%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP609-1 : 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 06:44:26 AM UTC 2025
% Result : Unsatisfiable 0.36s 0.53s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 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 : 61 ( 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,
inverse(double_divide(inverse(double_divide(inverse(double_divide(X,Y)),Z)),double_divide(X,Z))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
inverse(double_divide(X,double_divide(inverse(double_divide(Y,X)),double_divide(Y,Z)))) = Z,
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y))) = double_divide(inverse(double_divide(W,Z)),double_divide(W,X)),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(X,inverse(double_divide(Y,Z)))) = Z,
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(X,Z)) = double_divide(inverse(double_divide(W,Y)),double_divide(W,Z)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
inverse(inverse(double_divide(inverse(double_divide(X,Y)),double_divide(X,Y)))) = double_divide(inverse(double_divide(Z,W)),double_divide(Z,W)),
inference(equational,[status(thm)],[c4]) ).
cnf(c8,plain,
inverse(inverse(double_divide(inverse(X),X))) = double_divide(inverse(double_divide(Y,Z)),double_divide(Y,Z)),
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
double_divide(inverse(X),X) = inverse(inverse(double_divide(inverse(Y),Y))),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
double_divide(inverse(X),X) = double_divide(inverse(double_divide(Y,Z)),double_divide(Y,Z)),
inference(equational,[status(thm)],[c5,c7,c9]) ).
cnf(c12,plain,
inverse(double_divide(X,double_divide(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c13,plain,
double_divide(X,double_divide(X,Y)) = double_divide(Z,double_divide(Z,Y)),
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c15,plain,
inverse(double_divide(X,double_divide(X,Y))) = inverse(Y),
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c16,plain,
inverse(double_divide(inverse(double_divide(inverse(X),Y)),X)) = Y,
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c17,plain,
inverse(double_divide(inverse(X),X)) = double_divide(inverse(Y),Y),
inference(equational,[status(thm)],[c12,c16]) ).
cnf(c18,plain,
inverse(double_divide(inverse(X),Y)) = double_divide(inverse(Y),X),
inference(equational,[status(thm)],[c13,c15,c16]) ).
cnf(c19,plain,
double_divide(double_divide(inverse(X),Y),Y) = inverse(X),
inference(equational,[status(thm)],[c13,c15,c18]) ).
cnf(c20,plain,
double_divide(double_divide(X,Y),Y) = X,
inference(equational,[status(thm)],[c12,c19]) ).
cnf(c21,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c16,c18,c19,c20]) ).
cnf(c22,plain,
double_divide(X,inverse(X)) = double_divide(inverse(Y),Y),
inference(equational,[status(thm)],[c17,c18,c21]) ).
cnf(c23,plain,
double_divide(X,double_divide(X,Y)) = Y,
inference(equational,[status(thm)],[c15,c21]) ).
cnf(c24,plain,
double_divide(double_divide(inverse(X),X),Y) = inverse(Y),
inference(equational,[status(thm)],[c12,c18]) ).
cnf(c25,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference(equational,[status(thm)],[c4,c12,c18,c21,c23,c24]) ).
cnf(c26,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c13,c23,c25]) ).
cnf(c29,plain,
inverse(double_divide(X,inverse(X))) = inverse(double_divide(Y,inverse(Y))),
inference(equational,[status(thm)],[c8,c12,c21,c22,c26]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c1,c29]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP609-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 14 08:33:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.36/0.53 % SZS status Unsatisfiable
% 0.36/0.53 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------