%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP579-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 3.39s 3.58s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 4 RR)
% Number of literals : 47 ( 46 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 87 ( 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(double_divide(Y,X),Z),double_divide(Y,identity))),double_divide(identity,identity)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
double_divide(double_divide(X,double_divide(identity,double_divide(Y,identity))),double_divide(identity,identity)) = double_divide(double_divide(Y,X),identity),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
double_divide(double_divide(X,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,X),identity),
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
double_divide(double_divide(identity,X),double_divide(double_divide(X,identity),double_divide(identity,identity))) = identity,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
double_divide(double_divide(double_divide(X,double_divide(identity,Y)),Z),double_divide(X,identity)) = double_divide(double_divide(Y,Z),double_divide(identity,identity)),
inference(equational,[status(thm)],[c5]) ).
cnf(c10,plain,
double_divide(double_divide(double_divide(X,identity),Y),double_divide(X,identity)) = double_divide(double_divide(double_divide(identity,identity),Y),double_divide(identity,identity)),
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c12,plain,
double_divide(double_divide(X,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,X))),identity),
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c13,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,X))),identity) = double_divide(double_divide(identity,X),identity),
inference(equational,[status(thm)],[c7,c12]) ).
cnf(c14,plain,
double_divide(double_divide(X,double_divide(identity,double_divide(Y,identity))),double_divide(identity,identity)) = double_divide(double_divide(Y,double_divide(identity,double_divide(identity,X))),identity),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c15,plain,
double_divide(double_divide(X,double_divide(identity,double_divide(identity,Y))),identity) = double_divide(double_divide(X,Y),identity),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c16,plain,
double_divide(double_divide(double_divide(X,Y),identity),double_divide(X,identity)) = double_divide(double_divide(identity,double_divide(identity,Y)),identity),
inference(equational,[status(thm)],[c9,c12,c13,c15]) ).
cnf(c17,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X,identity))),identity) = double_divide(double_divide(identity,identity),double_divide(X,identity)),
inference(equational,[status(thm)],[c3,c16]) ).
cnf(c18,plain,
double_divide(double_divide(double_divide(X,Y),identity),double_divide(Y,identity)) = double_divide(double_divide(double_divide(X,identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c19,plain,
double_divide(double_divide(double_divide(X,Y),identity),double_divide(Y,identity)) = double_divide(double_divide(identity,double_divide(identity,X)),identity),
inference(equational,[status(thm)],[c7,c16,c18]) ).
cnf(c20,plain,
double_divide(double_divide(identity,X),identity) = double_divide(double_divide(identity,identity),double_divide(X,identity)),
inference(equational,[status(thm)],[c13,c16,c17,c18,c19]) ).
cnf(c21,plain,
double_divide(identity,identity) = identity,
inference(equational,[status(thm)],[c3,c20]) ).
cnf(c22,plain,
double_divide(double_divide(identity,X),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
double_divide(double_divide(X,identity),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c12,c13,c21,c22]) ).
cnf(c24,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,identity))) = identity,
inference(equational,[status(thm)],[c8,c21,c23]) ).
cnf(c25,plain,
double_divide(double_divide(X,double_divide(identity,X)),identity) = identity,
inference(equational,[status(thm)],[c14,c15,c21,c24]) ).
cnf(c26,plain,
double_divide(identity,double_divide(X,identity)) = X,
inference(equational,[status(thm)],[c5,c17,c21,c22,c25]) ).
cnf(c27,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c6,c21,c26]) ).
cnf(c29,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference(equational,[status(thm)],[c20,c21,c22,c26,c27]) ).
cnf(c30,plain,
double_divide(double_divide(identity,double_divide(X,Y)),double_divide(Y,identity)) = double_divide(X,identity),
inference(equational,[status(thm)],[c12,c13,c16,c18,c27,c29]) ).
cnf(c31,plain,
double_divide(X,double_divide(X,Y)) = Y,
inference(equational,[status(thm)],[c16,c22,c23,c26,c30]) ).
cnf(c33,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(double_divide(Y,identity),X)),
inference(equational,[status(thm)],[c10,c21,c22,c23,c26,c27,c30]) ).
cnf(c34,plain,
double_divide(double_divide(X,identity),double_divide(Y,identity)) = double_divide(identity,double_divide(Y,X)),
inference(equational,[status(thm)],[c16,c27,c29,c31]) ).
cnf(c37,plain,
double_divide(double_divide(X,identity),double_divide(identity,Y)) = double_divide(identity,double_divide(Y,X)),
inference(equational,[status(thm)],[c9,c21,c22,c26,c27,c33]) ).
cnf(c38,plain,
double_divide(double_divide(X,identity),Y) = double_divide(identity,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c6,c21,c22,c26,c27,c33]) ).
cnf(c40,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c14,c21,c22,c23,c26,c27,c37]) ).
cnf(c47,plain,
double_divide(double_divide(X,Y),Z) = double_divide(identity,double_divide(double_divide(Z,double_divide(identity,X)),Y)),
inference(equational,[status(thm)],[c9,c21,c23,c26,c27,c30]) ).
cnf(c49,plain,
double_divide(double_divide(X,double_divide(identity,Y)),Z) = double_divide(identity,double_divide(double_divide(Y,Z),X)),
inference(equational,[status(thm)],[c15,c22,c26,c29,c47]) ).
cnf(c50,plain,
double_divide(double_divide(X,double_divide(identity,Y)),Z) = double_divide(identity,double_divide(X,double_divide(Y,Z))),
inference(equational,[status(thm)],[c6,c21,c22,c26,c27,c47]) ).
cnf(c51,plain,
double_divide(double_divide(X,double_divide(Y,Z)),W) = double_divide(Z,double_divide(X,double_divide(Y,W))),
inference(equational,[status(thm)],[c29,c49,c50]) ).
cnf(c53,plain,
double_divide(double_divide(X,Y),double_divide(identity,Z)) = double_divide(double_divide(Y,Z),double_divide(X,identity)),
inference(equational,[status(thm)],[c29,c38,c40,c47]) ).
cnf(c59,plain,
double_divide(identity,double_divide(double_divide(X,Y),Z)) = double_divide(X,double_divide(Z,double_divide(identity,Y))),
inference(equational,[status(thm)],[c22,c26,c29,c47,c51]) ).
cnf(c60,plain,
double_divide(double_divide(X,Y),double_divide(identity,Z)) = double_divide(double_divide(Z,Y),double_divide(X,identity)),
inference(equational,[status(thm)],[c26,c29,c34,c40,c49]) ).
cnf(c67,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(X,W),double_divide(Z,Y)),
inference(equational,[status(thm)],[c29,c47,c51,c60]) ).
cnf(c69,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(Z,X),double_divide(W,Y)),
inference(equational,[status(thm)],[c29,c51,c53,c59]) ).
cnf(c102,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(Y,Z),double_divide(X,W)),
inference(equational,[status(thm)],[c67,c69]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c6,c15,c17,c21,c26,c27,c29,c40,c102]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP579-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:32:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.39/3.58 % SZS status Unsatisfiable
% 3.39/3.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------