%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP571-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 6.43s 6.63s
% Output : CNFRefutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 4 RR)
% Number of literals : 56 ( 55 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 : 108 ( 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(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(c23,plain,
double_divide(identity,double_divide(X,double_divide(identity,double_divide(Y,double_divide(X,identity))))) = Y,
inference(equational,[status(thm)],[c5,c8,c12]) ).
cnf(c24,plain,
double_divide(identity,double_divide(X,double_divide(identity,Y))) = double_divide(Y,double_divide(X,identity)),
inference(equational,[status(thm)],[c16,c23]) ).
cnf(c25,plain,
double_divide(X,double_divide(identity,double_divide(Y,double_divide(X,identity)))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c11,c23]) ).
cnf(c26,plain,
double_divide(X,double_divide(identity,Y)) = double_divide(identity,double_divide(Y,double_divide(X,identity))),
inference(equational,[status(thm)],[c12,c16,c25]) ).
cnf(c28,plain,
double_divide(identity,double_divide(X,Y)) = double_divide(double_divide(identity,Y),double_divide(X,identity)),
inference(equational,[status(thm)],[c8,c15,c24,c26]) ).
cnf(c30,plain,
double_divide(X,double_divide(identity,Y)) = double_divide(identity,double_divide(Y,double_divide(identity,X))),
inference(equational,[status(thm)],[c12,c24]) ).
cnf(c31,plain,
double_divide(identity,double_divide(X,Y)) = double_divide(double_divide(identity,Y),double_divide(identity,X)),
inference(equational,[status(thm)],[c11,c26]) ).
cnf(c33,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(Y,X))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c11,c25]) ).
cnf(c34,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(Y,X))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c9,c25]) ).
cnf(c38,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(double_divide(Y,identity),X)),
inference(equational,[status(thm)],[c16,c28]) ).
cnf(c39,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(double_divide(identity,Y),X)),
inference(equational,[status(thm)],[c8,c15,c30,c31]) ).
cnf(c40,plain,
double_divide(identity,double_divide(double_divide(identity,X),double_divide(identity,double_divide(Y,X)))) = Y,
inference(equational,[status(thm)],[c5,c8,c11,c12]) ).
cnf(c41,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(Y,X))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c17,c40]) ).
cnf(c42,plain,
double_divide(double_divide(X,identity),double_divide(identity,double_divide(X,Y))) = double_divide(identity,Y),
inference(equational,[status(thm)],[c5,c8,c11,c12,c33]) ).
cnf(c43,plain,
double_divide(identity,double_divide(double_divide(identity,X),double_divide(double_divide(X,identity),Y))) = double_divide(Y,identity),
inference(equational,[status(thm)],[c18,c33,c39]) ).
cnf(c44,plain,
double_divide(X,double_divide(Y,identity)) = double_divide(identity,double_divide(double_divide(X,identity),Y)),
inference(equational,[status(thm)],[c11,c42,c43]) ).
cnf(c45,plain,
double_divide(identity,double_divide(X,double_divide(Y,identity))) = double_divide(double_divide(X,identity),Y),
inference(equational,[status(thm)],[c17,c44]) ).
cnf(c47,plain,
double_divide(double_divide(identity,X),double_divide(Y,identity)) = double_divide(identity,double_divide(X,Y)),
inference(equational,[status(thm)],[c11,c44]) ).
cnf(c49,plain,
double_divide(identity,double_divide(double_divide(X,identity),Y)) = double_divide(X,double_divide(identity,Y)),
inference(equational,[status(thm)],[c33,c41,c44]) ).
cnf(c55,plain,
double_divide(double_divide(X,identity),Y) = double_divide(identity,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c12,c45]) ).
cnf(c56,plain,
double_divide(identity,double_divide(double_divide(identity,X),Y)) = double_divide(X,double_divide(identity,Y)),
inference(equational,[status(thm)],[c12,c49]) ).
cnf(c58,plain,
double_divide(double_divide(identity,X),Y) = double_divide(identity,double_divide(X,double_divide(identity,Y))),
inference(equational,[status(thm)],[c8,c17,c38,c47]) ).
cnf(c59,plain,
double_divide(identity,double_divide(X,double_divide(Y,double_divide(Z,identity)))) = double_divide(Y,double_divide(X,Z)),
inference(equational,[status(thm)],[c5,c8,c12,c16]) ).
cnf(c60,plain,
double_divide(identity,double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(X,double_divide(Z,identity))),
inference(equational,[status(thm)],[c16,c59]) ).
cnf(c61,plain,
double_divide(identity,double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(X,double_divide(identity,Z))),
inference(equational,[status(thm)],[c11,c59]) ).
cnf(c65,plain,
double_divide(X,double_divide(Y,double_divide(identity,Z))) = double_divide(identity,double_divide(double_divide(X,Z),Y)),
inference(equational,[status(thm)],[c28,c47,c61]) ).
cnf(c66,plain,
double_divide(identity,double_divide(X,double_divide(Y,Z))) = double_divide(double_divide(X,double_divide(Z,identity)),Y),
inference(equational,[status(thm)],[c21,c60]) ).
cnf(c72,plain,
double_divide(identity,double_divide(double_divide(X,Y),Z)) = double_divide(double_divide(Z,double_divide(identity,Y)),X),
inference(equational,[status(thm)],[c21,c65]) ).
cnf(c77,plain,
double_divide(X,double_divide(Y,identity)) = double_divide(Z,double_divide(identity,double_divide(X,double_divide(Y,Z)))),
inference(equational,[status(thm)],[c11,c17,c34,c55,c59]) ).
cnf(c85,plain,
double_divide(double_divide(X,double_divide(Y,identity)),Z) = double_divide(identity,double_divide(X,double_divide(Y,Z))),
inference(equational,[status(thm)],[c21,c66]) ).
cnf(c97,plain,
double_divide(X,double_divide(identity,double_divide(double_divide(Y,X),Z))) = double_divide(Z,double_divide(Y,identity)),
inference(equational,[status(thm)],[c28,c47,c77]) ).
cnf(c99,plain,
double_divide(double_divide(X,Y),double_divide(Z,identity)) = double_divide(double_divide(Z,Y),double_divide(X,identity)),
inference(equational,[status(thm)],[c77,c97]) ).
cnf(c100,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(W,X),double_divide(Z,Y)),
inference(equational,[status(thm)],[c15,c17,c72,c85,c99]) ).
cnf(c138,plain,
double_divide(double_divide(X,Y),double_divide(Z,W)) = double_divide(double_divide(Z,X),double_divide(Y,W)),
inference(equational,[status(thm)],[c21,c100]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c12,c21,c56,c58,c138]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP571-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n001.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 08:32:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.43/6.63 % SZS status Unsatisfiable
% 6.43/6.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------