%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT042-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 07:05:40 AM UTC 2025
% Result : Unsatisfiable 1.40s 1.59s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% 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 : 23 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(a,meet(b,join(a,c))) != meet(join(a,b),join(a,c)),
file('theBenchmark.p',prove_modular_law) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT001-0.ax',idempotence_of_meet) ).
cnf(c5,axiom,
meet(X,Y) = meet(Y,X),
file('LAT001-0.ax',commutativity_of_meet) ).
cnf(c13,axiom,
join(X,meet(X,Y)) = X,
file('LAT001-0.ax',absorption2) ).
cnf(c24,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('LAT001-0.ax',associativity_of_join) ).
cnf(c50,axiom,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)),
file('theBenchmark.p',distributivity) ).
cnf(c52,plain,
join(X,join(meet(X,Y),Z)) = join(X,Z),
inference(equational,[status(thm)],[c13,c24]) ).
cnf(c65,plain,
join(meet(X,Y),meet(X,Z)) = meet(join(Y,Z),X),
inference(equational,[status(thm)],[c5,c50]) ).
cnf(c94,plain,
join(meet(X,Y),meet(Z,X)) = meet(join(Y,Z),X),
inference(equational,[status(thm)],[c5,c65]) ).
cnf(c160,plain,
meet(join(X,Y),Z) = join(meet(X,Z),meet(Y,Z)),
inference(equational,[status(thm)],[c5,c94]) ).
cnf(g1,plain,
join(a,meet(b,join(a,c))) = meet(join(a,b),join(a,c)),
inference(equational,[status(thm)],[c1,c5,c13,c50,c52,c160]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT042-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n006.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 11:34:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.40/1.59 % SZS status Unsatisfiable
% 1.40/1.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------