%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT019-1 : 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 07:05:38 AM UTC 2025
% Result : Unsatisfiable 61.08s 61.20s
% Output : CNFRefutation 61.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 3 RR)
% Number of literals : 26 ( 25 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 : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('theBenchmark.p',prove_distributivity_law_dual) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT004-0.ax',idempotence_of_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT004-0.ax',idempotence_of_join) ).
cnf(c3,axiom,
meet(X,Y) = meet(Y,X),
file('LAT004-0.ax',commutativity_of_meet) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('LAT004-0.ax',commutativity_of_join) ).
cnf(c5,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT004-0.ax',associativity_of_meet) ).
cnf(c6,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('LAT004-0.ax',associativity_of_join) ).
cnf(c7,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c13,axiom,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)),
file('theBenchmark.p',distributivity_law) ).
cnf(c14,plain,
join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c21,plain,
meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c35,plain,
meet(X,join(Y,meet(Z,X))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c36,axiom,
meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)),
file('LAT004-0.ax',quasi_lattice2) ).
cnf(c37,plain,
meet(join(X,Y),join(X,meet(Y,Z))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c36]) ).
cnf(c38,plain,
meet(join(X,Y),join(X,Z)) = join(X,meet(join(X,Y),Z)),
inference(equational,[status(thm)],[c7,c21,c37]) ).
cnf(c43,plain,
join(X,meet(join(X,Y),Z)) = join(X,meet(join(X,Z),Y)),
inference(equational,[status(thm)],[c3,c38]) ).
cnf(c44,plain,
meet(join(X,Y),join(Z,X)) = join(X,meet(join(X,Y),Z)),
inference(equational,[status(thm)],[c4,c38]) ).
cnf(c60,plain,
join(X,meet(join(X,Y),meet(Z,Y))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c37,c38]) ).
cnf(c67,plain,
meet(join(X,Y),join(Z,Y)) = join(Y,meet(join(Y,X),Z)),
inference(equational,[status(thm)],[c4,c44]) ).
cnf(c71,plain,
join(X,meet(join(X,Y),Z)) = join(X,meet(Y,join(X,Z))),
inference(equational,[status(thm)],[c3,c43]) ).
cnf(c72,plain,
join(X,meet(Y,join(X,Z))) = join(X,meet(Z,join(X,Y))),
inference(equational,[status(thm)],[c7,c43,c71]) ).
cnf(c76,plain,
join(X,meet(Y,join(X,Z))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c35,c60,c71]) ).
cnf(c83,plain,
join(X,meet(Y,join(Z,X))) = join(X,meet(Z,Y)),
inference(equational,[status(thm)],[c4,c72,c76]) ).
cnf(g1,plain,
join(a,meet(b,c)) = meet(join(a,b),join(a,c)),
inference(equational,[status(thm)],[c3,c4,c67,c83]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT019-1 : TPTP v9.0.0. Released v2.2.0.
% 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 11:33:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 61.08/61.20 % SZS status Unsatisfiable
% 61.08/61.20 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------