%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP455-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 10:10:31 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 104 ( 104 unt; 0 nHn; 9 RR)
% Number of literals : 104 ( 103 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 176 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c2,axiom,
inverse(A) = divide(identity,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(X2,inverse(X)) = divide(X2,divide(identity,X)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(A2,B) = divide(A2,divide(identity,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c6,plain,
multiply(X2,X) = divide(X2,divide(identity,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
divide(X2,divide(identity,X)) = multiply(X2,X),
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(identity,inverse(X)) = multiply(identity,X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(identity,X) = divide(identity,inverse(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(inverse(X)) = divide(identity,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
divide(identity,inverse(X)) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c15,plain,
inverse(multiply(X2,X)) = inverse(divide(X2,inverse(X))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(inverse(multiply(X2,X))) = inverse(inverse(divide(X2,inverse(X)))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
divide(inverse(inverse(multiply(X2,X))),X) = divide(inverse(inverse(divide(X2,inverse(X)))),X),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
divide(X2,inverse(X)) = divide(X2,divide(identity,X)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(divide(X2,inverse(X))) = inverse(divide(X2,divide(identity,X))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
inverse(inverse(divide(X2,inverse(X)))) = inverse(inverse(divide(X2,divide(identity,X)))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
divide(inverse(inverse(divide(X2,inverse(X)))),X) = divide(inverse(inverse(divide(X2,divide(identity,X)))),X),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
inverse(divide(X2,divide(identity,X))) = divide(identity,divide(X2,divide(identity,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
inverse(inverse(divide(X2,divide(identity,X)))) = inverse(divide(identity,divide(X2,divide(identity,X)))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
divide(inverse(inverse(divide(X2,divide(identity,X)))),X) = divide(inverse(divide(identity,divide(X2,divide(identity,X)))),X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(identity) = divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,axiom,
identity = divide(A2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(c28,plain,
identity = divide(identity,identity),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c26,c29]) ).
cnf(c31,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
divide(identity,X) = divide(inverse(identity),X),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
divide(X2,divide(identity,X)) = divide(X2,divide(inverse(identity),X)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
divide(identity,divide(X2,divide(identity,X))) = divide(identity,divide(X2,divide(inverse(identity),X))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(divide(identity,divide(X2,divide(identity,X)))) = inverse(divide(identity,divide(X2,divide(inverse(identity),X)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
divide(inverse(divide(identity,divide(X2,divide(identity,X)))),X) = divide(inverse(divide(identity,divide(X2,divide(inverse(identity),X)))),X),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
divide(inverse(X),X2) = divide(divide(identity,X),X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
divide(X2,divide(inverse(X3),X)) = divide(X2,divide(divide(identity,X3),X)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
divide(X3,divide(X2,divide(inverse(X3),X))) = divide(X3,divide(X2,divide(divide(identity,X3),X))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
inverse(divide(X3,divide(X2,divide(inverse(X3),X)))) = inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
divide(inverse(divide(X3,divide(X2,divide(inverse(X3),X)))),X) = divide(inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))),X),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c27]) ).
cnf(c44,plain,
divide(identity,X) = divide(divide(X,X),X),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
divide(divide(identity,X2),X) = divide(divide(divide(X2,X2),X2),X),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
divide(X2,divide(divide(identity,X3),X)) = divide(X2,divide(divide(divide(X3,X3),X3),X)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
divide(X3,divide(X2,divide(divide(identity,X3),X))) = divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))) = inverse(divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
divide(inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))),X) = divide(inverse(divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))),X),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
inverse(divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))) = divide(identity,divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
divide(inverse(divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))),X) = divide(divide(identity,divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))),X),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,axiom,
divide(divide(identity,divide(A2,divide(B2,divide(divide(divide(A2,A2),A2),C)))),C) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c53,plain,
divide(divide(identity,divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))),X) = X2,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
divide(inverse(divide(X3,divide(X2,divide(divide(divide(X3,X3),X3),X)))),X) = X2,
inference(transitivity,[status(thm)],[c51,c53]) ).
cnf(c55,plain,
divide(inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))),X) = X2,
inference(transitivity,[status(thm)],[c49,c54]) ).
cnf(c56,plain,
divide(inverse(divide(X3,divide(X2,divide(inverse(X3),X)))),X) = X2,
inference(transitivity,[status(thm)],[c42,c55]) ).
cnf(c57,plain,
divide(inverse(divide(identity,divide(X2,divide(inverse(identity),X)))),X) = X2,
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
divide(inverse(divide(identity,divide(X2,divide(identity,X)))),X) = X2,
inference(transitivity,[status(thm)],[c36,c57]) ).
cnf(c59,plain,
divide(inverse(inverse(divide(X2,divide(identity,X)))),X) = X2,
inference(transitivity,[status(thm)],[c25,c58]) ).
cnf(c60,plain,
divide(inverse(inverse(divide(X2,inverse(X)))),X) = X2,
inference(transitivity,[status(thm)],[c22,c59]) ).
cnf(c61,plain,
divide(inverse(inverse(multiply(X2,X))),X) = X2,
inference(transitivity,[status(thm)],[c17,c60]) ).
cnf(c62,plain,
divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
inverse(inverse(X)) = divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
divide(inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))),X) = inverse(multiply(X3,identity)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c65,plain,
inverse(multiply(X3,identity)) = divide(inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))),X),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c67,plain,
divide(X,identity) = divide(X,inverse(identity)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
divide(X,inverse(identity)) = multiply(X,identity),
inference(substitution,[status(thm)],[c8]) ).
cnf(c69,plain,
divide(X,identity) = multiply(X,identity),
inference(transitivity,[status(thm)],[c67,c68]) ).
cnf(c70,plain,
multiply(X,identity) = divide(X,identity),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
inverse(multiply(X,identity)) = inverse(divide(X,identity)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
divide(inverse(multiply(X2,identity)),X) = divide(inverse(divide(X2,identity)),X),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
identity = divide(divide(inverse(X2),X),divide(inverse(X2),X)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c74,plain,
divide(X2,identity) = divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
inverse(divide(X2,identity)) = inverse(divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X)))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
divide(inverse(divide(X2,identity)),X) = divide(inverse(divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X)))),X),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
divide(inverse(divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X)))),X) = divide(inverse(X2),X),
inference(substitution,[status(thm)],[c56]) ).
cnf(c78,plain,
divide(inverse(divide(X2,identity)),X) = divide(inverse(X2),X),
inference(transitivity,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
divide(inverse(multiply(X2,identity)),X) = divide(inverse(X2),X),
inference(transitivity,[status(thm)],[c72,c78]) ).
cnf(c80,plain,
divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)) = divide(inverse(X3),divide(inverse(X2),X)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X))) = divide(X2,divide(inverse(X3),divide(inverse(X2),X))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))) = inverse(divide(X2,divide(inverse(X3),divide(inverse(X2),X)))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
divide(inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))),X) = divide(inverse(divide(X2,divide(inverse(X3),divide(inverse(X2),X)))),X),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
divide(inverse(divide(X2,divide(inverse(X3),divide(inverse(X2),X)))),X) = inverse(X3),
inference(substitution,[status(thm)],[c56]) ).
cnf(c85,plain,
divide(inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))),X) = inverse(X3),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
inverse(multiply(X,identity)) = inverse(X),
inference(transitivity,[status(thm)],[c65,c85]) ).
cnf(c87,plain,
inverse(X) = inverse(multiply(X,identity)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
inverse(inverse(X)) = inverse(inverse(multiply(X,identity))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(inverse(inverse(X)),identity) = multiply(inverse(inverse(multiply(X,identity))),identity),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
divide(inverse(inverse(multiply(X,identity))),identity) = multiply(inverse(inverse(multiply(X,identity))),identity),
inference(substitution,[status(thm)],[c69]) ).
cnf(c91,plain,
multiply(inverse(inverse(multiply(X,identity))),identity) = divide(inverse(inverse(multiply(X,identity))),identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
divide(inverse(inverse(multiply(X,identity))),identity) = X,
inference(substitution,[status(thm)],[c61]) ).
cnf(c93,plain,
multiply(inverse(inverse(multiply(X,identity))),identity) = X,
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(transitivity,[status(thm)],[c89,c93]) ).
cnf(c95,plain,
inverse(multiply(inverse(inverse(X)),identity)) = inverse(X),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
inverse(inverse(multiply(inverse(inverse(X)),identity))) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity) = divide(inverse(inverse(X)),identity),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
divide(inverse(inverse(X)),identity) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c69]) ).
cnf(c99,plain,
divide(inverse(inverse(X)),identity) = X,
inference(transitivity,[status(thm)],[c98,c94]) ).
cnf(c100,plain,
divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity) = X,
inference(transitivity,[status(thm)],[c97,c99]) ).
cnf(c101,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c63,c100]) ).
cnf(c102,plain,
multiply(identity,X) = X,
inference(transitivity,[status(thm)],[c13,c101]) ).
cnf(c103,plain,
multiply(identity,a2) = a2,
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
$false,
inference(resolution,[status(thm)],[c1,c103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP455-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:05:01 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 Command-line arguments: --flatten --complete-subsets
% 0.14/0.42
% 0.14/0.42 % SZS status Unsatisfiable
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44
% 0.14/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------