%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP580-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 0.41s 0.57s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 4 RR)
% Number of literals : 27 ( 26 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
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(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(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c4,c6,c21,c26]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP580-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n008.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 08:32:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.41/0.57 % SZS status Unsatisfiable
% 0.41/0.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------