%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP608-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 06:44:26 AM UTC 2025
% Result : Unsatisfiable 0.73s 0.92s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 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 : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c1,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
double_divide(inverse(double_divide(X,inverse(double_divide(inverse(Y),double_divide(X,Z))))),Z) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(inverse(double_divide(X,inverse(Y))),Z) = double_divide(W,inverse(double_divide(inverse(Y),double_divide(W,double_divide(X,Z))))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(inverse(double_divide(inverse(double_divide(X,inverse(Y))),Z)),double_divide(X,Z)) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
double_divide(inverse(X),double_divide(inverse(double_divide(Y,inverse(X))),double_divide(Y,inverse(Z)))) = Z,
inference(equational,[status(thm)],[c4]) ).
cnf(c15,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),Z))) = double_divide(inverse(double_divide(inverse(double_divide(W,inverse(X))),inverse(Y))),double_divide(W,inverse(Z))),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c16,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c17,plain,
double_divide(inverse(double_divide(inverse(X),inverse(Y))),X) = Y,
inference(equational,[status(thm)],[c4,c16]) ).
cnf(c18,plain,
double_divide(inverse(X),X) = double_divide(inverse(Y),Y),
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
double_divide(inverse(X),X) = inverse(double_divide(inverse(Y),Y)),
inference(equational,[status(thm)],[c16,c18]) ).
cnf(c21,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c16]) ).
cnf(c23,plain,
double_divide(double_divide(inverse(X),X),inverse(Y)) = Y,
inference(equational,[status(thm)],[c17,c19]) ).
cnf(c24,plain,
double_divide(inverse(double_divide(X,Y)),inverse(Z)) = double_divide(inverse(double_divide(X,inverse(Z))),Y),
inference(equational,[status(thm)],[c4,c21]) ).
cnf(c25,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c23,c24]) ).
cnf(c29,plain,
double_divide(inverse(double_divide(inverse(X),X)),inverse(Y)) = Y,
inference(equational,[status(thm)],[c17,c24]) ).
cnf(c30,plain,
double_divide(inverse(X),inverse(inverse(X))) = double_divide(inverse(Y),Y),
inference(equational,[status(thm)],[c21,c25,c29]) ).
cnf(c31,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c16,c21,c30]) ).
cnf(c33,plain,
double_divide(X,inverse(Y)) = double_divide(inverse(Y),X),
inference(equational,[status(thm)],[c25,c31]) ).
cnf(c34,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c31,c33]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c1,c34]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP608-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n013.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 08:33:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.73/0.92 % SZS status Unsatisfiable
% 0.73/0.92 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------