%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP564-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 10:11:15 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 3
% Syntax : Number of clauses : 107 ( 107 unt; 0 nHn; 4 RR)
% Number of literals : 107 ( 106 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 : 280 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
cnf(c2,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c3,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(multiply(X2,X),X3) = divide(divide(X2,inverse(X)),X3),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
divide(divide(multiply(X3,X2),X),divide(X3,X)) = divide(divide(divide(X3,inverse(X2)),X),divide(X3,X)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
divide(divide(divide(A2,inverse(B2)),C),divide(A2,C)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(divide(divide(X3,inverse(X2)),X),divide(X3,X)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
divide(divide(multiply(X3,X2),X),divide(X3,X)) = X2,
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
divide(divide(multiply(X2,X3),inverse(X)),divide(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
X3 = divide(divide(multiply(X2,X3),inverse(X)),divide(X2,inverse(X))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
divide(X3,divide(multiply(X2,X3),divide(X2,inverse(X)))) = divide(divide(divide(multiply(X2,X3),inverse(X)),divide(X2,inverse(X))),divide(multiply(X2,X3),divide(X2,inverse(X)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
divide(divide(divide(multiply(X2,X3),inverse(X)),divide(X2,inverse(X))),divide(multiply(X2,X3),divide(X2,inverse(X)))) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c13,plain,
divide(X3,divide(multiply(X2,X3),divide(X2,inverse(X)))) = X,
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
divide(X,divide(multiply(X3,X),divide(X3,inverse(inverse(X2))))) = inverse(X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(X3) = divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3))))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
divide(X4,inverse(X3)) = divide(X4,divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
divide(divide(X4,inverse(X3)),X4) = divide(divide(X4,divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))),X4),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
X = divide(X3,divide(multiply(X2,X3),divide(X2,inverse(X)))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c19,plain,
divide(divide(multiply(X4,X3),divide(multiply(X2,X4),divide(X2,inverse(X)))),X) = divide(divide(multiply(X4,X3),divide(multiply(X2,X4),divide(X2,inverse(X)))),divide(X4,divide(multiply(X2,X4),divide(X2,inverse(X))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
divide(divide(multiply(X4,X3),divide(multiply(X2,X4),divide(X2,inverse(X)))),divide(X4,divide(multiply(X2,X4),divide(X2,inverse(X))))) = X3,
inference(substitution,[status(thm)],[c8]) ).
cnf(c21,plain,
divide(divide(multiply(X4,X3),divide(multiply(X2,X4),divide(X2,inverse(X)))),X) = X3,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
divide(divide(multiply(X2,X4),divide(multiply(X,X2),divide(X,inverse(inverse(X3))))),inverse(X3)) = X4,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
X4 = divide(divide(multiply(X2,X4),divide(multiply(X,X2),divide(X,inverse(inverse(X3))))),inverse(X3)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
divide(X4,divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))) = divide(divide(divide(multiply(X2,X4),divide(multiply(X,X2),divide(X,inverse(inverse(X3))))),inverse(X3)),divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
divide(divide(X4,divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))),X4) = divide(divide(divide(divide(multiply(X2,X4),divide(multiply(X,X2),divide(X,inverse(inverse(X3))))),inverse(X3)),divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))),X4),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
X2 = divide(divide(multiply(X3,X2),X),divide(X3,X)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c27,plain,
divide(divide(divide(divide(multiply(X4,X3),X2),inverse(X)),divide(X4,X2)),X3) = divide(divide(divide(divide(multiply(X4,X3),X2),inverse(X)),divide(X4,X2)),divide(divide(multiply(X4,X3),X2),divide(X4,X2))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
divide(divide(divide(divide(multiply(X4,X3),X2),inverse(X)),divide(X4,X2)),divide(divide(multiply(X4,X3),X2),divide(X4,X2))) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c29,plain,
divide(divide(divide(divide(multiply(X4,X3),X2),inverse(X)),divide(X4,X2)),X3) = X,
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
divide(divide(divide(divide(multiply(X2,X4),divide(multiply(X,X2),divide(X,inverse(inverse(X3))))),inverse(X3)),divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))),X4) = X3,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
divide(divide(X4,divide(X2,divide(multiply(X,X2),divide(X,inverse(inverse(X3)))))),X4) = X3,
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
divide(divide(X2,inverse(X)),X2) = X,
inference(transitivity,[status(thm)],[c17,c31]) ).
cnf(c33,plain,
divide(divide(X,inverse(X2)),X) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
X2 = divide(divide(X,inverse(X2)),X),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
divide(X2,divide(X,X)) = divide(divide(divide(X,inverse(X2)),X),divide(X,X)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
divide(divide(divide(X,inverse(X2)),X),divide(X,X)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c37,plain,
divide(X2,divide(X,X)) = X2,
inference(transitivity,[status(thm)],[c35,c36]) ).
cnf(c38,plain,
divide(divide(divide(X2,X2),inverse(X)),divide(X2,X2)) = divide(divide(X2,X2),inverse(X)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
divide(divide(X2,X2),inverse(X)) = divide(divide(divide(X2,X2),inverse(X)),divide(X2,X2)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
divide(divide(divide(X2,X2),inverse(X)),divide(X2,X2)) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c41,plain,
divide(divide(X2,X2),inverse(X)) = X,
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
divide(divide(X,X),inverse(X2)) = X2,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
X2 = divide(divide(X,X),inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
divide(X3,X2) = divide(X3,divide(divide(X,X),inverse(X2))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
divide(X3,divide(X3,X2)) = divide(X3,divide(X3,divide(divide(X,X),inverse(X2)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
divide(divide(X,X),inverse(X2)) = X2,
inference(substitution,[status(thm)],[c41]) ).
cnf(c47,plain,
X2 = divide(divide(X,X),inverse(X2)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
divide(X3,divide(divide(X,X),inverse(X2))) = divide(divide(divide(X,X),inverse(X3)),divide(divide(X,X),inverse(X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
divide(X3,divide(X3,divide(divide(X,X),inverse(X2)))) = divide(X3,divide(divide(divide(X,X),inverse(X3)),divide(divide(X,X),inverse(X2)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
divide(divide(divide(X2,inverse(X3)),inverse(X)),divide(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c51,plain,
X3 = divide(divide(divide(X2,inverse(X3)),inverse(X)),divide(X2,inverse(X))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
divide(X3,divide(divide(X2,inverse(X3)),divide(X2,inverse(X)))) = divide(divide(divide(divide(X2,inverse(X3)),inverse(X)),divide(X2,inverse(X))),divide(divide(X2,inverse(X3)),divide(X2,inverse(X)))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
divide(divide(divide(divide(X2,inverse(X3)),inverse(X)),divide(X2,inverse(X))),divide(divide(X2,inverse(X3)),divide(X2,inverse(X)))) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c54,plain,
divide(X3,divide(divide(X2,inverse(X3)),divide(X2,inverse(X)))) = X,
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
divide(X3,divide(divide(divide(X,X),inverse(X3)),divide(divide(X,X),inverse(X2)))) = X2,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
divide(X3,divide(X3,divide(divide(X,X),inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c49,c55]) ).
cnf(c57,plain,
divide(X2,divide(X2,X)) = X,
inference(transitivity,[status(thm)],[c45,c56]) ).
cnf(c58,plain,
divide(X,divide(X,multiply(X2,X))) = multiply(X2,X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X2,X) = divide(X,divide(X,multiply(X2,X))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2))) = multiply(X2,X3),
inference(substitution,[status(thm)],[c37]) ).
cnf(c61,plain,
multiply(X2,X3) = divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
divide(X3,multiply(X2,X3)) = divide(X3,divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2)))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
divide(divide(multiply(X3,X2),inverse(X)),multiply(X3,X)) = divide(divide(multiply(X3,X2),inverse(X)),divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
divide(divide(multiply(X3,X2),inverse(X)),divide(X3,inverse(X))) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c66,plain,
divide(divide(multiply(X3,X2),inverse(X)),multiply(X3,X)) = X2,
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
divide(divide(multiply(X2,X3),inverse(X)),multiply(X2,X)) = X3,
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
X3 = divide(divide(multiply(X2,X3),inverse(X)),multiply(X2,X)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
divide(X3,divide(multiply(X2,X3),multiply(X2,X))) = divide(divide(divide(multiply(X2,X3),inverse(X)),multiply(X2,X)),divide(multiply(X2,X3),multiply(X2,X))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
divide(divide(divide(multiply(X2,X3),inverse(X)),multiply(X2,X)),divide(multiply(X2,X3),multiply(X2,X))) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c71,plain,
divide(X3,divide(multiply(X2,X3),multiply(X2,X))) = X,
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
X = divide(X3,divide(multiply(X2,X3),multiply(X2,X))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
divide(divide(multiply(X4,X3),divide(multiply(X2,X4),multiply(X2,X))),X) = divide(divide(multiply(X4,X3),divide(multiply(X2,X4),multiply(X2,X))),divide(X4,divide(multiply(X2,X4),multiply(X2,X)))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
divide(divide(multiply(X4,X3),divide(multiply(X2,X4),multiply(X2,X))),divide(X4,divide(multiply(X2,X4),multiply(X2,X)))) = X3,
inference(substitution,[status(thm)],[c8]) ).
cnf(c75,plain,
divide(divide(multiply(X4,X3),divide(multiply(X2,X4),multiply(X2,X))),X) = X3,
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
divide(divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2))),X2) = X3,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
X3 = divide(divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2))),X2),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
divide(X3,divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2)))) = divide(divide(divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2))),X2),divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
divide(inverse(inverse(X2)),divide(X,X)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c80,plain,
inverse(inverse(X2)) = divide(inverse(inverse(X2)),divide(X,X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
X = divide(divide(X2,X2),inverse(X)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c82,plain,
divide(divide(X2,X2),X) = divide(divide(X2,X2),divide(divide(X2,X2),inverse(X))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
divide(divide(X2,X2),divide(divide(X2,X2),inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c84,plain,
divide(divide(X2,X2),X) = inverse(X),
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
divide(divide(X,X),inverse(X2)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
inverse(inverse(X2)) = divide(divide(X,X),inverse(X2)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
divide(inverse(inverse(X2)),divide(X,X)) = divide(divide(divide(X,X),inverse(X2)),divide(X,X)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
divide(divide(divide(X,X),inverse(X2)),divide(X,X)) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c89,plain,
divide(inverse(inverse(X2)),divide(X,X)) = X2,
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c80,c89]) ).
cnf(c91,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
divide(X2,X) = divide(X2,inverse(inverse(X))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
divide(divide(X2,X),X2) = divide(divide(X2,inverse(inverse(X))),X2),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
divide(divide(X2,inverse(inverse(X))),X2) = inverse(X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c95,plain,
divide(divide(X2,X),X2) = inverse(X),
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
divide(divide(divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2))),X2),divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2)))) = inverse(X2),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
divide(X3,divide(multiply(X2,X3),divide(multiply(X,X2),multiply(X,X2)))) = inverse(X2),
inference(transitivity,[status(thm)],[c78,c96]) ).
cnf(c98,plain,
divide(X2,multiply(X,X2)) = inverse(X),
inference(transitivity,[status(thm)],[c62,c97]) ).
cnf(c99,plain,
divide(X,multiply(X2,X)) = inverse(X2),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
divide(X,divide(X,multiply(X2,X))) = divide(X,inverse(X2)),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(X,X2) = divide(X,inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c102,plain,
divide(X,inverse(X2)) = multiply(X,X2),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
divide(X,divide(X,multiply(X2,X))) = multiply(X,X2),
inference(transitivity,[status(thm)],[c100,c102]) ).
cnf(c104,plain,
multiply(X2,X) = multiply(X,X2),
inference(transitivity,[status(thm)],[c59,c103]) ).
cnf(c105,plain,
multiply(b,a) = multiply(a,b),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(a,b) = multiply(b,a),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
$false,
inference(resolution,[status(thm)],[c1,c106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP564-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 10:12:16 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.12/0.44
% 0.12/0.44 % SZS status Unsatisfiable
% 0.12/0.44
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.47
% 0.12/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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