%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP529-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:11:10 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.34s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of clauses : 85 ( 85 unt; 0 nHn; 3 RR)
% Number of literals : 85 ( 84 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 : 166 ( 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,
inverse(A) = divide(divide(B,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(X) = divide(divide(X,X),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(inverse(X)) = inverse(divide(divide(X,X),X)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
inverse(divide(divide(X,X2),X)) = divide(divide(divide(X,X2),divide(X,X2)),divide(divide(X,X2),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,axiom,
divide(divide(A2,divide(B2,C)),divide(A2,B2)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(divide(divide(X2,X),divide(X2,X)),divide(divide(X2,X),X2)) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
inverse(divide(divide(X2,X),X2)) = X,
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
inverse(divide(divide(X,X),X)) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c4,c9]) ).
cnf(c11,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
divide(X2,X) = divide(X2,inverse(inverse(X))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(X) = divide(divide(X2,X2),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
divide(X3,inverse(X2)) = divide(X3,divide(divide(X,X),X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
multiply(A2,B2) = divide(A2,divide(divide(C2,C2),B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c16,plain,
multiply(X3,X2) = divide(X3,divide(divide(X,X),X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
divide(X3,divide(divide(X,X),X2)) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
divide(X2,inverse(X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c14,c17]) ).
cnf(c19,plain,
divide(X2,inverse(inverse(X))) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
divide(X2,X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c12,c19]) ).
cnf(c21,plain,
divide(X,X) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X,inverse(X)) = divide(X,X),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X2,multiply(X,inverse(X))) = multiply(X2,divide(X,X)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c25,plain,
multiply(X2,divide(X,X)) = multiply(inverse(inverse(X2)),divide(X,X)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c27,plain,
inverse(inverse(X)) = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(inverse(inverse(X2)),divide(X,X)) = multiply(inverse(inverse(inverse(inverse(X2)))),divide(X,X)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
divide(divide(X2,X2),inverse(X)) = multiply(divide(X2,X2),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c30,plain,
multiply(divide(X2,X2),X) = divide(divide(X2,X2),inverse(X)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(inverse(X)) = divide(divide(X2,X2),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
divide(divide(X2,X2),inverse(X)) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(divide(X2,X2),X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
multiply(divide(X,X),inverse(X2)) = inverse(inverse(inverse(X2))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(inverse(inverse(X2))) = multiply(divide(X,X),inverse(X2)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(inverse(inverse(inverse(X2)))) = inverse(multiply(divide(X,X),inverse(X2))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(inverse(inverse(inverse(inverse(X2)))),divide(X,X)) = multiply(inverse(multiply(divide(X,X),inverse(X2))),divide(X,X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c39,plain,
multiply(inverse(multiply(X2,inverse(X))),X2) = multiply(inverse(multiply(X2,inverse(X))),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(X2) = divide(divide(X,X),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c41,plain,
inverse(inverse(X2)) = inverse(divide(divide(X,X),X2)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(inverse(multiply(X3,inverse(X2))),inverse(inverse(X3))) = multiply(inverse(multiply(X3,inverse(X2))),inverse(divide(divide(X,X),X3))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X2,inverse(X)) = divide(X2,X),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c44,plain,
inverse(multiply(X2,inverse(X))) = inverse(divide(X2,X)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(multiply(X3,inverse(X2))),inverse(divide(divide(X,X),X3))) = multiply(inverse(divide(X3,X2)),inverse(divide(divide(X,X),X3))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
divide(inverse(divide(X3,X2)),divide(divide(X,X),X3)) = multiply(inverse(divide(X3,X2)),inverse(divide(divide(X,X),X3))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c47,plain,
multiply(inverse(divide(X3,X2)),inverse(divide(divide(X,X),X3))) = divide(inverse(divide(X3,X2)),divide(divide(X,X),X3)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
inverse(divide(X3,X2)) = divide(divide(X,X),divide(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
divide(inverse(divide(X3,X2)),divide(divide(X,X),X3)) = divide(divide(divide(X,X),divide(X3,X2)),divide(divide(X,X),X3)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
divide(divide(divide(X,X),divide(X3,X2)),divide(divide(X,X),X3)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c51,plain,
divide(inverse(divide(X3,X2)),divide(divide(X,X),X3)) = X2,
inference(transitivity,[status(thm)],[c49,c50]) ).
cnf(c52,plain,
multiply(inverse(divide(X3,X2)),inverse(divide(divide(X,X),X3))) = X2,
inference(transitivity,[status(thm)],[c47,c51]) ).
cnf(c53,plain,
multiply(inverse(multiply(X3,inverse(X2))),inverse(divide(divide(X,X),X3))) = X2,
inference(transitivity,[status(thm)],[c45,c52]) ).
cnf(c54,plain,
multiply(inverse(multiply(X2,inverse(X))),inverse(inverse(X2))) = X,
inference(transitivity,[status(thm)],[c42,c53]) ).
cnf(c55,plain,
multiply(inverse(multiply(X2,inverse(X))),X2) = X,
inference(transitivity,[status(thm)],[c39,c54]) ).
cnf(c56,plain,
multiply(inverse(multiply(divide(X,X),inverse(X2))),divide(X,X)) = X2,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(inverse(inverse(inverse(X2)))),divide(X,X)) = X2,
inference(transitivity,[status(thm)],[c37,c56]) ).
cnf(c58,plain,
multiply(inverse(inverse(X2)),divide(X,X)) = X2,
inference(transitivity,[status(thm)],[c28,c57]) ).
cnf(c59,plain,
multiply(X2,divide(X,X)) = X2,
inference(transitivity,[status(thm)],[c25,c58]) ).
cnf(c60,plain,
multiply(X2,multiply(X,inverse(X))) = X2,
inference(transitivity,[status(thm)],[c23,c59]) ).
cnf(c61,plain,
multiply(multiply(inverse(X2),X2),multiply(X,inverse(X))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(inverse(X2),X2) = multiply(multiply(inverse(X2),X2),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
inverse(divide(divide(X,X2),X)) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c64,plain,
X2 = inverse(divide(divide(X,X2),X)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(multiply(inverse(X3),X3),inverse(divide(divide(X,X2),X))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
divide(multiply(inverse(X2),X2),X) = multiply(multiply(inverse(X2),X2),inverse(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c67,plain,
multiply(multiply(inverse(X2),X2),inverse(X)) = divide(multiply(inverse(X2),X2),X),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
divide(inverse(X),inverse(X)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c69,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
divide(multiply(inverse(X2),X2),X) = divide(divide(inverse(X2),inverse(X2)),X),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
inverse(X) = divide(divide(inverse(X2),inverse(X2)),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c72,plain,
divide(divide(inverse(X2),inverse(X2)),X) = inverse(X),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
divide(multiply(inverse(X2),X2),X) = inverse(X),
inference(transitivity,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
multiply(multiply(inverse(X2),X2),inverse(X)) = inverse(X),
inference(transitivity,[status(thm)],[c67,c73]) ).
cnf(c75,plain,
multiply(multiply(inverse(X3),X3),inverse(divide(divide(X,X2),X))) = inverse(divide(divide(X,X2),X)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
inverse(divide(divide(X,X2),X)) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c77,plain,
multiply(multiply(inverse(X3),X3),inverse(divide(divide(X,X2),X))) = X2,
inference(transitivity,[status(thm)],[c75,c76]) ).
cnf(c78,plain,
multiply(multiply(inverse(X2),X2),X) = X,
inference(transitivity,[status(thm)],[c65,c77]) ).
cnf(c79,plain,
multiply(multiply(inverse(X2),X2),multiply(X,inverse(X))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(inverse(X2),X2) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c62,c79]) ).
cnf(c81,plain,
multiply(inverse(a1),a1) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(inverse(b1),b1) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c83,plain,
multiply(X,inverse(X)) = multiply(inverse(b1),b1),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[c81,c83]) ).
cnf(c85,plain,
$false,
inference(resolution,[status(thm)],[c1,c84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP529-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 27 10:06:19 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 Command-line arguments: --no-flatten-goal
% 0.07/0.34
% 0.07/0.34 % SZS status Unsatisfiable
% 0.07/0.34
% 0.07/0.34 % SZS output start CNFRefutation
% See solution above
% 0.07/0.36
% 0.07/0.36 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------