%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP583-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 06:44:23 AM UTC 2025
% Result : Unsatisfiable 3.37s 3.58s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% 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 : 8 ( 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 : 79 ( 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(identity,Y),double_divide(Z,double_divide(Y,X)))),double_divide(identity,identity)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X),identity)),double_divide(identity,identity)) = X,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
double_divide(identity,identity) = identity,
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X),identity)),identity) = X,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X,identity))),identity) = X,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c10,plain,
double_divide(double_divide(identity,X),identity) = double_divide(identity,double_divide(X,identity)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X,identity))),X) = identity,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c12,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,identity))) = identity,
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c13,plain,
double_divide(double_divide(double_divide(X,identity),identity),identity) = double_divide(identity,X),
inference(equational,[status(thm)],[c5,c7,c12]) ).
cnf(c14,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X,identity),identity))) = X,
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c15,plain,
double_divide(X,identity) = double_divide(identity,double_divide(identity,double_divide(identity,X))),
inference(equational,[status(thm)],[c10,c13,c14]) ).
cnf(c16,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X,identity)))))) = X,
inference(equational,[status(thm)],[c8,c10,c15]) ).
cnf(c18,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,X))))))) = Y,
inference(equational,[status(thm)],[c5,c7,c15]) ).
cnf(c20,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X,double_divide(identity,double_divide(Y,identity)))))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(Y,X)))))),
inference(equational,[status(thm)],[c5,c7,c10,c11,c15]) ).
cnf(c21,plain,
double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X)))) = double_divide(identity,double_divide(identity,double_divide(Z,identity))),
inference(equational,[status(thm)],[c5,c7,c10]) ).
cnf(c22,plain,
double_divide(double_divide(identity,X),double_divide(Y,double_divide(X,identity))) = double_divide(identity,double_divide(Y,identity)),
inference(equational,[status(thm)],[c6,c7,c9,c10,c21]) ).
cnf(c23,plain,
double_divide(X,double_divide(identity,double_divide(Y,identity))) = double_divide(identity,double_divide(identity,double_divide(Y,X))),
inference(equational,[status(thm)],[c9,c10,c11,c21]) ).
cnf(c24,plain,
double_divide(X,double_divide(identity,X)) = identity,
inference(equational,[status(thm)],[c7,c9,c11,c23]) ).
cnf(c25,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X,identity)))) = X,
inference(equational,[status(thm)],[c5,c7,c15,c24]) ).
cnf(c26,plain,
double_divide(X,identity) = double_divide(identity,X),
inference(equational,[status(thm)],[c9,c10,c25]) ).
cnf(c28,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference(equational,[status(thm)],[c16,c25]) ).
cnf(c30,plain,
double_divide(identity,double_divide(X,identity)) = X,
inference(equational,[status(thm)],[c16,c28]) ).
cnf(c31,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c23,c28,c30]) ).
cnf(c32,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference(equational,[status(thm)],[c9,c22,c25,c30]) ).
cnf(c33,plain,
double_divide(X,double_divide(X,Y)) = Y,
inference(equational,[status(thm)],[c23,c28,c30,c32]) ).
cnf(c34,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,X)))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c3,c7,c21,c30]) ).
cnf(c38,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(X,Y))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c23,c28,c34]) ).
cnf(c39,plain,
double_divide(X,double_divide(identity,Y)) = double_divide(identity,double_divide(Y,double_divide(X,identity))),
inference(equational,[status(thm)],[c10,c22,c30,c38]) ).
cnf(c43,plain,
double_divide(X,double_divide(Y,identity)) = double_divide(identity,double_divide(double_divide(identity,X),Y)),
inference(equational,[status(thm)],[c20,c28,c30,c39]) ).
cnf(c47,plain,
double_divide(double_divide(X,identity),Y) = double_divide(identity,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c23,c30,c39]) ).
cnf(c53,plain,
double_divide(identity,double_divide(double_divide(identity,X),Y)) = double_divide(X,double_divide(identity,Y)),
inference(equational,[status(thm)],[c15,c28,c43]) ).
cnf(c54,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c7,c13,c30,c47]) ).
cnf(c55,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,double_divide(Z,double_divide(Y,X)))))) = double_divide(Z,identity),
inference(equational,[status(thm)],[c5,c7,c28,c54]) ).
cnf(c56,plain,
double_divide(X,double_divide(Y,double_divide(identity,double_divide(X,double_divide(Y,Z))))) = double_divide(Z,identity),
inference(equational,[status(thm)],[c28,c30,c31,c55]) ).
cnf(c64,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,Z)))) = double_divide(Z,double_divide(Y,double_divide(identity,double_divide(Z,double_divide(Y,double_divide(Z,double_divide(Y,X))))))),
inference(equational,[status(thm)],[c21,c28,c30,c54,c56]) ).
cnf(c67,plain,
double_divide(X,double_divide(Y,double_divide(identity,double_divide(X,double_divide(Y,Z))))) = double_divide(identity,Z),
inference(equational,[status(thm)],[c7,c21,c30,c31,c55]) ).
cnf(c73,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,Z)))) = double_divide(identity,double_divide(Z,double_divide(Y,X))),
inference(equational,[status(thm)],[c21,c28,c30,c54,c67]) ).
cnf(c74,plain,
double_divide(X,double_divide(identity,double_divide(Y,Z))) = double_divide(Z,double_divide(identity,double_divide(Y,X))),
inference(equational,[status(thm)],[c18,c28,c34,c54,c73]) ).
cnf(c91,plain,
double_divide(double_divide(X,double_divide(identity,Y)),double_divide(identity,Z)) = double_divide(Y,double_divide(X,Z)),
inference(equational,[status(thm)],[c28,c33,c64,c73]) ).
cnf(c92,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(X,Z),double_divide(Y,W)),
inference(equational,[status(thm)],[c74,c91]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c10,c15,c23,c26,c28,c53,c54,c92]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP583-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n014.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 08:33:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.37/3.58 % SZS status Unsatisfiable
% 3.37/3.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------