%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP682-10 : TPTP v9.0.0. Released v8.1.0.
% 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 06:44:42 AM UTC 2025
% Result : Unsatisfiable 0.63s 0.83s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 3 RR)
% Number of literals : 12 ( 11 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 : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
ld(X,mult(X,X)) = X,
file('theBenchmark.p',f01) ).
cnf(c3,axiom,
mult(X,ld(X,Y)) = ld(X,mult(X,Y)),
file('theBenchmark.p',f03) ).
cnf(c4,plain,
ld(X,mult(X,Y)) = mult(X,ld(X,Y)),
inference(equational,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(X,ld(X,X)) = X,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c19,axiom,
ld(ld(X,Y),mult(ld(X,Y),mult(Z,W))) = mult(ld(X,mult(X,Z)),W),
file('theBenchmark.p',f05) ).
cnf(c20,plain,
mult(ld(X,Y),ld(ld(X,Y),mult(Z,W))) = mult(mult(X,ld(X,Z)),W),
inference(equational,[status(thm)],[c4,c19]) ).
cnf(c21,plain,
mult(X,ld(X,mult(Y,Z))) = mult(mult(X,ld(X,Y)),Z),
inference(equational,[status(thm)],[c1,c4,c5,c20]) ).
cnf(c24,plain,
mult(mult(X,ld(X,Y)),ld(Y,Y)) = mult(X,ld(X,Y)),
inference(equational,[status(thm)],[c5,c21]) ).
cnf(c27,plain,
mult(ld(X,Y),ld(ld(X,Y),Z)) = mult(X,ld(X,Z)),
inference(equational,[status(thm)],[c5,c20,c24]) ).
cnf(g1,plain,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) = ld(x0,mult(x0,x2)),
inference(equational,[status(thm)],[c4,c27]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP682-10 : TPTP v9.0.0. Released v8.1.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:52:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.63/0.83 % SZS status Unsatisfiable
% 0.63/0.83 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------