%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP586-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 0.71s 0.92s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 3 RR)
% Number of literals : 30 ( 29 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c1,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
double_divide(X,inverse(double_divide(inverse(double_divide(double_divide(X,Y),inverse(Z))),Y))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(X,inverse(double_divide(inverse(Y),Z))) = double_divide(inverse(double_divide(double_divide(double_divide(X,Z),W),inverse(Y))),W),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(inverse(Z),Y))))) = Z,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
double_divide(double_divide(double_divide(inverse(X),Y),inverse(double_divide(inverse(Z),Y))),inverse(Z)) = X,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,plain,
double_divide(X,inverse(double_divide(double_divide(double_divide(inverse(Y),Z),Z),inverse(X)))) = Y,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
double_divide(X,inverse(double_divide(inverse(Y),Z))) = double_divide(double_divide(double_divide(inverse(Y),W),W),inverse(double_divide(X,Z))),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
double_divide(inverse(double_divide(X,inverse(double_divide(inverse(Y),Z)))),W) = double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(X,Z)),W))),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
double_divide(double_divide(double_divide(inverse(X),Y),Y),inverse(double_divide(Z,W))) = double_divide(inverse(double_divide(double_divide(double_divide(Z,W),V),inverse(X))),V),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c10,plain,
double_divide(inverse(double_divide(double_divide(X,Y),inverse(Z))),Y) = double_divide(double_divide(double_divide(inverse(Z),W),W),inverse(X)),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c11,plain,
double_divide(double_divide(double_divide(inverse(double_divide(double_divide(X,Y),inverse(Z))),W),W),inverse(double_divide(X,Y))) = Z,
inference(equational,[status(thm)],[c2,c3,c9]) ).
cnf(c12,plain,
double_divide(double_divide(double_divide(inverse(double_divide(X,inverse(Y))),Z),Z),inverse(X)) = Y,
inference(equational,[status(thm)],[c11]) ).
cnf(c13,plain,
double_divide(double_divide(double_divide(inverse(X),Y),Y),inverse(Z)) = double_divide(double_divide(double_divide(inverse(X),Z),Z),inverse(Z)),
inference(equational,[status(thm)],[c2,c10,c12]) ).
cnf(c15,plain,
double_divide(inverse(double_divide(X,inverse(Y))),inverse(double_divide(inverse(X),Z))) = double_divide(inverse(Y),Z),
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c16,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),Z))) = double_divide(inverse(double_divide(inverse(X),inverse(Y))),Z),
inference(equational,[status(thm)],[c8,c15]) ).
cnf(c17,plain,
double_divide(double_divide(inverse(double_divide(X,inverse(Y))),Z),inverse(double_divide(inverse(Y),Z))) = X,
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c18,plain,
double_divide(double_divide(inverse(X),Y),Y) = double_divide(double_divide(inverse(X),Z),Z),
inference(equational,[status(thm)],[c13,c17]) ).
cnf(c19,plain,
double_divide(double_divide(inverse(X),Y),Y) = inverse(X),
inference(equational,[status(thm)],[c16,c17,c18]) ).
cnf(c21,plain,
double_divide(X,inverse(double_divide(inverse(Y),inverse(X)))) = Y,
inference(equational,[status(thm)],[c6,c19]) ).
cnf(c22,plain,
double_divide(double_divide(X,inverse(X)),inverse(Y)) = Y,
inference(equational,[status(thm)],[c2,c21]) ).
cnf(c23,plain,
double_divide(inverse(double_divide(X,inverse(Y))),inverse(X)) = Y,
inference(equational,[status(thm)],[c12,c19]) ).
cnf(c24,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(Y,inverse(X)),
inference(equational,[status(thm)],[c19,c23]) ).
cnf(c25,plain,
double_divide(X,double_divide(X,inverse(Y))) = inverse(Y),
inference(equational,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
double_divide(X,inverse(inverse(Y))) = double_divide(X,Y),
inference(equational,[status(thm)],[c21,c24,c25]) ).
cnf(c28,plain,
double_divide(X,double_divide(X,Y)) = Y,
inference(equational,[status(thm)],[c6,c19,c24,c26]) ).
cnf(c29,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c26,c28]) ).
cnf(c31,plain,
inverse(X) = double_divide(X,double_divide(Y,inverse(Y))),
inference(equational,[status(thm)],[c22,c24]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c1,c24,c29,c31]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP586-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.31 % Computer : n006.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon Jul 14 08:33:04 EDT 2025
% 0.12/0.31 % CPUTime :
% 0.71/0.92 % SZS status Unsatisfiable
% 0.71/0.92 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------