
inference(resolution,[status(thm)],[c1,c63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP558-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:07:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 Command-line arguments: --no-flatten-goal
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46
% 0.19/0.47 % SZS output start CNFRefutation
% See solution above
% 0.19/0.49
% 0.19/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------