%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP498-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 06:44:11 AM UTC 2025
% Result : Unsatisfiable 1.07s 1.24s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 4 RR)
% Number of literals : 32 ( 31 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 50 ( 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(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
double_divide(identity,identity) = identity,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
double_divide(identity,double_divide(double_divide(X,double_divide(Y,X)),identity)) = Y,
inference(equational,[status(thm)],[c3,c5,c6]) ).
cnf(c8,plain,
double_divide(identity,double_divide(X,identity)) = double_divide(Y,double_divide(X,Y)),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,plain,
double_divide(X,double_divide(identity,X)) = identity,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c10,plain,
double_divide(double_divide(X,identity),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c11,plain,
double_divide(double_divide(identity,X),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c12,plain,
double_divide(X,identity) = double_divide(identity,X),
inference(equational,[status(thm)],[c7,c10,c11]) ).
cnf(c13,plain,
double_divide(identity,double_divide(identity,X)) = double_divide(Y,double_divide(X,Y)),
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c15,plain,
double_divide(identity,double_divide(identity,double_divide(X,double_divide(Y,X)))) = Y,
inference(equational,[status(thm)],[c7,c8,c13]) ).
cnf(c20,plain,
double_divide(double_divide(X,Y),double_divide(identity,double_divide(X,identity))) = double_divide(identity,double_divide(Y,identity)),
inference(equational,[status(thm)],[c8]) ).
cnf(c22,plain,
double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,Z))) = double_divide(identity,double_divide(Y,identity)),
inference(equational,[status(thm)],[c8,c20]) ).
cnf(c33,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X,identity))),double_divide(identity,double_divide(X,identity))) = identity,
inference(equational,[status(thm)],[c5,c6,c10]) ).
cnf(c34,plain,
double_divide(double_divide(identity,X),X) = identity,
inference(equational,[status(thm)],[c7,c33]) ).
cnf(c35,plain,
double_divide(identity,double_divide(X,identity)) = X,
inference(equational,[status(thm)],[c11,c15,c20,c34]) ).
cnf(c36,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference(equational,[status(thm)],[c8,c35]) ).
cnf(c37,plain,
double_divide(double_divide(X,Y),X) = Y,
inference(equational,[status(thm)],[c20,c35]) ).
cnf(c38,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference(equational,[status(thm)],[c15,c35]) ).
cnf(c39,plain,
double_divide(double_divide(double_divide(identity,X),Y),double_divide(X,identity)) = Y,
inference(equational,[status(thm)],[c22,c34,c35]) ).
cnf(c44,plain,
double_divide(double_divide(identity,double_divide(X,double_divide(Y,Z))),Y) = double_divide(identity,double_divide(Z,double_divide(X,identity))),
inference(equational,[status(thm)],[c5,c12,c36]) ).
cnf(c46,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(double_divide(identity,Y),X)),
inference(equational,[status(thm)],[c35,c39,c44]) ).
cnf(c47,plain,
double_divide(X,double_divide(identity,Y)) = double_divide(identity,double_divide(Y,double_divide(X,identity))),
inference(equational,[status(thm)],[c34,c35,c44]) ).
cnf(c58,plain,
double_divide(X,Y) = double_divide(identity,double_divide(double_divide(identity,Y),double_divide(X,identity))),
inference(equational,[status(thm)],[c11,c13,c35,c36,c44]) ).
cnf(c73,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(Z,identity)))) = double_divide(identity,double_divide(Z,double_divide(X,Y))),
inference(equational,[status(thm)],[c5,c12,c37]) ).
cnf(c75,plain,
double_divide(double_divide(identity,double_divide(X,Y)),Z) = double_divide(X,double_divide(identity,double_divide(Y,Z))),
inference(equational,[status(thm)],[c11,c35,c46,c73]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c12,c38,c46,c47,c58,c75]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP498-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:30:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.07/1.24 % SZS status Unsatisfiable
% 1.07/1.24 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------