%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT045-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 07:05:41 AM UTC 2025
% Result : Unsatisfiable 0.79s 0.95s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 3 RR)
% Number of literals : 13 ( 12 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(a,meet(complement(a),join(a,b))) != join(a,b),
file('theBenchmark.p',prove_orthomodular_law) ).
cnf(c4,axiom,
meet(X,Y) = meet(Y,X),
file('LAT001-0.ax',commutativity_of_meet) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('LAT001-0.ax',commutativity_of_join) ).
cnf(c8,axiom,
join(complement(X),X) = n1,
file('theBenchmark.p',invertability1) ).
cnf(c9,plain,
join(X,complement(X)) = n1,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,axiom,
meet(X,join(X,Y)) = X,
file('LAT001-0.ax',absorption1) ).
cnf(c11,plain,
meet(X,n1) = X,
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c12,plain,
meet(n1,X) = X,
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c60,axiom,
join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)),
file('theBenchmark.p',modular_law) ).
cnf(c61,plain,
meet(join(X,Y),join(X,Z)) = join(X,meet(Y,join(X,Z))),
inference(equational,[status(thm)],[c60]) ).
cnf(c81,plain,
join(X,meet(complement(X),join(X,Y))) = join(X,Y),
inference(equational,[status(thm)],[c9,c12,c61]) ).
cnf(g1,plain,
join(a,meet(complement(a),join(a,b))) = join(a,b),
inference(equational,[status(thm)],[c81]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT045-1 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 11:34:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.79/0.95 % SZS status Unsatisfiable
% 0.79/0.95 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------