%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP502-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 31.09s 31.22s
% Output : CNFRefutation 31.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 3 RR)
% Number of literals : 68 ( 67 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 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 : 247 ( 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(double_divide(X,inverse(double_divide(Y,Z))),double_divide(inverse(Y),inverse(double_divide(W,double_divide(X,W))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(double_divide(X,inverse(Y)),double_divide(inverse(double_divide(Z,inverse(double_divide(W,Y)))),inverse(double_divide(V,double_divide(X,V))))) = double_divide(inverse(W),inverse(double_divide(U,double_divide(Z,U)))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(double_divide(X,inverse(double_divide(Y,Z))),double_divide(double_divide(W,inverse(V)),double_divide(inverse(double_divide(X,inverse(double_divide(Y,V)))),inverse(double_divide(U,double_divide(W,U)))))) = Z,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c6,plain,
double_divide(double_divide(double_divide(X,inverse(double_divide(Y,Z))),inverse(double_divide(W,V))),double_divide(inverse(W),inverse(double_divide(double_divide(inverse(Y),inverse(double_divide(U,double_divide(X,U)))),Z)))) = V,
inference(equational,[status(thm)],[c2]) ).
cnf(c7,plain,
double_divide(double_divide(X,inverse(Y)),double_divide(inverse(double_divide(double_divide(Z,inverse(double_divide(W,V))),inverse(double_divide(U,Y)))),inverse(double_divide(U2,double_divide(X,U2))))) = double_divide(inverse(U),inverse(double_divide(double_divide(inverse(W),inverse(double_divide(U3,double_divide(Z,U3)))),V))),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
double_divide(inverse(X),inverse(double_divide(double_divide(inverse(Y),inverse(double_divide(Z,double_divide(W,Z)))),V))) = double_divide(inverse(X),inverse(double_divide(U,double_divide(double_divide(W,inverse(double_divide(Y,V))),U)))),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
inverse(double_divide(double_divide(inverse(X),inverse(double_divide(Y,double_divide(Z,Y)))),W)) = inverse(double_divide(V,double_divide(double_divide(Z,inverse(double_divide(X,W))),V))),
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c11,plain,
double_divide(inverse(X),inverse(double_divide(Y,double_divide(double_divide(Z,inverse(double_divide(W,V))),Y)))) = double_divide(inverse(X),inverse(double_divide(U,double_divide(double_divide(Z,inverse(double_divide(W,V))),U)))),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c12,plain,
inverse(double_divide(X,double_divide(double_divide(Y,inverse(double_divide(Z,W))),X))) = inverse(double_divide(V,double_divide(double_divide(Y,inverse(double_divide(Z,W))),V))),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
inverse(double_divide(X,double_divide(double_divide(Y,inverse(Z)),X))) = inverse(double_divide(W,double_divide(double_divide(Y,inverse(Z)),W))),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c16,plain,
inverse(double_divide(X,double_divide(double_divide(Y,inverse(double_divide(Z,double_divide(inverse(W),inverse(double_divide(V,double_divide(inverse(Z),V))))))),X))) = inverse(double_divide(Y,W)),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c17,plain,
inverse(double_divide(X,double_divide(Y,double_divide(double_divide(Z,inverse(W)),Y)))) = inverse(double_divide(X,double_divide(V,double_divide(double_divide(Z,inverse(W)),V)))),
inference(equational,[status(thm)],[c13,c16]) ).
cnf(c18,plain,
double_divide(X,double_divide(double_divide(Y,inverse(Z)),X)) = double_divide(W,double_divide(double_divide(Y,inverse(Z)),W)),
inference(equational,[status(thm)],[c6,c17]) ).
cnf(c25,plain,
inverse(double_divide(X,double_divide(Y,double_divide(Z,double_divide(double_divide(W,inverse(V)),Z))))) = inverse(double_divide(X,double_divide(Y,double_divide(U,double_divide(double_divide(W,inverse(V)),U))))),
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c26,plain,
double_divide(X,double_divide(Y,double_divide(double_divide(Z,inverse(W)),Y))) = double_divide(X,double_divide(V,double_divide(double_divide(Z,inverse(W)),V))),
inference(equational,[status(thm)],[c6,c25]) ).
cnf(c42,plain,
double_divide(double_divide(X,inverse(double_divide(Y,Z))),double_divide(inverse(W),inverse(double_divide(V,double_divide(X,V))))) = double_divide(double_divide(Y,inverse(double_divide(U,double_divide(inverse(Z),inverse(double_divide(U2,double_divide(inverse(U),U2))))))),W),
inference(equational,[status(thm)],[c2,c16]) ).
cnf(c43,plain,
double_divide(double_divide(X,inverse(double_divide(Y,double_divide(inverse(Z),inverse(double_divide(W,double_divide(inverse(Y),W))))))),X) = Z,
inference(equational,[status(thm)],[c2,c42]) ).
cnf(c44,plain,
double_divide(X,double_divide(Y,X)) = double_divide(Z,double_divide(Y,Z)),
inference(equational,[status(thm)],[c18,c43]) ).
cnf(c45,plain,
inverse(double_divide(X,double_divide(Y,X))) = inverse(double_divide(Z,double_divide(Y,Z))),
inference(equational,[status(thm)],[c13,c43]) ).
cnf(c46,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)],[c26,c43]) ).
cnf(c47,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)],[c17,c43]) ).
cnf(c49,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)],[c44]) ).
cnf(c50,plain,
double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(Y,Z)),X)))) = Z,
inference(equational,[status(thm)],[c2,c16,c43]) ).
cnf(c51,plain,
double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(Z),X)))) = double_divide(inverse(W),inverse(double_divide(inverse(double_divide(W,Z)),Y))),
inference(equational,[status(thm)],[c50]) ).
cnf(c54,plain,
double_divide(X,double_divide(Y,double_divide(inverse(X),inverse(double_divide(inverse(Z),Y))))) = Z,
inference(equational,[status(thm)],[c50,c51]) ).
cnf(c55,plain,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),Y))) = Z,
inference(equational,[status(thm)],[c2,c51]) ).
cnf(c56,plain,
inverse(double_divide(inverse(double_divide(X,Y)),Z)) = double_divide(inverse(Z),inverse(double_divide(inverse(Y),inverse(X)))),
inference(equational,[status(thm)],[c50,c55]) ).
cnf(c57,plain,
inverse(double_divide(X,double_divide(Y,double_divide(Z,double_divide(W,Z))))) = inverse(double_divide(X,double_divide(Y,double_divide(V,double_divide(W,V))))),
inference(equational,[status(thm)],[c16,c47]) ).
cnf(c59,plain,
double_divide(inverse(X),double_divide(inverse(Y),double_divide(inverse(inverse(Z)),inverse(double_divide(inverse(Z),inverse(Y)))))) = X,
inference(equational,[status(thm)],[c44,c55,c56]) ).
cnf(c63,plain,
double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(Z),X)))) = double_divide(W,double_divide(inverse(Y),inverse(double_divide(inverse(Z),W)))),
inference(equational,[status(thm)],[c50,c54]) ).
cnf(c69,plain,
double_divide(double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(Z),X)))),Z) = double_divide(W,double_divide(Y,W)),
inference(equational,[status(thm)],[c44,c54]) ).
cnf(c90,plain,
double_divide(inverse(X),double_divide(Y,double_divide(inverse(inverse(Z)),inverse(double_divide(inverse(Z),Y))))) = X,
inference(equational,[status(thm)],[c59,c63]) ).
cnf(c91,plain,
double_divide(inverse(inverse(X)),inverse(double_divide(inverse(X),Y))) = double_divide(inverse(inverse(Z)),inverse(double_divide(inverse(Z),Y))),
inference(equational,[status(thm)],[c55,c90]) ).
cnf(c92,plain,
double_divide(inverse(inverse(X)),inverse(X)) = double_divide(inverse(inverse(Y)),inverse(Y)),
inference(equational,[status(thm)],[c90,c91]) ).
cnf(c104,plain,
inverse(double_divide(X,double_divide(Y,X))) = inverse(double_divide(double_divide(Z,double_divide(W,Z)),double_divide(Y,double_divide(V,double_divide(W,V))))),
inference(equational,[status(thm)],[c44,c57]) ).
cnf(c105,plain,
inverse(double_divide(double_divide(X,double_divide(Y,X)),Z)) = inverse(double_divide(double_divide(W,double_divide(Y,W)),Z)),
inference(equational,[status(thm)],[c16,c43,c104]) ).
cnf(c106,plain,
double_divide(double_divide(X,double_divide(Y,X)),Z) = double_divide(double_divide(W,double_divide(Y,W)),Z),
inference(equational,[status(thm)],[c90,c105]) ).
cnf(c107,plain,
double_divide(X,double_divide(double_divide(Y,double_divide(Z,Y)),X)) = double_divide(W,double_divide(double_divide(V,double_divide(Z,V)),W)),
inference(equational,[status(thm)],[c44,c106]) ).
cnf(c110,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(Z,Y)),X))) = inverse(double_divide(W,double_divide(double_divide(V,double_divide(Z,V)),W))),
inference(equational,[status(thm)],[c45,c106]) ).
cnf(c111,plain,
double_divide(double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,Z))),W) = double_divide(double_divide(V,double_divide(Y,V)),W),
inference(equational,[status(thm)],[c46,c106]) ).
cnf(c115,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(inverse(Z),double_divide(inverse(inverse(W)),inverse(double_divide(inverse(W),inverse(Y)))))) = double_divide(X,Z),
inference(equational,[status(thm)],[c49,c55,c56]) ).
cnf(c116,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(inverse(inverse(W)),Z))) = double_divide(X,double_divide(inverse(W),inverse(Y))),
inference(equational,[status(thm)],[c44,c115]) ).
cnf(c117,plain,
double_divide(double_divide(X,double_divide(Y,double_divide(inverse(inverse(Z)),Y))),X) = Z,
inference(equational,[status(thm)],[c43,c56,c90,c116]) ).
cnf(c118,plain,
double_divide(double_divide(inverse(inverse(X)),Y),X) = double_divide(Z,double_divide(double_divide(W,double_divide(Y,W)),Z)),
inference(equational,[status(thm)],[c107,c117]) ).
cnf(c119,plain,
double_divide(double_divide(inverse(inverse(X)),Y),X) = double_divide(double_divide(inverse(inverse(Z)),Y),Z),
inference(equational,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
double_divide(inverse(X),X) = double_divide(inverse(Y),Y),
inference(equational,[status(thm)],[c90,c119]) ).
cnf(c121,plain,
double_divide(X,double_divide(inverse(Y),Y)) = double_divide(Z,double_divide(inverse(X),Z)),
inference(equational,[status(thm)],[c44,c120]) ).
cnf(c122,plain,
double_divide(X,double_divide(inverse(Y),Y)) = double_divide(X,double_divide(inverse(Z),Z)),
inference(equational,[status(thm)],[c120,c121]) ).
cnf(c124,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(inverse(inverse(Z)),Y)) = Z,
inference(equational,[status(thm)],[c106,c117]) ).
cnf(c127,plain,
double_divide(double_divide(inverse(inverse(X)),inverse(X)),Y) = double_divide(double_divide(inverse(inverse(Z)),inverse(Y)),Z),
inference(equational,[status(thm)],[c92,c119]) ).
cnf(c134,plain,
inverse(double_divide(double_divide(inverse(inverse(X)),Y),X)) = inverse(double_divide(Z,double_divide(double_divide(W,double_divide(Y,W)),Z))),
inference(equational,[status(thm)],[c110,c117]) ).
cnf(c135,plain,
inverse(double_divide(double_divide(inverse(inverse(X)),Y),X)) = inverse(double_divide(double_divide(inverse(inverse(Z)),Y),Z)),
inference(equational,[status(thm)],[c118,c134]) ).
cnf(c137,plain,
double_divide(double_divide(X,double_divide(inverse(Y),inverse(Z))),inverse(double_divide(X,Z))) = Y,
inference(equational,[status(thm)],[c115,c117]) ).
cnf(c138,plain,
double_divide(inverse(double_divide(inverse(X),X)),Y) = double_divide(double_divide(inverse(inverse(Z)),inverse(Y)),Z),
inference(equational,[status(thm)],[c118,c137]) ).
cnf(c139,plain,
double_divide(double_divide(inverse(X),X),Y) = double_divide(inverse(double_divide(inverse(Z),Z)),Y),
inference(equational,[status(thm)],[c120,c138]) ).
cnf(c140,plain,
double_divide(X,inverse(double_divide(Y,double_divide(inverse(double_divide(Z,X)),Y)))) = Z,
inference(equational,[status(thm)],[c50,c137]) ).
cnf(c141,plain,
double_divide(inverse(X),X) = inverse(double_divide(inverse(Y),Y)),
inference(equational,[status(thm)],[c139,c140]) ).
cnf(c145,plain,
double_divide(X,inverse(double_divide(inverse(Y),Y))) = double_divide(Z,double_divide(inverse(X),Z)),
inference(equational,[status(thm)],[c121,c141]) ).
cnf(c146,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference(equational,[status(thm)],[c69,c117,c145]) ).
cnf(c147,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c124,c146]) ).
cnf(c148,plain,
double_divide(double_divide(X,Y),X) = Y,
inference(equational,[status(thm)],[c111,c146]) ).
cnf(c152,plain,
inverse(X) = double_divide(X,double_divide(inverse(Y),Y)),
inference(equational,[status(thm)],[c122,c146]) ).
cnf(c165,plain,
inverse(double_divide(X,inverse(X))) = inverse(double_divide(inverse(Y),Y)),
inference(equational,[status(thm)],[c127,c147,c148,c152]) ).
cnf(c174,plain,
inverse(double_divide(X,inverse(X))) = inverse(double_divide(Y,inverse(Y))),
inference(equational,[status(thm)],[c135,c147,c148,c165]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c1,c174]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP502-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:30:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 31.09/31.22 % SZS status Unsatisfiable
% 31.09/31.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------