%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP492-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 06:44:10 AM UTC 2025
% Result : Unsatisfiable 1.30s 1.47s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 4 RR)
% Number of literals : 35 ( 34 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 : 51 ( 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,X),double_divide(identity,double_divide(double_divide(double_divide(X,Y),identity),double_divide(Z,Y)))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
double_divide(double_divide(identity,X),double_divide(identity,identity)) = double_divide(double_divide(X,identity),identity),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))) = identity,
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
double_divide(double_divide(identity,X),double_divide(identity,identity)) = double_divide(identity,double_divide(X,double_divide(identity,identity))),
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
double_divide(double_divide(X,identity),identity) = double_divide(identity,double_divide(X,double_divide(identity,identity))),
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
double_divide(double_divide(identity,double_divide(X,double_divide(identity,identity))),identity) = double_divide(identity,double_divide(double_divide(X,identity),double_divide(identity,identity))),
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c11,plain,
double_divide(identity,identity) = identity,
inference(equational,[status(thm)],[c3,c8,c9,c10]) ).
cnf(c12,plain,
double_divide(double_divide(identity,X),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c14,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X,identity)))) = X,
inference(equational,[status(thm)],[c5,c11]) ).
cnf(c15,plain,
double_divide(X,identity) = double_divide(identity,X),
inference(equational,[status(thm)],[c9,c11,c12,c14]) ).
cnf(c16,plain,
double_divide(X,double_divide(identity,X)) = identity,
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c17,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,identity))) = identity,
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c18,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X,identity))),X) = identity,
inference(equational,[status(thm)],[c9,c10,c11,c14,c17]) ).
cnf(c21,plain,
double_divide(X,double_divide(identity,double_divide(identity,double_divide(Y,X)))) = Y,
inference(equational,[status(thm)],[c5,c11,c14,c18]) ).
cnf(c24,plain,
double_divide(identity,double_divide(X,identity)) = X,
inference(equational,[status(thm)],[c11,c12,c16,c21]) ).
cnf(c25,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference(equational,[status(thm)],[c15,c24]) ).
cnf(c30,plain,
double_divide(double_divide(identity,X),double_divide(Y,double_divide(X,identity))) = Y,
inference(equational,[status(thm)],[c3,c5,c11,c25]) ).
cnf(c31,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,double_divide(Y,identity)))) = Y,
inference(equational,[status(thm)],[c3,c5,c12,c15,c25]) ).
cnf(c32,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,Y))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c6,c11,c12,c24,c31]) ).
cnf(c33,plain,
double_divide(X,double_divide(identity,Y)) = double_divide(identity,double_divide(Y,double_divide(X,identity))),
inference(equational,[status(thm)],[c15,c25,c30,c32]) ).
cnf(c36,plain,
double_divide(identity,double_divide(X,Y)) = double_divide(double_divide(Y,identity),double_divide(identity,X)),
inference(equational,[status(thm)],[c6,c11,c12,c24,c33]) ).
cnf(c38,plain,
double_divide(double_divide(X,identity),Y) = double_divide(identity,double_divide(double_divide(identity,Y),X)),
inference(equational,[status(thm)],[c11,c24,c33,c36]) ).
cnf(c40,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,Y))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c9,c10,c11,c24,c32]) ).
cnf(c50,plain,
double_divide(X,Y) = double_divide(identity,double_divide(double_divide(identity,Y),double_divide(X,identity))),
inference(equational,[status(thm)],[c11,c24,c33]) ).
cnf(c52,plain,
double_divide(double_divide(identity,double_divide(X,Y)),double_divide(Z,Y)) = double_divide(X,double_divide(identity,Z)),
inference(equational,[status(thm)],[c5,c15,c25,c40]) ).
cnf(c67,plain,
double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,identity))) = double_divide(double_divide(identity,Y),double_divide(identity,Z)),
inference(equational,[status(thm)],[c50,c52]) ).
cnf(c77,plain,
double_divide(double_divide(X,Y),double_divide(identity,double_divide(X,Z))) = double_divide(double_divide(identity,Y),Z),
inference(equational,[status(thm)],[c24,c38,c67]) ).
cnf(c78,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)],[c21,c25,c77]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c15,c25,c33,c36,c50,c78]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP492-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:30:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.30/1.47 % SZS status Unsatisfiable
% 1.30/1.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------