%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT012-1 : TPTP v9.0.0. Released v2.2.0.
% 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 07:05:37 AM UTC 2025
% Result : Unsatisfiable 1.51s 1.78s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% Number of literals : 18 ( 17 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(b,a) != meet(a,b),
file('theBenchmark.p',prove_commutativity_of_meet) ).
cnf(c1,axiom,
join(X,meet(Y,meet(X,Z))) = X,
file('theBenchmark.p',mckenzie1) ).
cnf(c2,axiom,
meet(X,join(Y,join(X,Z))) = X,
file('theBenchmark.p',mckenzie2) ).
cnf(c3,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c7,axiom,
join(join(meet(X,Y),meet(Y,Z)),Y) = Y,
file('theBenchmark.p',mckenzie3) ).
cnf(c8,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c11,plain,
join(meet(X,Y),Y) = Y,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c12,plain,
join(X,join(Y,X)) = join(Y,X),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c15,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c16,plain,
join(meet(X,Y),X) = X,
inference(equational,[status(thm)],[c12,c15]) ).
cnf(c17,plain,
meet(meet(X,Y),X) = meet(X,Y),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c22,axiom,
meet(meet(join(X,Y),join(Y,Z)),Y) = Y,
file('theBenchmark.p',mckenzie4) ).
cnf(c194,plain,
meet(meet(X,join(meet(Y,X),Z)),meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c195,plain,
meet(meet(X,Y),meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c16,c194]) ).
cnf(c196,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c17,c195]) ).
cnf(g1,plain,
meet(b,a) = meet(a,b),
inference(equational,[status(thm)],[c196]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT012-1 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Jul 14 11:33:04 EDT 2025
% 0.10/0.31 % CPUTime :
% 1.51/1.78 % SZS status Unsatisfiable
% 1.51/1.78 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------