%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP449-1 : 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 10:10:30 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.35s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 4
% Syntax : Number of clauses : 111 ( 111 unt; 0 nHn; 5 RR)
% Number of literals : 111 ( 110 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 238 ( 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,
inverse(A) = divide(divide(B,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(X2) = divide(divide(X,X),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(X3,inverse(X2)) = divide(X3,divide(divide(X,X),X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(A2,B2) = divide(A2,divide(divide(C,C),B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c6,plain,
multiply(X3,X2) = divide(X3,divide(divide(X,X),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
divide(X3,divide(divide(X,X),X2)) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
divide(X2,inverse(X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
divide(inverse(X),inverse(X)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(multiply(inverse(X2),X2),X) = multiply(divide(inverse(X2),inverse(X2)),X),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
divide(divide(X2,X2),inverse(X)) = multiply(divide(X2,X2),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c13,plain,
multiply(divide(X2,X2),X) = divide(divide(X2,X2),inverse(X)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
inverse(inverse(X)) = divide(divide(X2,X2),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
divide(divide(X2,X2),inverse(X)) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(divide(X2,X2),X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
multiply(divide(inverse(X2),inverse(X2)),X) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(multiply(inverse(X2),X2),X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c11,c17]) ).
cnf(c19,plain,
multiply(multiply(inverse(b2),b2),a2) = inverse(inverse(a2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
divide(inverse(X2),inverse(X)) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c21,plain,
multiply(inverse(X2),X) = divide(inverse(X2),inverse(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X2,multiply(inverse(X2),X)) = multiply(X2,divide(inverse(X2),inverse(X))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
divide(X2,inverse(divide(inverse(X2),inverse(X)))) = multiply(X2,divide(inverse(X2),inverse(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c24,plain,
multiply(X2,divide(inverse(X2),inverse(X))) = divide(X2,inverse(divide(inverse(X2),inverse(X)))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
inverse(divide(inverse(X2),inverse(X))) = divide(divide(inverse(X),inverse(X)),divide(inverse(X2),inverse(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
divide(X2,inverse(divide(inverse(X2),inverse(X)))) = divide(X2,divide(divide(inverse(X),inverse(X)),divide(inverse(X2),inverse(X)))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
inverse(X2) = divide(divide(X,X),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c28,plain,
divide(inverse(X3),X) = divide(divide(divide(X2,X2),X3),X),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
divide(divide(inverse(X2),X),divide(inverse(X3),X)) = divide(divide(inverse(X2),X),divide(divide(divide(X2,X2),X3),X)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
divide(X3,divide(divide(inverse(X2),X),divide(inverse(X3),X))) = divide(X3,divide(divide(inverse(X2),X),divide(divide(divide(X2,X2),X3),X))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(X) = divide(divide(X,X),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
divide(inverse(X2),X) = divide(divide(divide(X2,X2),X2),X),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
divide(divide(inverse(X2),X),divide(divide(divide(X2,X2),X3),X)) = divide(divide(divide(divide(X2,X2),X2),X),divide(divide(divide(X2,X2),X3),X)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
divide(X3,divide(divide(inverse(X2),X),divide(divide(divide(X2,X2),X3),X))) = divide(X3,divide(divide(divide(divide(X2,X2),X2),X),divide(divide(divide(X2,X2),X3),X))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
divide(A2,divide(divide(divide(divide(B2,B2),B2),C2),divide(divide(divide(B2,B2),A2),C2))) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c36,plain,
divide(X3,divide(divide(divide(divide(X2,X2),X2),X),divide(divide(divide(X2,X2),X3),X))) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
divide(X3,divide(divide(inverse(X2),X),divide(divide(divide(X2,X2),X3),X))) = X2,
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
divide(X3,divide(divide(inverse(X2),X),divide(inverse(X3),X))) = X2,
inference(transitivity,[status(thm)],[c30,c37]) ).
cnf(c39,plain,
divide(X2,divide(divide(inverse(X),inverse(X)),divide(inverse(X2),inverse(X)))) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
divide(X2,inverse(divide(inverse(X2),inverse(X)))) = X,
inference(transitivity,[status(thm)],[c26,c39]) ).
cnf(c41,plain,
multiply(X2,divide(inverse(X2),inverse(X))) = X,
inference(transitivity,[status(thm)],[c24,c40]) ).
cnf(c42,plain,
multiply(X2,multiply(inverse(X2),X)) = X,
inference(transitivity,[status(thm)],[c22,c41]) ).
cnf(c43,plain,
multiply(X,multiply(inverse(X),inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
inverse(X2) = multiply(X,multiply(inverse(X),inverse(X2))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
inverse(inverse(X2)) = inverse(multiply(X,multiply(inverse(X),inverse(X2)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
divide(inverse(X),inverse(X2)) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c47,plain,
multiply(inverse(X),X2) = divide(inverse(X),inverse(X2)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
divide(X2,multiply(inverse(X),X2)) = divide(X2,divide(inverse(X),inverse(X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
inverse(divide(X,X)) = divide(divide(X,X),divide(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
divide(inverse(divide(X2,X2)),X) = divide(divide(divide(X2,X2),divide(X2,X2)),X),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
inverse(X) = divide(divide(divide(X2,X2),divide(X2,X2)),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
divide(divide(divide(X2,X2),divide(X2,X2)),X) = inverse(X),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
divide(inverse(divide(X2,X2)),X) = inverse(X),
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
divide(inverse(divide(X,X)),X2) = inverse(X2),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
inverse(X2) = divide(inverse(divide(X,X)),X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(inverse(X2),X2) = multiply(divide(inverse(divide(X,X)),X2),X2),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(divide(inverse(divide(X,X)),X2),X2)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
divide(divide(inverse(X2),X),inverse(X)) = multiply(divide(inverse(X2),X),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c59,plain,
multiply(divide(inverse(X2),X),X) = divide(divide(inverse(X2),X),inverse(X)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
inverse(multiply(divide(inverse(X2),X),X)) = inverse(divide(divide(inverse(X2),X),inverse(X))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
inverse(divide(divide(inverse(X3),X2),inverse(X2))) = divide(divide(X,X),divide(divide(inverse(X3),X2),inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
divide(inverse(divide(X,X)),X2) = inverse(X2),
inference(substitution,[status(thm)],[c53]) ).
cnf(c63,plain,
inverse(X2) = divide(inverse(divide(X,X)),X2),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
divide(divide(inverse(X3),X2),inverse(X2)) = divide(divide(inverse(X3),X2),divide(inverse(divide(X,X)),X2)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
divide(divide(X,X),divide(divide(inverse(X3),X2),inverse(X2))) = divide(divide(X,X),divide(divide(inverse(X3),X2),divide(inverse(divide(X,X)),X2))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
divide(divide(X,X),divide(divide(inverse(X3),X2),divide(inverse(divide(X,X)),X2))) = X3,
inference(substitution,[status(thm)],[c38]) ).
cnf(c67,plain,
divide(divide(X,X),divide(divide(inverse(X3),X2),inverse(X2))) = X3,
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
inverse(divide(divide(inverse(X2),X),inverse(X))) = X2,
inference(transitivity,[status(thm)],[c61,c67]) ).
cnf(c69,plain,
inverse(multiply(divide(inverse(X2),X),X)) = X2,
inference(transitivity,[status(thm)],[c60,c68]) ).
cnf(c70,plain,
inverse(multiply(divide(inverse(divide(X,X)),X2),X2)) = divide(X,X),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
inverse(multiply(inverse(X2),X2)) = divide(X,X),
inference(transitivity,[status(thm)],[c57,c70]) ).
cnf(c72,plain,
inverse(multiply(inverse(X),X)) = divide(X2,X2),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
divide(X2,X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
inverse(X) = divide(divide(X2,X2),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
multiply(inverse(X2),X2) = multiply(divide(divide(X,X),X2),X2),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(divide(divide(X,X),X2),X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
divide(X,X) = inverse(multiply(inverse(X2),X2)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c78,plain,
divide(divide(X,X),X2) = divide(inverse(multiply(inverse(X3),X3)),X2),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(divide(divide(X,X),X2),X2) = multiply(divide(inverse(multiply(inverse(X3),X3)),X2),X2),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
inverse(multiply(divide(divide(X,X),X2),X2)) = inverse(multiply(divide(inverse(multiply(inverse(X3),X3)),X2),X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
inverse(multiply(divide(inverse(multiply(inverse(X2),X2)),X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c69]) ).
cnf(c82,plain,
inverse(multiply(divide(divide(X,X),X2),X2)) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c76,c82]) ).
cnf(c84,plain,
divide(X2,X2) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c73,c83]) ).
cnf(c85,plain,
divide(divide(inverse(X3),X),divide(inverse(X3),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(inverse(X2),X2) = divide(divide(inverse(X3),X),divide(inverse(X3),X)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
divide(X3,multiply(inverse(X2),X2)) = divide(X3,divide(divide(inverse(X3),X),divide(inverse(X3),X))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X))) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c89,plain,
divide(X2,multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
divide(inverse(X2),multiply(inverse(X),X)) = inverse(X2),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
inverse(X2) = divide(inverse(X2),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
divide(inverse(X2),inverse(X3)) = divide(inverse(X2),divide(inverse(X3),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
divide(X3,divide(inverse(X2),inverse(X3))) = divide(X3,divide(inverse(X2),divide(inverse(X3),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
divide(inverse(X2),multiply(inverse(X),X)) = inverse(X2),
inference(substitution,[status(thm)],[c89]) ).
cnf(c95,plain,
inverse(X2) = divide(inverse(X2),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
divide(inverse(X2),divide(inverse(X3),multiply(inverse(X),X))) = divide(divide(inverse(X2),multiply(inverse(X),X)),divide(inverse(X3),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
divide(X3,divide(inverse(X2),divide(inverse(X3),multiply(inverse(X),X)))) = divide(X3,divide(divide(inverse(X2),multiply(inverse(X),X)),divide(inverse(X3),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
divide(X3,divide(divide(inverse(X2),multiply(inverse(X),X)),divide(inverse(X3),multiply(inverse(X),X)))) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c99,plain,
divide(X3,divide(inverse(X2),divide(inverse(X3),multiply(inverse(X),X)))) = X2,
inference(transitivity,[status(thm)],[c97,c98]) ).
cnf(c100,plain,
divide(X2,divide(inverse(X),inverse(X2))) = X,
inference(transitivity,[status(thm)],[c93,c99]) ).
cnf(c101,plain,
divide(X2,multiply(inverse(X),X2)) = X,
inference(transitivity,[status(thm)],[c48,c100]) ).
cnf(c102,plain,
divide(inverse(X2),multiply(inverse(X),inverse(X2))) = X,
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
X = divide(inverse(X2),multiply(inverse(X),inverse(X2))),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(X,multiply(inverse(X),inverse(X2))) = multiply(divide(inverse(X2),multiply(inverse(X),inverse(X2))),multiply(inverse(X),inverse(X2))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
inverse(multiply(X,multiply(inverse(X),inverse(X2)))) = inverse(multiply(divide(inverse(X2),multiply(inverse(X),inverse(X2))),multiply(inverse(X),inverse(X2)))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
inverse(multiply(divide(inverse(X2),multiply(inverse(X),inverse(X2))),multiply(inverse(X),inverse(X2)))) = X2,
inference(substitution,[status(thm)],[c69]) ).
cnf(c107,plain,
inverse(multiply(X,multiply(inverse(X),inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c105,c106]) ).
cnf(c108,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c45,c107]) ).
cnf(c109,plain,
inverse(inverse(a2)) = a2,
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[c19,c109]) ).
cnf(c111,plain,
$false,
inference(resolution,[status(thm)],[c1,c110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP449-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 10:04:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.35 Command-line arguments: --no-flatten-goal
% 0.06/0.35
% 0.06/0.35 % SZS status Unsatisfiable
% 0.06/0.35
% 0.06/0.35 % SZS output start CNFRefutation
% See solution above
% 0.06/0.37
% 0.06/0.37 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------