%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP572-1 : 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 06:44:21 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.43s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 4 RR)
% Number of literals : 22 ( 21 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 : 26 ( 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(Y,double_divide(X,Z)),double_divide(Z,identity))),double_divide(identity,identity)) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
double_divide(double_divide(X,identity),double_divide(identity,identity)) = X,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
double_divide(double_divide(identity,double_divide(X,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(X,identity),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
double_divide(identity,identity) = identity,
inference(equational,[status(thm)],[c3,c6,c7]) ).
cnf(c9,plain,
double_divide(double_divide(X,identity),identity) = X,
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c11,plain,
double_divide(double_divide(identity,X),identity) = X,
inference(equational,[status(thm)],[c6,c7,c8,c9]) ).
cnf(c12,plain,
double_divide(X,identity) = double_divide(identity,X),
inference(equational,[status(thm)],[c6,c8,c11]) ).
cnf(c14,plain,
double_divide(X,double_divide(identity,X)) = identity,
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c15,plain,
double_divide(identity,double_divide(X,identity)) = X,
inference(equational,[status(thm)],[c9,c12]) ).
cnf(c16,plain,
double_divide(double_divide(X,Y),Y) = X,
inference(equational,[status(thm)],[c5,c8,c9,c11,c15]) ).
cnf(c17,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference(equational,[status(thm)],[c12,c15]) ).
cnf(c18,plain,
double_divide(identity,double_divide(X,double_divide(double_divide(Y,identity),X))) = Y,
inference(equational,[status(thm)],[c5,c8,c11,c12,c14]) ).
cnf(c19,plain,
double_divide(X,double_divide(double_divide(Y,identity),X)) = double_divide(identity,Y),
inference(equational,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference(equational,[status(thm)],[c9,c15,c19]) ).
cnf(c21,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c16,c20]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c4,c12,c21]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP572-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.31 % Computer : n008.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Jul 14 08:32:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.17/0.43 % SZS status Unsatisfiable
% 0.17/0.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------