%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP561-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 10:11:14 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of clauses : 101 ( 101 unt; 0 nHn; 3 RR)
% Number of literals : 101 ( 100 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 : 270 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
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),X2) = divide(divide(X2,inverse(X)),X2),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
divide(multiply(X2,X),X3) = divide(divide(X2,inverse(X)),X3),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
divide(divide(multiply(X3,X2),X),divide(X3,X)) = divide(divide(divide(X3,inverse(X2)),X),divide(X3,X)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
divide(divide(divide(A2,inverse(B2)),C),divide(A2,C)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c9,plain,
divide(divide(divide(X3,inverse(X2)),X),divide(X3,X)) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
divide(divide(multiply(X3,X2),X),divide(X3,X)) = X2,
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
divide(divide(multiply(X,inverse(X2)),X3),divide(X,X3)) = inverse(X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
inverse(X3) = divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
divide(X4,inverse(X3)) = divide(X4,divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
divide(divide(X4,inverse(X3)),X4) = divide(divide(X4,divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(divide(multiply(divide(multiply(X4,inverse(X3)),X2),X),divide(X4,X2)),X3) = divide(divide(multiply(divide(multiply(X4,inverse(X3)),X2),X),divide(X4,X2)),inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
X2 = divide(divide(multiply(X3,X2),X),divide(X3,X)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c17,plain,
divide(divide(multiply(divide(multiply(X4,X3),X2),X),divide(X4,X2)),X3) = divide(divide(multiply(divide(multiply(X4,X3),X2),X),divide(X4,X2)),divide(divide(multiply(X4,X3),X2),divide(X4,X2))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
divide(divide(multiply(divide(multiply(X4,X3),X2),X),divide(X4,X2)),divide(divide(multiply(X4,X3),X2),divide(X4,X2))) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c19,plain,
divide(divide(multiply(divide(multiply(X4,X3),X2),X),divide(X4,X2)),X3) = X,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
divide(divide(multiply(divide(multiply(X4,inverse(X3)),X2),X),divide(X4,X2)),inverse(X3)) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(divide(multiply(divide(multiply(X4,inverse(X3)),X2),X),divide(X4,X2)),X3) = X,
inference(transitivity,[status(thm)],[c15,c20]) ).
cnf(c22,plain,
multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),X4),divide(X2,X)),X3) = X4,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
X4 = multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),X4),divide(X2,X)),X3),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
divide(X4,divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))) = divide(multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),X4),divide(X2,X)),X3),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
divide(divide(X4,divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4) = divide(divide(multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),X4),divide(X2,X)),X3),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
divide(divide(multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),X4),divide(X2,X)),X3),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4) = X3,
inference(substitution,[status(thm)],[c19]) ).
cnf(c27,plain,
divide(divide(X4,divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4) = X3,
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
divide(divide(X2,inverse(X)),X2) = X,
inference(transitivity,[status(thm)],[c14,c27]) ).
cnf(c29,plain,
divide(multiply(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c4,c28]) ).
cnf(c30,plain,
divide(multiply(X,X2),X) = X2,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
X2 = divide(multiply(X,X2),X),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
divide(X2,divide(X,X)) = divide(divide(multiply(X,X2),X),divide(X,X)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
divide(divide(multiply(X,X2),X),divide(X,X)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c34,plain,
divide(X2,divide(X,X)) = X2,
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
divide(multiply(divide(X2,X2),X),divide(X2,X2)) = multiply(divide(X2,X2),X),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(divide(X2,X2),X) = divide(multiply(divide(X2,X2),X),divide(X2,X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
divide(multiply(divide(X2,X2),X),divide(X2,X2)) = X,
inference(substitution,[status(thm)],[c29]) ).
cnf(c38,plain,
multiply(divide(X2,X2),X) = X,
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
multiply(divide(X,X),X2) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
X2 = multiply(divide(X,X),X2),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(inverse(X2),X2) = multiply(inverse(X2),multiply(divide(X,X),X2)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(divide(X,X),X2) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c43,plain,
X2 = multiply(divide(X,X),X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
inverse(X2) = inverse(multiply(divide(X,X),X2)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(X3),multiply(X2,X3)) = multiply(inverse(multiply(divide(X,X),X3)),multiply(X2,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(inverse(X2),X) = divide(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
multiply(multiply(inverse(X2),X),X2) = multiply(divide(inverse(X2),inverse(X)),X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X)) = inverse(X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c49,plain,
inverse(X3) = divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
divide(inverse(X4),inverse(X3)) = divide(inverse(X4),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(divide(inverse(X4),inverse(X3)),X4) = multiply(divide(inverse(X4),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),inverse(X4)),divide(X2,X)),X3) = inverse(X4),
inference(substitution,[status(thm)],[c21]) ).
cnf(c53,plain,
inverse(X4) = multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),inverse(X4)),divide(X2,X)),X3),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
divide(inverse(X4),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))) = divide(multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),inverse(X4)),divide(X2,X)),X3),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(divide(inverse(X4),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4) = multiply(divide(multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),inverse(X4)),divide(X2,X)),X3),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(divide(multiply(divide(multiply(divide(multiply(X2,inverse(X3)),X),inverse(X4)),divide(X2,X)),X3),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4) = X3,
inference(substitution,[status(thm)],[c21]) ).
cnf(c57,plain,
multiply(divide(inverse(X4),divide(divide(multiply(X2,inverse(X3)),X),divide(X2,X))),X4) = X3,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
multiply(divide(inverse(X2),inverse(X)),X2) = X,
inference(transitivity,[status(thm)],[c51,c57]) ).
cnf(c59,plain,
multiply(multiply(inverse(X2),X),X2) = X,
inference(transitivity,[status(thm)],[c47,c58]) ).
cnf(c60,plain,
multiply(multiply(inverse(X),X2),X) = X2,
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
X2 = multiply(multiply(inverse(X),X2),X),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
divide(X2,multiply(inverse(X),X2)) = divide(multiply(multiply(inverse(X),X2),X),multiply(inverse(X),X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
divide(multiply(multiply(inverse(X),X2),X),multiply(inverse(X),X2)) = X,
inference(substitution,[status(thm)],[c29]) ).
cnf(c64,plain,
divide(X2,multiply(inverse(X),X2)) = X,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
divide(multiply(inverse(X),X2),multiply(inverse(X),multiply(inverse(X),X2))) = X,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
X = divide(multiply(inverse(X),X2),multiply(inverse(X),multiply(inverse(X),X2))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
divide(X2,X) = divide(X2,divide(multiply(inverse(X),X2),multiply(inverse(X),multiply(inverse(X),X2)))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
divide(multiply(multiply(X3,X2),X),multiply(X3,X)) = divide(multiply(multiply(X3,X2),X),divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(multiply(X3,X2),X) = divide(multiply(X3,X2),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
divide(multiply(multiply(X3,X2),X),divide(X3,inverse(X))) = divide(divide(multiply(X3,X2),inverse(X)),divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
divide(divide(multiply(X3,X2),inverse(X)),divide(X3,inverse(X))) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c73,plain,
divide(multiply(multiply(X3,X2),X),divide(X3,inverse(X))) = X2,
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
divide(multiply(multiply(X3,X2),X),multiply(X3,X)) = X2,
inference(transitivity,[status(thm)],[c69,c73]) ).
cnf(c75,plain,
divide(multiply(multiply(X2,X3),X),multiply(X2,X)) = X3,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
X3 = divide(multiply(multiply(X2,X3),X),multiply(X2,X)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
divide(X3,divide(multiply(X2,X3),multiply(X2,X))) = divide(divide(multiply(multiply(X2,X3),X),multiply(X2,X)),divide(multiply(X2,X3),multiply(X2,X))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
divide(divide(multiply(multiply(X2,X3),X),multiply(X2,X)),divide(multiply(X2,X3),multiply(X2,X))) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c79,plain,
divide(X3,divide(multiply(X2,X3),multiply(X2,X))) = X,
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
divide(X2,divide(multiply(inverse(X),X2),multiply(inverse(X),multiply(inverse(X),X2)))) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
divide(X2,X) = multiply(inverse(X),X2),
inference(transitivity,[status(thm)],[c67,c80]) ).
cnf(c82,plain,
divide(multiply(X2,X3),multiply(divide(X,X),X3)) = multiply(inverse(multiply(divide(X,X),X3)),multiply(X2,X3)),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(inverse(multiply(divide(X,X),X3)),multiply(X2,X3)) = divide(multiply(X2,X3),multiply(divide(X,X),X3)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(divide(X,X),X2) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c85,plain,
X2 = multiply(divide(X,X),X2),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(X2,X3) = multiply(multiply(divide(X,X),X2),X3),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
divide(multiply(X2,X3),multiply(divide(X,X),X3)) = divide(multiply(multiply(divide(X,X),X2),X3),multiply(divide(X,X),X3)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
divide(multiply(multiply(divide(X,X),X2),X3),multiply(divide(X,X),X3)) = X2,
inference(substitution,[status(thm)],[c74]) ).
cnf(c89,plain,
divide(multiply(X2,X3),multiply(divide(X,X),X3)) = X2,
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
multiply(inverse(multiply(divide(X,X),X3)),multiply(X2,X3)) = X2,
inference(transitivity,[status(thm)],[c83,c89]) ).
cnf(c91,plain,
multiply(inverse(X2),multiply(X,X2)) = X,
inference(transitivity,[status(thm)],[c45,c90]) ).
cnf(c92,plain,
multiply(inverse(X2),multiply(divide(X,X),X2)) = divide(X,X),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(inverse(X2),multiply(divide(X,X),X2)) = divide(X,X),
inference(substitution,[status(thm)],[c91]) ).
cnf(c94,plain,
divide(X,X) = multiply(inverse(X2),multiply(divide(X,X),X2)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(divide(X,X),X2) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c96,plain,
multiply(inverse(X2),multiply(divide(X,X),X2)) = multiply(inverse(X2),X2),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
divide(X,X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c94,c96]) ).
cnf(c98,plain,
multiply(inverse(X2),multiply(divide(X,X),X2)) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c92,c97]) ).
cnf(c99,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c41,c98]) ).
cnf(c100,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
$false,
inference(resolution,[status(thm)],[c1,c100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP561-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 10:07:10 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 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
% 0.13/0.47
% 0.13/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------