%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP598-1 : 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 06:44:25 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.44s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 3 RR)
% Number of literals : 13 ( 12 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 23 ( 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(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(inverse(Z),Y))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(double_divide(double_divide(inverse(X),Y),inverse(double_divide(inverse(Z),Y))),inverse(Z)) = X,
inference(equational,[status(thm)],[c2]) ).
cnf(c5,plain,
double_divide(X,inverse(double_divide(double_divide(Y,Z),inverse(double_divide(inverse(W),inverse(double_divide(Y,inverse(double_divide(inverse(X),Z))))))))) = W,
inference(equational,[status(thm)],[c2]) ).
cnf(c6,plain,
double_divide(X,inverse(double_divide(inverse(Y),inverse(X)))) = Y,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
double_divide(double_divide(X,inverse(X)),inverse(Y)) = Y,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
double_divide(inverse(X),inverse(double_divide(Y,inverse(Y)))) = X,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
double_divide(double_divide(X,inverse(Y)),inverse(Y)) = X,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c11,plain,
double_divide(X,inverse(double_divide(Y,inverse(Y)))) = inverse(X),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c12,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c1,c11,c12]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP598-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 14 08:33:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------