%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP575-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:44:22 AM UTC 2025
% Result : Unsatisfiable 11.43s 11.63s
% Output : CNFRefutation 11.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 5 RR)
% Number of literals : 70 ( 69 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 145 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c1,axiom,
inverse(X) = double_divide(X,identity),
file('theBenchmark.p',inverse) ).
cnf(c2,axiom,
identity = double_divide(X,inverse(X)),
file('theBenchmark.p',identity) ).
cnf(c3,plain,
double_divide(X,double_divide(X,identity)) = identity,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,axiom,
multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('theBenchmark.p',multiply) ).
cnf(c5,axiom,
double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),double_divide(Z,identity))),double_divide(identity,identity)) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X,identity))),double_divide(identity,identity)) = X,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
double_divide(identity,identity) = identity,
inference(equational,[status(thm)],[c3,c5,c7]) ).
cnf(c9,plain,
double_divide(double_divide(double_divide(X,identity),X),identity) = identity,
inference(equational,[status(thm)],[c5,c6,c8]) ).
cnf(c10,plain,
double_divide(double_divide(X,identity),X) = identity,
inference(equational,[status(thm)],[c6,c8,c9]) ).
cnf(c11,plain,
double_divide(double_divide(identity,double_divide(double_divide(X,identity),identity)),identity) = X,
inference(equational,[status(thm)],[c5,c8,c9]) ).
cnf(c12,plain,
double_divide(double_divide(identity,double_divide(X,identity)),identity) = double_divide(identity,double_divide(double_divide(X,identity),identity)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,plain,
double_divide(double_divide(identity,double_divide(identity,X)),identity) = double_divide(identity,double_divide(double_divide(X,identity),identity)),
inference(equational,[status(thm)],[c6,c8,c11]) ).
cnf(c14,plain,
double_divide(double_divide(identity,double_divide(double_divide(X,Y),Y)),identity) = X,
inference(equational,[status(thm)],[c5,c8,c11]) ).
cnf(c15,plain,
double_divide(double_divide(identity,X),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c12,c14]) ).
cnf(c16,plain,
double_divide(identity,double_divide(X,identity)) = double_divide(identity,double_divide(identity,X)),
inference(equational,[status(thm)],[c13,c14,c15]) ).
cnf(c17,plain,
double_divide(identity,double_divide(identity,double_divide(X,identity))) = double_divide(X,identity),
inference(equational,[status(thm)],[c10,c14,c15]) ).
cnf(c18,plain,
double_divide(double_divide(X,identity),identity) = X,
inference(equational,[status(thm)],[c6,c8,c17]) ).
cnf(c19,plain,
double_divide(identity,X) = double_divide(X,identity),
inference(equational,[status(thm)],[c11,c12,c18]) ).
cnf(c20,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference(equational,[status(thm)],[c14,c17]) ).
cnf(c21,plain,
double_divide(identity,double_divide(X,identity)) = X,
inference(equational,[status(thm)],[c16,c20]) ).
cnf(c22,plain,
double_divide(double_divide(identity,X),X) = identity,
inference(equational,[status(thm)],[c10,c19]) ).
cnf(c24,plain,
double_divide(identity,double_divide(X,Y)) = double_divide(identity,double_divide(Y,X)),
inference(equational,[status(thm)],[c5,c8,c19,c21,c22]) ).
cnf(c25,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c20,c24]) ).
cnf(c26,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference(equational,[status(thm)],[c14,c15,c21,c24]) ).
cnf(c27,plain,
double_divide(X,double_divide(X,Y)) = Y,
inference(equational,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
double_divide(identity,double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,X))))) = Y,
inference(equational,[status(thm)],[c5,c8,c19]) ).
cnf(c29,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,X)))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c15,c21,c28]) ).
cnf(c30,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(Y,X))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c16,c20,c29]) ).
cnf(c31,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(Y,X))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c16,c21,c29]) ).
cnf(c33,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(X,Y))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c14,c15,c21,c30]) ).
cnf(c34,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(Y,X))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c19,c30]) ).
cnf(c36,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(Y,X))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c19,c31]) ).
cnf(c37,plain,
double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),double_divide(Z,identity))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c5,c20,c28]) ).
cnf(c38,plain,
double_divide(X,double_divide(identity,Y)) = double_divide(identity,double_divide(Y,double_divide(X,identity))),
inference(equational,[status(thm)],[c18,c34,c37]) ).
cnf(c42,plain,
double_divide(identity,double_divide(X,double_divide(identity,Y))) = double_divide(Y,double_divide(X,identity)),
inference(equational,[status(thm)],[c20,c38]) ).
cnf(c46,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,double_divide(Z,double_divide(Y,X)))))) = double_divide(Z,identity),
inference(equational,[status(thm)],[c5,c8,c21,c42]) ).
cnf(c47,plain,
double_divide(X,double_divide(Y,double_divide(identity,double_divide(X,double_divide(Y,Z))))) = double_divide(Z,identity),
inference(equational,[status(thm)],[c20,c21,c25,c46]) ).
cnf(c48,plain,
double_divide(double_divide(X,identity),double_divide(identity,Y)) = double_divide(identity,double_divide(X,Y)),
inference(equational,[status(thm)],[c19,c21,c33,c47]) ).
cnf(c49,plain,
double_divide(double_divide(X,identity),double_divide(Y,identity)) = double_divide(identity,double_divide(X,Y)),
inference(equational,[status(thm)],[c19,c20,c33,c47]) ).
cnf(c50,plain,
double_divide(double_divide(identity,X),double_divide(identity,Y)) = double_divide(identity,double_divide(X,Y)),
inference(equational,[status(thm)],[c31,c36,c48]) ).
cnf(c51,plain,
double_divide(identity,double_divide(double_divide(identity,X),Y)) = double_divide(X,double_divide(identity,Y)),
inference(equational,[status(thm)],[c11,c18,c48]) ).
cnf(c55,plain,
double_divide(X,double_divide(Y,double_divide(identity,double_divide(X,double_divide(Y,double_divide(X,double_divide(Y,double_divide(identity,double_divide(X,double_divide(Y,Z)))))))))) = Z,
inference(equational,[status(thm)],[c5,c8,c18,c25,c46,c47]) ).
cnf(c56,plain,
double_divide(identity,double_divide(X,double_divide(identity,Y))) = double_divide(Z,double_divide(identity,double_divide(Y,double_divide(Z,X)))),
inference(equational,[status(thm)],[c20,c21,c27,c46,c55]) ).
cnf(c57,plain,
double_divide(identity,double_divide(X,Y)) = double_divide(Z,double_divide(Y,double_divide(identity,double_divide(Z,X)))),
inference(equational,[status(thm)],[c20,c27,c51,c55,c56]) ).
cnf(c58,plain,
double_divide(X,double_divide(Y,double_divide(Z,identity))) = double_divide(identity,double_divide(double_divide(X,Z),Y)),
inference(equational,[status(thm)],[c20,c47,c57]) ).
cnf(c60,plain,
double_divide(X,double_divide(identity,double_divide(Y,Z))) = double_divide(Y,double_divide(identity,double_divide(X,Z))),
inference(equational,[status(thm)],[c49,c51,c58]) ).
cnf(c65,plain,
double_divide(X,double_divide(identity,double_divide(Y,Z))) = double_divide(Z,double_divide(identity,double_divide(X,Y))),
inference(equational,[status(thm)],[c20,c57,c60]) ).
cnf(c68,plain,
double_divide(X,double_divide(Y,double_divide(identity,double_divide(Z,X)))) = double_divide(identity,double_divide(Z,Y)),
inference(equational,[status(thm)],[c20,c57]) ).
cnf(c70,plain,
double_divide(X,double_divide(Y,Z)) = double_divide(identity,double_divide(double_divide(X,double_divide(identity,Z)),Y)),
inference(equational,[status(thm)],[c20,c27,c55,c57]) ).
cnf(c71,plain,
double_divide(identity,double_divide(X,double_divide(Y,Z))) = double_divide(double_divide(X,double_divide(identity,Z)),Y),
inference(equational,[status(thm)],[c20,c27,c55,c70]) ).
cnf(c72,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c20,c56,c71]) ).
cnf(c73,plain,
double_divide(double_divide(X,double_divide(Y,identity)),Z) = double_divide(identity,double_divide(X,double_divide(Z,Y))),
inference(equational,[status(thm)],[c20,c27,c47,c71]) ).
cnf(c74,plain,
double_divide(double_divide(X,double_divide(identity,Y)),Z) = double_divide(identity,double_divide(double_divide(Z,Y),X)),
inference(equational,[status(thm)],[c20,c70,c71]) ).
cnf(c75,plain,
double_divide(X,double_divide(Y,Z)) = double_divide(double_divide(Z,double_divide(identity,X)),double_divide(identity,Y)),
inference(equational,[status(thm)],[c28,c51,c57]) ).
cnf(c77,plain,
double_divide(identity,double_divide(X,double_divide(Y,Z))) = double_divide(Z,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c20,c65,c72]) ).
cnf(c85,plain,
double_divide(double_divide(X,double_divide(identity,Y)),double_divide(Z,Y)) = double_divide(identity,double_divide(X,Z)),
inference(equational,[status(thm)],[c20,c27,c55,c68]) ).
cnf(c94,plain,
double_divide(double_divide(X,double_divide(identity,Y)),double_divide(Z,identity)) = double_divide(Y,double_divide(Z,X)),
inference(equational,[status(thm)],[c13,c18,c20,c75]) ).
cnf(c95,plain,
double_divide(double_divide(X,double_divide(Y,identity)),double_divide(identity,Z)) = double_divide(Y,double_divide(Z,X)),
inference(equational,[status(thm)],[c13,c18,c20,c75]) ).
cnf(c96,plain,
double_divide(identity,double_divide(double_divide(X,Y),Z)) = double_divide(Y,double_divide(Z,double_divide(X,identity))),
inference(equational,[status(thm)],[c8,c50,c85,c95]) ).
cnf(c98,plain,
double_divide(X,double_divide(Y,double_divide(Z,identity))) = double_divide(double_divide(Y,double_divide(identity,X)),Z),
inference(equational,[status(thm)],[c74,c96]) ).
cnf(c107,plain,
double_divide(double_divide(X,double_divide(identity,Y)),Z) = double_divide(Y,double_divide(X,double_divide(identity,Z))),
inference(equational,[status(thm)],[c21,c95,c98]) ).
cnf(c109,plain,
double_divide(double_divide(X,double_divide(Y,identity)),Z) = double_divide(Y,double_divide(X,double_divide(identity,Z))),
inference(equational,[status(thm)],[c73,c77]) ).
cnf(c113,plain,
double_divide(X,double_divide(Y,double_divide(Z,double_divide(identity,W)))) = double_divide(double_divide(W,double_divide(X,Z)),double_divide(identity,Y)),
inference(equational,[status(thm)],[c20,c51,c56,c57]) ).
cnf(c114,plain,
double_divide(X,double_divide(Y,double_divide(Z,W))) = double_divide(Z,double_divide(Y,double_divide(X,W))),
inference(equational,[status(thm)],[c20,c21,c58,c107,c113]) ).
cnf(c116,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(Z,Y),double_divide(W,X)),
inference(equational,[status(thm)],[c21,c94,c107,c114]) ).
cnf(c128,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(Z,Y),double_divide(X,W)),
inference(equational,[status(thm)],[c20,c95,c109,c116]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c19,c24,c51,c72,c114,c128]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP575-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:32:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 11.43/11.63 % SZS status Unsatisfiable
% 11.43/11.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------