%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP538-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 10:11:11 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 8 RR)
% Number of literals : 52 ( 51 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 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,
identity = divide(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c3,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(identity,X2) = divide(divide(X,X),X2),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
inverse(A2) = divide(divide(B,B),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c6,plain,
inverse(X2) = divide(divide(X,X),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
divide(divide(X,X),X2) = inverse(X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
divide(identity,X) = inverse(X),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
inverse(X) = divide(identity,X),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
divide(X2,inverse(X)) = divide(X2,divide(identity,X)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
divide(identity,X2) = divide(divide(X,X),X2),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
divide(X3,divide(identity,X2)) = divide(X3,divide(divide(X,X),X2)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(A2,B2) = divide(A2,divide(divide(C,C),B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c15,plain,
multiply(X3,X2) = divide(X3,divide(divide(X,X),X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
divide(X3,divide(divide(X,X),X2)) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
divide(X2,divide(identity,X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c13,c16]) ).
cnf(c18,plain,
divide(X2,inverse(X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c10,c17]) ).
cnf(c19,plain,
divide(inverse(X),inverse(X)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
identity = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
divide(inverse(X),inverse(X)) = identity,
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
multiply(inverse(b2),b2) = identity,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
divide(identity,inverse(X)) = multiply(identity,X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c27,plain,
multiply(identity,X) = divide(identity,inverse(X)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
divide(identity,inverse(X)) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c29,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
multiply(identity,a2) = inverse(inverse(a2)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(inverse(X)) = multiply(identity,X),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c32,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
multiply(identity,X) = multiply(divide(X,X),X),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
divide(divide(X2,X),inverse(X)) = multiply(divide(X2,X),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c35,plain,
multiply(divide(X2,X),X) = divide(divide(X2,X),inverse(X)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(X) = divide(identity,X),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c37,plain,
divide(divide(X2,X),inverse(X)) = divide(divide(X2,X),divide(identity,X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
divide(identity,X) = divide(divide(X2,X2),X),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
divide(divide(X2,X),divide(identity,X)) = divide(divide(X2,X),divide(divide(X2,X2),X)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,axiom,
divide(divide(A2,B2),divide(divide(A2,C2),B2)) = C2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c42,plain,
divide(divide(X2,X),divide(divide(X2,X2),X)) = X2,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
divide(divide(X2,X),divide(identity,X)) = X2,
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
divide(divide(X2,X),inverse(X)) = X2,
inference(transitivity,[status(thm)],[c37,c43]) ).
cnf(c45,plain,
multiply(divide(X2,X),X) = X2,
inference(transitivity,[status(thm)],[c35,c44]) ).
cnf(c46,plain,
multiply(divide(X,X),X) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(identity,X) = X,
inference(transitivity,[status(thm)],[c33,c46]) ).
cnf(c48,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c31,c47]) ).
cnf(c49,plain,
inverse(inverse(a2)) = a2,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[c30,c49]) ).
cnf(c51,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[c25,c50]) ).
cnf(c52,plain,
$false,
inference(resolution,[status(thm)],[c1,c51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP538-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.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 10:12:15 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.43 Command-line arguments: --no-flatten-goal
% 0.12/0.43
% 0.12/0.43 % SZS status Unsatisfiable
% 0.12/0.43
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44
% 0.12/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------