%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP751-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 06:44:50 AM UTC 2025
% Result : Unsatisfiable 79.10s 79.31s
% Output : CNFRefutation 79.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 3 RR)
% Number of literals : 14 ( 13 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(a,mult(b,c)) != mult(mult(rd(a,a),b),mult(a,c)),
file('theBenchmark.p',goals) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c4,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c8,axiom,
mult(mult(X,Y),mult(Z,Z)) = mult(mult(X,Z),mult(Y,Z)),
file('theBenchmark.p',f07) ).
cnf(c9,plain,
mult(mult(rd(X,Y),Z),mult(Y,Y)) = mult(X,mult(Z,Y)),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c16,axiom,
mult(mult(X,mult(X,X)),mult(Y,Z)) = mult(mult(X,Y),mult(mult(X,X),Z)),
file('theBenchmark.p',f05) ).
cnf(c32,plain,
rd(mult(X,mult(Y,Z)),mult(Z,Z)) = mult(rd(X,Z),Y),
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c34,plain,
mult(rd(X,Y),rd(Z,Y)) = rd(mult(X,Z),mult(Y,Y)),
inference(equational,[status(thm)],[c3,c32]) ).
cnf(c56,plain,
rd(mult(mult(X,Y),Z),mult(Y,Y)) = mult(X,rd(Z,Y)),
inference(equational,[status(thm)],[c4,c34]) ).
cnf(c252,plain,
mult(mult(X,Y),mult(mult(X,Z),mult(X,X))) = mult(mult(X,mult(X,X)),mult(Y,mult(Z,X))),
inference(equational,[status(thm)],[c8,c16]) ).
cnf(c312,plain,
mult(rd(mult(X,Y),mult(X,X)),mult(X,Z)) = mult(X,mult(rd(Y,X),Z)),
inference(equational,[status(thm)],[c32,c56,c252]) ).
cnf(c315,plain,
mult(mult(rd(X,X),Y),mult(X,Z)) = mult(X,mult(Y,Z)),
inference(equational,[status(thm)],[c4,c32,c312]) ).
cnf(g1,plain,
mult(a,mult(b,c)) = mult(mult(rd(a,a),b),mult(a,c)),
inference(equational,[status(thm)],[c315]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP751-1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n015.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 09:02:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 79.10/79.31 % SZS status Unsatisfiable
% 79.10/79.31 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------