%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP489-1 : TPTP v9.0.0. Released v2.6.0.
% 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 06:44:10 AM UTC 2025
% Result : Unsatisfiable 12.35s 12.56s
% Output : CNFRefutation 12.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 6 RR)
% Number of literals : 47 ( 46 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 69 ( 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(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),double_divide(Y,Z))),Y),identity)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
double_divide(X,double_divide(double_divide(double_divide(identity,identity),double_divide(X,identity)),identity)) = identity,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),identity)) = identity,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
double_divide(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),identity)),Y),identity)) = double_divide(Y,identity),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c10,plain,
double_divide(double_divide(identity,X),double_divide(double_divide(X,identity),identity)) = identity,
inference(equational,[status(thm)],[c6,c8,c9]) ).
cnf(c11,plain,
double_divide(double_divide(identity,X),identity) = double_divide(double_divide(X,identity),identity),
inference(equational,[status(thm)],[c5,c9,c10]) ).
cnf(c13,plain,
double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),identity)) = identity,
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c14,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(identity,X),identity)) = double_divide(X,identity),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c15,plain,
double_divide(identity,identity) = identity,
inference(equational,[status(thm)],[c10,c14]) ).
cnf(c16,plain,
double_divide(identity,double_divide(double_divide(identity,X),identity)) = double_divide(X,identity),
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c17,plain,
double_divide(identity,double_divide(double_divide(X,identity),identity)) = double_divide(X,identity),
inference(equational,[status(thm)],[c11,c16]) ).
cnf(c18,plain,
double_divide(double_divide(identity,double_divide(X,identity)),identity) = double_divide(X,identity),
inference(equational,[status(thm)],[c11,c16,c17]) ).
cnf(c19,plain,
double_divide(double_divide(X,identity),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
double_divide(double_divide(identity,X),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c16,c18,c19]) ).
cnf(c21,plain,
double_divide(identity,double_divide(identity,double_divide(X,identity))) = double_divide(X,identity),
inference(equational,[status(thm)],[c11,c14,c15,c19]) ).
cnf(c22,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(X,identity))) = identity,
inference(equational,[status(thm)],[c13,c18,c19,c21]) ).
cnf(c24,plain,
double_divide(identity,double_divide(X,identity)) = X,
inference(equational,[status(thm)],[c5,c15,c17,c20,c21]) ).
cnf(c25,plain,
double_divide(identity,X) = double_divide(X,identity),
inference(equational,[status(thm)],[c16,c24]) ).
cnf(c26,plain,
double_divide(double_divide(X,identity),X) = identity,
inference(equational,[status(thm)],[c22,c24]) ).
cnf(c27,plain,
double_divide(double_divide(X,Y),X) = Y,
inference(equational,[status(thm)],[c5,c15,c20,c24,c26]) ).
cnf(c30,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference(equational,[status(thm)],[c24,c25]) ).
cnf(c32,plain,
double_divide(X,double_divide(identity,double_divide(double_divide(X,identity),Y))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c9,c17,c25]) ).
cnf(c34,plain,
double_divide(double_divide(X,identity),Y) = double_divide(identity,double_divide(double_divide(identity,Y),X)),
inference(equational,[status(thm)],[c9,c19,c24,c25,c27]) ).
cnf(c36,plain,
double_divide(X,double_divide(X,double_divide(identity,double_divide(double_divide(X,identity),double_divide(double_divide(X,identity),Y))))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c9,c24,c32]) ).
cnf(c37,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(X,Y))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c11,c20,c24,c32]) ).
cnf(c38,plain,
double_divide(double_divide(X,identity),double_divide(Y,identity)) = double_divide(identity,double_divide(Y,X)),
inference(equational,[status(thm)],[c27,c37]) ).
cnf(c39,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,Y))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c11,c19,c24,c32]) ).
cnf(c48,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(double_divide(identity,Y),X)),
inference(equational,[status(thm)],[c25,c34]) ).
cnf(c53,plain,
double_divide(X,double_divide(X,double_divide(X,double_divide(identity,double_divide(double_divide(X,identity),double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),Y))))))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c9,c20,c24,c25,c36]) ).
cnf(c56,plain,
double_divide(X,double_divide(identity,double_divide(double_divide(X,identity),Y))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c25,c32]) ).
cnf(c57,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,Y))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c25,c39]) ).
cnf(c58,plain,
double_divide(X,double_divide(X,double_divide(identity,double_divide(double_divide(identity,X),double_divide(double_divide(identity,X),Y))))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c9,c24,c25,c53,c56]) ).
cnf(c64,plain,
double_divide(double_divide(identity,X),Y) = double_divide(Y,double_divide(Y,double_divide(identity,double_divide(double_divide(identity,Y),double_divide(double_divide(identity,Y),double_divide(double_divide(identity,Y),X)))))),
inference(equational,[status(thm)],[c16,c24,c48,c58]) ).
cnf(c66,plain,
double_divide(X,double_divide(identity,double_divide(double_divide(identity,X),Y))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c30,c57]) ).
cnf(c74,plain,
double_divide(X,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(X,identity),Y)),Z))) = double_divide(double_divide(identity,W),double_divide(double_divide(Z,identity),double_divide(W,Y))),
inference(equational,[status(thm)],[c5,c20,c25,c30,c58,c64,c66]) ).
cnf(c75,plain,
double_divide(X,Y) = double_divide(double_divide(identity,Z),double_divide(double_divide(Y,identity),double_divide(Z,X))),
inference(equational,[status(thm)],[c6,c15,c19,c20,c24,c30,c74]) ).
cnf(c76,plain,
double_divide(identity,double_divide(double_divide(X,identity),double_divide(identity,Y))) = double_divide(Y,X),
inference(equational,[status(thm)],[c3,c15,c75]) ).
cnf(c81,plain,
double_divide(X,double_divide(identity,double_divide(Y,Z))) = double_divide(identity,double_divide(double_divide(Z,identity),double_divide(X,Y))),
inference(equational,[status(thm)],[c9,c19,c24,c25,c58,c66,c75]) ).
cnf(c82,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)],[c24,c25,c30,c76,c81]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c25,c34,c38,c76,c82]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP489-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 14 08:30:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 12.35/12.56 % SZS status Unsatisfiable
% 12.35/12.56 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------