%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP499-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 06:44:11 AM UTC 2025
% Result : Unsatisfiable 8.63s 8.77s
% Output : CNFRefutation 8.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 3 RR)
% Number of literals : 46 ( 45 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c1,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(W,double_divide(Y,W))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(inverse(W),Z))))) = inverse(double_divide(inverse(double_divide(W,double_divide(V,Y))),double_divide(U,double_divide(V,U)))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Z)))),double_divide(W,double_divide(Y,W)))) = Z,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(W,double_divide(Y,W)))) = inverse(double_divide(inverse(double_divide(X,double_divide(V,Z))),double_divide(U,double_divide(V,U)))),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
double_divide(inverse(X),double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(W,double_divide(inverse(X),W)))))) = Z,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c7,plain,
inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(inverse(W),Z)))) = inverse(double_divide(inverse(double_divide(X,Y)),double_divide(V,double_divide(inverse(W),V)))),
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
double_divide(X,double_divide(inverse(Y),X)) = double_divide(Z,double_divide(inverse(Y),Z)),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
double_divide(X,double_divide(Y,X)) = double_divide(Z,double_divide(Y,Z)),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
inverse(double_divide(X,double_divide(Y,double_divide(inverse(Z),Y)))) = inverse(double_divide(X,double_divide(W,double_divide(inverse(Z),W)))),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c11,plain,
inverse(double_divide(X,double_divide(Y,double_divide(Z,Y)))) = inverse(double_divide(X,double_divide(W,double_divide(Z,W)))),
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c12,plain,
double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,Z))) = double_divide(W,double_divide(Y,W)),
inference(equational,[status(thm)],[c9]) ).
cnf(c13,plain,
inverse(double_divide(X,double_divide(Y,X))) = inverse(double_divide(Y,double_divide(Y,Y))),
inference(equational,[status(thm)],[c9,c11,c12]) ).
cnf(c20,plain,
inverse(double_divide(X,double_divide(double_divide(Y,Z),double_divide(W,double_divide(Y,W))))) = inverse(double_divide(X,double_divide(V,double_divide(Z,V)))),
inference(equational,[status(thm)],[c9,c11]) ).
cnf(c22,plain,
double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(W,double_divide(X,W)))))) = Z,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c25,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),double_divide(Z,double_divide(inverse(W),Z))))) = inverse(double_divide(inverse(double_divide(W,Y)),double_divide(V,double_divide(X,V)))),
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c34,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Y)))),double_divide(Z,double_divide(W,Z)))) = W,
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c39,plain,
double_divide(inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(W,double_divide(Y,W)))),Z) = double_divide(V,double_divide(inverse(X),V)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c40,plain,
inverse(double_divide(double_divide(X,Y),double_divide(double_divide(Z,X),double_divide(W,double_divide(Z,W))))) = inverse(double_divide(Y,double_divide(Y,Y))),
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c44,plain,
double_divide(inverse(X),double_divide(inverse(inverse(Y)),inverse(double_divide(inverse(Z),double_divide(X,double_divide(inverse(X),X)))))) = inverse(double_divide(inverse(double_divide(Y,double_divide(W,Z))),double_divide(V,double_divide(W,V)))),
inference(equational,[status(thm)],[c5,c9,c25]) ).
cnf(c45,plain,
double_divide(inverse(X),double_divide(inverse(inverse(Y)),inverse(double_divide(inverse(Y),double_divide(X,double_divide(inverse(X),X)))))) = inverse(double_divide(inverse(double_divide(Z,double_divide(W,Z))),double_divide(V,double_divide(W,V)))),
inference(equational,[status(thm)],[c5,c9,c44]) ).
cnf(c47,plain,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(Y,double_divide(Z,Y))),double_divide(W,double_divide(Z,W))))) = X,
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c48,plain,
double_divide(X,double_divide(Y,double_divide(Z,Y))) = double_divide(X,double_divide(W,double_divide(Z,W))),
inference(equational,[status(thm)],[c11,c47]) ).
cnf(c49,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(inverse(Y),Z))) = double_divide(W,double_divide(inverse(X),W)),
inference(equational,[status(thm)],[c39,c47]) ).
cnf(c59,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(W,double_divide(Y,W)))) = double_divide(V,double_divide(Z,V)),
inference(equational,[status(thm)],[c9,c48]) ).
cnf(c69,plain,
double_divide(inverse(X),inverse(double_divide(Y,double_divide(inverse(X),Y)))) = inverse(double_divide(inverse(double_divide(Z,double_divide(W,Z))),double_divide(V,double_divide(W,V)))),
inference(equational,[status(thm)],[c45,c47]) ).
cnf(c70,plain,
double_divide(double_divide(X,double_divide(inverse(Y),X)),double_divide(Z,double_divide(inverse(W),Z))) = double_divide(V,double_divide(inverse(double_divide(W,Y)),V)),
inference(equational,[status(thm)],[c8,c49]) ).
cnf(c71,plain,
double_divide(X,double_divide(inverse(double_divide(Y,Z)),X)) = double_divide(W,double_divide(double_divide(inverse(Z),inverse(Y)),W)),
inference(equational,[status(thm)],[c59,c70]) ).
cnf(c72,plain,
inverse(double_divide(X,Y)) = double_divide(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c34,c71]) ).
cnf(c83,plain,
double_divide(X,double_divide(double_divide(inverse(Y),inverse(X)),inverse(Y))) = double_divide(double_divide(double_divide(inverse(Z),inverse(W)),inverse(Z)),double_divide(V,double_divide(inverse(inverse(W)),V))),
inference(equational,[status(thm)],[c4,c9,c69,c72]) ).
cnf(c86,plain,
double_divide(inverse(X),double_divide(double_divide(double_divide(inverse(Y),inverse(Z)),inverse(Y)),double_divide(inverse(inverse(W)),double_divide(inverse(inverse(Z)),inverse(inverse(W)))))) = X,
inference(equational,[status(thm)],[c2,c9,c72]) ).
cnf(c88,plain,
double_divide(inverse(X),double_divide(Y,double_divide(double_divide(inverse(Z),inverse(Y)),inverse(Z)))) = X,
inference(equational,[status(thm)],[c83,c86]) ).
cnf(c92,plain,
double_divide(double_divide(double_divide(inverse(X),inverse(inverse(Y))),inverse(X)),inverse(Y)) = double_divide(inverse(Z),inverse(inverse(Z))),
inference(equational,[status(thm)],[c34,c72,c88]) ).
cnf(c94,plain,
double_divide(double_divide(double_divide(inverse(X),inverse(Y)),inverse(X)),double_divide(inverse(inverse(Z)),double_divide(W,double_divide(inverse(inverse(inverse(Z))),W)))) = Y,
inference(equational,[status(thm)],[c4,c11,c48,c72]) ).
cnf(c95,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(W,double_divide(Y,W)))) = double_divide(double_divide(V,Z),double_divide(U,double_divide(V,U))),
inference(equational,[status(thm)],[c12,c48]) ).
cnf(c97,plain,
double_divide(double_divide(double_divide(inverse(X),inverse(X)),inverse(X)),inverse(Y)) = double_divide(double_divide(double_divide(inverse(Z),inverse(X)),inverse(Z)),inverse(Y)),
inference(equational,[status(thm)],[c20,c40,c72,c95]) ).
cnf(c98,plain,
double_divide(double_divide(double_divide(inverse(X),Y),inverse(X)),inverse(Z)) = double_divide(double_divide(double_divide(Y,Y),Y),inverse(Z)),
inference(equational,[status(thm)],[c34,c72,c94,c97]) ).
cnf(c99,plain,
double_divide(double_divide(double_divide(X,Y),X),inverse(Z)) = double_divide(double_divide(double_divide(Y,Y),Y),inverse(Z)),
inference(equational,[status(thm)],[c34,c72,c94,c98]) ).
cnf(c103,plain,
double_divide(double_divide(double_divide(X,inverse(inverse(Y))),X),inverse(Y)) = double_divide(inverse(Z),inverse(inverse(Z))),
inference(equational,[status(thm)],[c92,c99]) ).
cnf(c104,plain,
double_divide(inverse(X),inverse(inverse(X))) = double_divide(inverse(Y),inverse(inverse(Y))),
inference(equational,[status(thm)],[c92,c103]) ).
cnf(c105,plain,
double_divide(X,inverse(X)) = double_divide(inverse(Y),inverse(inverse(Y))),
inference(equational,[status(thm)],[c34,c72,c94,c104]) ).
cnf(c106,plain,
double_divide(X,inverse(X)) = double_divide(Y,inverse(Y)),
inference(equational,[status(thm)],[c34,c72,c94,c105]) ).
cnf(c107,plain,
double_divide(inverse(inverse(X)),inverse(X)) = double_divide(inverse(inverse(Y)),inverse(Y)),
inference(equational,[status(thm)],[c72,c106]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c1,c72,c107]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP499-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:30:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 8.63/8.77 % SZS status Unsatisfiable
% 8.63/8.77 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------