%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP459-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:10:32 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 5
% Syntax : Number of clauses : 173 ( 173 unt; 0 nHn; 9 RR)
% Number of literals : 173 ( 172 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 340 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c2,axiom,
inverse(A) = divide(identity,A),
file('/export/starexec/sandbox/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/sandbox/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,
multiply(X2,X) = divide(X2,inverse(X)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(multiply(X2,X)) = inverse(divide(X2,inverse(X))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(inverse(multiply(X2,X))) = inverse(inverse(divide(X2,inverse(X)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
divide(inverse(inverse(multiply(X2,X))),X) = divide(inverse(inverse(divide(X2,inverse(X)))),X),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
divide(X2,inverse(X)) = divide(X2,divide(identity,X)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(divide(X2,inverse(X))) = inverse(divide(X2,divide(identity,X))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(inverse(divide(X2,inverse(X)))) = inverse(inverse(divide(X2,divide(identity,X)))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
divide(inverse(inverse(divide(X2,inverse(X)))),X) = divide(inverse(inverse(divide(X2,divide(identity,X)))),X),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
inverse(divide(X2,divide(identity,X))) = divide(identity,divide(X2,divide(identity,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
inverse(inverse(divide(X2,divide(identity,X)))) = inverse(divide(identity,divide(X2,divide(identity,X)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
divide(inverse(inverse(divide(X2,divide(identity,X)))),X) = divide(inverse(divide(identity,divide(X2,divide(identity,X)))),X),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
inverse(identity) = divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,axiom,
identity = divide(A2,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c23,plain,
identity = divide(identity,identity),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c21,c24]) ).
cnf(c26,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
divide(identity,X) = divide(inverse(identity),X),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
divide(X2,divide(identity,X)) = divide(X2,divide(inverse(identity),X)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
divide(identity,divide(X2,divide(identity,X))) = divide(identity,divide(X2,divide(inverse(identity),X))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(divide(identity,divide(X2,divide(identity,X)))) = inverse(divide(identity,divide(X2,divide(inverse(identity),X)))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,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)],[c30]) ).
cnf(c32,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
divide(inverse(X),X2) = divide(divide(identity,X),X2),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
divide(X2,divide(inverse(X3),X)) = divide(X2,divide(divide(identity,X3),X)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
divide(X3,divide(X2,divide(inverse(X3),X))) = divide(X3,divide(X2,divide(divide(identity,X3),X))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(divide(X3,divide(X2,divide(inverse(X3),X)))) = inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,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)],[c36]) ).
cnf(c38,plain,
inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))) = divide(identity,divide(X3,divide(X2,divide(divide(identity,X3),X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
divide(inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))),X) = divide(divide(identity,divide(X3,divide(X2,divide(divide(identity,X3),X)))),X),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c41,plain,
divide(identity,divide(X3,divide(X2,divide(divide(identity,X3),X)))) = divide(divide(X3,X3),divide(X3,divide(X2,divide(divide(identity,X3),X)))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
divide(divide(identity,divide(X3,divide(X2,divide(divide(identity,X3),X)))),X) = divide(divide(divide(X3,X3),divide(X3,divide(X2,divide(divide(identity,X3),X)))),X),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,axiom,
divide(divide(divide(A2,A2),divide(A2,divide(B2,divide(divide(identity,A2),C)))),C) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c44,plain,
divide(divide(divide(X3,X3),divide(X3,divide(X2,divide(divide(identity,X3),X)))),X) = X2,
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
divide(divide(identity,divide(X3,divide(X2,divide(divide(identity,X3),X)))),X) = X2,
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
divide(inverse(divide(X3,divide(X2,divide(divide(identity,X3),X)))),X) = X2,
inference(transitivity,[status(thm)],[c39,c45]) ).
cnf(c47,plain,
divide(inverse(divide(X3,divide(X2,divide(inverse(X3),X)))),X) = X2,
inference(transitivity,[status(thm)],[c37,c46]) ).
cnf(c48,plain,
divide(inverse(divide(identity,divide(X2,divide(inverse(identity),X)))),X) = X2,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
divide(inverse(divide(identity,divide(X2,divide(identity,X)))),X) = X2,
inference(transitivity,[status(thm)],[c31,c48]) ).
cnf(c50,plain,
divide(inverse(inverse(divide(X2,divide(identity,X)))),X) = X2,
inference(transitivity,[status(thm)],[c20,c49]) ).
cnf(c51,plain,
divide(inverse(inverse(divide(X2,inverse(X)))),X) = X2,
inference(transitivity,[status(thm)],[c17,c50]) ).
cnf(c52,plain,
divide(inverse(inverse(multiply(X2,X))),X) = X2,
inference(transitivity,[status(thm)],[c12,c51]) ).
cnf(c53,plain,
divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
inverse(inverse(X)) = divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
divide(inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))),X) = inverse(multiply(X3,identity)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c56,plain,
inverse(multiply(X3,identity)) = divide(inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))),X),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c58,plain,
divide(X,identity) = divide(X,inverse(identity)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
divide(X,inverse(identity)) = multiply(X,identity),
inference(substitution,[status(thm)],[c8]) ).
cnf(c60,plain,
divide(X,identity) = multiply(X,identity),
inference(transitivity,[status(thm)],[c58,c59]) ).
cnf(c61,plain,
multiply(X,identity) = divide(X,identity),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
inverse(multiply(X,identity)) = inverse(divide(X,identity)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
divide(inverse(multiply(X2,identity)),X) = divide(inverse(divide(X2,identity)),X),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
identity = divide(divide(inverse(X2),X),divide(inverse(X2),X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c65,plain,
divide(X2,identity) = divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
inverse(divide(X2,identity)) = inverse(divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X)))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,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)],[c66]) ).
cnf(c68,plain,
divide(inverse(divide(X2,divide(divide(inverse(X2),X),divide(inverse(X2),X)))),X) = divide(inverse(X2),X),
inference(substitution,[status(thm)],[c47]) ).
cnf(c69,plain,
divide(inverse(divide(X2,identity)),X) = divide(inverse(X2),X),
inference(transitivity,[status(thm)],[c67,c68]) ).
cnf(c70,plain,
divide(inverse(multiply(X2,identity)),X) = divide(inverse(X2),X),
inference(transitivity,[status(thm)],[c63,c69]) ).
cnf(c71,plain,
divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)) = divide(inverse(X3),divide(inverse(X2),X)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,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)],[c71]) ).
cnf(c73,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)],[c72]) ).
cnf(c74,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)],[c73]) ).
cnf(c75,plain,
divide(inverse(divide(X2,divide(inverse(X3),divide(inverse(X2),X)))),X) = inverse(X3),
inference(substitution,[status(thm)],[c47]) ).
cnf(c76,plain,
divide(inverse(divide(X2,divide(inverse(multiply(X3,identity)),divide(inverse(X2),X)))),X) = inverse(X3),
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
inverse(multiply(X,identity)) = inverse(X),
inference(transitivity,[status(thm)],[c56,c76]) ).
cnf(c78,plain,
inverse(X) = inverse(multiply(X,identity)),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
inverse(inverse(X)) = inverse(inverse(multiply(X,identity))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(inverse(inverse(X)),identity) = multiply(inverse(inverse(multiply(X,identity))),identity),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
divide(inverse(inverse(multiply(X,identity))),identity) = multiply(inverse(inverse(multiply(X,identity))),identity),
inference(substitution,[status(thm)],[c60]) ).
cnf(c82,plain,
multiply(inverse(inverse(multiply(X,identity))),identity) = divide(inverse(inverse(multiply(X,identity))),identity),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
divide(inverse(inverse(multiply(X,identity))),identity) = X,
inference(substitution,[status(thm)],[c52]) ).
cnf(c84,plain,
multiply(inverse(inverse(multiply(X,identity))),identity) = X,
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(transitivity,[status(thm)],[c80,c84]) ).
cnf(c86,plain,
inverse(multiply(inverse(inverse(X)),identity)) = inverse(X),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
inverse(inverse(multiply(inverse(inverse(X)),identity))) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity) = divide(inverse(inverse(X)),identity),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
divide(inverse(inverse(X)),identity) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c60]) ).
cnf(c90,plain,
divide(inverse(inverse(X)),identity) = X,
inference(transitivity,[status(thm)],[c89,c85]) ).
cnf(c91,plain,
divide(inverse(inverse(multiply(inverse(inverse(X)),identity))),identity) = X,
inference(transitivity,[status(thm)],[c88,c90]) ).
cnf(c92,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c54,c91]) ).
cnf(c93,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(multiply(X3,X2),X) = multiply(multiply(X3,X2),inverse(inverse(X))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c96,plain,
multiply(X2,X) = multiply(X2,inverse(inverse(X))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(multiply(X3,X2),inverse(X)) = multiply(multiply(X3,inverse(inverse(X2))),inverse(X)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
divide(inverse(inverse(multiply(inverse(multiply(X2,inverse(X))),X2))),X2) = inverse(multiply(X2,inverse(X))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c99,plain,
inverse(multiply(X2,inverse(X))) = divide(inverse(inverse(multiply(inverse(multiply(X2,inverse(X))),X2))),X2),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
inverse(X) = inverse(multiply(X,identity)),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c101,plain,
multiply(X2,inverse(X)) = multiply(X2,inverse(multiply(X,identity))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
inverse(multiply(X2,inverse(X))) = inverse(multiply(X2,inverse(multiply(X,identity)))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(inverse(multiply(X2,inverse(X))),X2) = multiply(inverse(multiply(X2,inverse(multiply(X,identity)))),X2),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(X,identity) = divide(X,identity),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c105,plain,
inverse(multiply(X,identity)) = inverse(divide(X,identity)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(X2,inverse(multiply(X,identity))) = multiply(X2,inverse(divide(X,identity))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
inverse(multiply(X2,inverse(multiply(X,identity)))) = inverse(multiply(X2,inverse(divide(X,identity)))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(inverse(multiply(X2,inverse(multiply(X,identity)))),X2) = multiply(inverse(multiply(X2,inverse(divide(X,identity)))),X2),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c110,plain,
divide(X2,X) = divide(X2,inverse(inverse(X))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
divide(X2,inverse(inverse(X))) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c112,plain,
divide(X2,X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
divide(X2,divide(X,identity)) = multiply(X2,inverse(divide(X,identity))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(X2,inverse(divide(X,identity))) = divide(X2,divide(X,identity)),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
inverse(multiply(X2,inverse(divide(X,identity)))) = inverse(divide(X2,divide(X,identity))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(inverse(multiply(X2,inverse(divide(X,identity)))),X2) = multiply(inverse(divide(X2,divide(X,identity))),X2),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
divide(inverse(divide(X2,divide(X,identity))),inverse(X2)) = multiply(inverse(divide(X2,divide(X,identity))),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c118,plain,
multiply(inverse(divide(X2,divide(X,identity))),X2) = divide(inverse(divide(X2,divide(X,identity))),inverse(X2)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
identity = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c120,plain,
divide(X,identity) = divide(X,divide(inverse(X2),inverse(X2))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
divide(X2,divide(X,identity)) = divide(X2,divide(X,divide(inverse(X2),inverse(X2)))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
inverse(divide(X2,divide(X,identity))) = inverse(divide(X2,divide(X,divide(inverse(X2),inverse(X2))))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
divide(inverse(divide(X2,divide(X,identity))),inverse(X2)) = divide(inverse(divide(X2,divide(X,divide(inverse(X2),inverse(X2))))),inverse(X2)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
divide(inverse(divide(X2,divide(X,divide(inverse(X2),inverse(X2))))),inverse(X2)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c125,plain,
divide(inverse(divide(X2,divide(X,identity))),inverse(X2)) = X,
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
multiply(inverse(divide(X2,divide(X,identity))),X2) = X,
inference(transitivity,[status(thm)],[c118,c125]) ).
cnf(c127,plain,
multiply(inverse(multiply(X2,inverse(divide(X,identity)))),X2) = X,
inference(transitivity,[status(thm)],[c116,c126]) ).
cnf(c128,plain,
multiply(inverse(multiply(X2,inverse(multiply(X,identity)))),X2) = X,
inference(transitivity,[status(thm)],[c108,c127]) ).
cnf(c129,plain,
multiply(inverse(multiply(X2,inverse(X))),X2) = X,
inference(transitivity,[status(thm)],[c103,c128]) ).
cnf(c130,plain,
inverse(multiply(inverse(multiply(X2,inverse(X))),X2)) = inverse(X),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
inverse(inverse(multiply(inverse(multiply(X2,inverse(X))),X2))) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
divide(inverse(inverse(multiply(inverse(multiply(X2,inverse(X))),X2))),X2) = divide(inverse(inverse(X)),X2),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
divide(inverse(inverse(X)),X2) = multiply(inverse(inverse(X)),inverse(X2)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c134,plain,
multiply(inverse(inverse(X)),inverse(X2)) = multiply(X,inverse(X2)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c135,plain,
divide(inverse(inverse(X)),X2) = multiply(X,inverse(X2)),
inference(transitivity,[status(thm)],[c133,c134]) ).
cnf(c136,plain,
divide(inverse(inverse(multiply(inverse(multiply(X2,inverse(X))),X2))),X2) = multiply(X,inverse(X2)),
inference(transitivity,[status(thm)],[c132,c135]) ).
cnf(c137,plain,
inverse(multiply(X2,inverse(X))) = multiply(X,inverse(X2)),
inference(transitivity,[status(thm)],[c99,c136]) ).
cnf(c138,plain,
inverse(multiply(X,inverse(X2))) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(X2,inverse(X)) = inverse(multiply(X,inverse(X2))),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(multiply(X3,inverse(X2)),inverse(X)) = multiply(inverse(multiply(X2,inverse(X3))),inverse(X)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
divide(X,X2) = multiply(X,inverse(X2)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c142,plain,
multiply(X,inverse(X2)) = divide(X,X2),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
inverse(multiply(X,inverse(X2))) = inverse(divide(X,X2)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(inverse(multiply(X2,inverse(X3))),inverse(X)) = multiply(inverse(divide(X2,X3)),inverse(X)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
divide(inverse(divide(X2,X3)),X) = multiply(inverse(divide(X2,X3)),inverse(X)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c146,plain,
multiply(inverse(divide(X2,X3)),inverse(X)) = divide(inverse(divide(X2,X3)),X),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
divide(inverse(inverse(multiply(X3,divide(inverse(X2),X)))),divide(inverse(X2),X)) = X3,
inference(substitution,[status(thm)],[c52]) ).
cnf(c148,plain,
X3 = divide(inverse(inverse(multiply(X3,divide(inverse(X2),X)))),divide(inverse(X2),X)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
divide(X2,X3) = divide(X2,divide(inverse(inverse(multiply(X3,divide(inverse(X2),X)))),divide(inverse(X2),X))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
inverse(divide(X2,X3)) = inverse(divide(X2,divide(inverse(inverse(multiply(X3,divide(inverse(X2),X)))),divide(inverse(X2),X)))),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
divide(inverse(divide(X2,X3)),X) = divide(inverse(divide(X2,divide(inverse(inverse(multiply(X3,divide(inverse(X2),X)))),divide(inverse(X2),X)))),X),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
divide(inverse(divide(X2,divide(inverse(inverse(multiply(X3,divide(inverse(X2),X)))),divide(inverse(X2),X)))),X) = inverse(inverse(multiply(X3,divide(inverse(X2),X)))),
inference(substitution,[status(thm)],[c47]) ).
cnf(c153,plain,
inverse(inverse(multiply(X3,divide(inverse(X2),X)))) = multiply(X3,divide(inverse(X2),X)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c154,plain,
divide(inverse(X2),X) = multiply(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c155,plain,
multiply(X3,divide(inverse(X2),X)) = multiply(X3,multiply(inverse(X2),inverse(X))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
inverse(inverse(multiply(X3,divide(inverse(X2),X)))) = multiply(X3,multiply(inverse(X2),inverse(X))),
inference(transitivity,[status(thm)],[c153,c155]) ).
cnf(c157,plain,
divide(inverse(divide(X2,divide(inverse(inverse(multiply(X3,divide(inverse(X2),X)))),divide(inverse(X2),X)))),X) = multiply(X3,multiply(inverse(X2),inverse(X))),
inference(transitivity,[status(thm)],[c152,c156]) ).
cnf(c158,plain,
divide(inverse(divide(X2,X3)),X) = multiply(X3,multiply(inverse(X2),inverse(X))),
inference(transitivity,[status(thm)],[c151,c157]) ).
cnf(c159,plain,
multiply(inverse(divide(X2,X3)),inverse(X)) = multiply(X3,multiply(inverse(X2),inverse(X))),
inference(transitivity,[status(thm)],[c146,c158]) ).
cnf(c160,plain,
multiply(inverse(multiply(X2,inverse(X3))),inverse(X)) = multiply(X3,multiply(inverse(X2),inverse(X))),
inference(transitivity,[status(thm)],[c144,c159]) ).
cnf(c161,plain,
multiply(multiply(X3,inverse(X2)),inverse(X)) = multiply(X3,multiply(inverse(X2),inverse(X))),
inference(transitivity,[status(thm)],[c140,c160]) ).
cnf(c162,plain,
multiply(multiply(X3,inverse(inverse(X2))),inverse(X)) = multiply(X3,multiply(inverse(inverse(X2)),inverse(X))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(inverse(inverse(X2)),inverse(X)) = multiply(X2,inverse(X)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c164,plain,
multiply(X3,multiply(inverse(inverse(X2)),inverse(X))) = multiply(X3,multiply(X2,inverse(X))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(multiply(X3,inverse(inverse(X2))),inverse(X)) = multiply(X3,multiply(X2,inverse(X))),
inference(transitivity,[status(thm)],[c162,c164]) ).
cnf(c166,plain,
multiply(multiply(X3,X2),inverse(X)) = multiply(X3,multiply(X2,inverse(X))),
inference(transitivity,[status(thm)],[c97,c165]) ).
cnf(c167,plain,
multiply(multiply(X3,X2),inverse(inverse(X))) = multiply(X3,multiply(X2,inverse(inverse(X)))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
multiply(X2,inverse(inverse(X))) = multiply(X2,X),
inference(congruence,[status(thm)],[c92]) ).
cnf(c169,plain,
multiply(X3,multiply(X2,inverse(inverse(X)))) = multiply(X3,multiply(X2,X)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(multiply(X3,X2),inverse(inverse(X))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c167,c169]) ).
cnf(c171,plain,
multiply(multiply(X3,X2),X) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c94,c170]) ).
cnf(c172,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
$false,
inference(resolution,[status(thm)],[c1,c172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP459-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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 10:03:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 Command-line arguments: --no-flatten-goal
% 0.09/0.45
% 0.09/0.45 % SZS status Unsatisfiable
% 0.09/0.45
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.57/0.52
% 0.57/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------