%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LAT045-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:33:41 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 22 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_orthomodular_law,plain,
~ $equal(join(a,meet(complement(a),join(a,b))),join(a,b)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),
[] ).
cnf(165530360,plain,
~ $equal(join(a,meet(complement(a),join(a,b))),join(a,b)),
inference(rewrite,[status(thm)],[prove_orthomodular_law]),
[] ).
fof(modular_law,plain,
! [A,B,C] : $equal(meet(join(A,B),join(A,C)),join(A,meet(B,join(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),
[] ).
cnf(165525744,plain,
$equal(meet(join(A,B),join(A,C)),join(A,meet(B,join(A,C)))),
inference(rewrite,[status(thm)],[modular_law]),
[] ).
cnf(173444936,plain,
~ $equal(meet(join(a,complement(a)),join(a,b)),join(a,b)),
inference(paramodulation,[status(thm)],[165530360,165525744,theory(equality)]),
[] ).
fof(commutativity_of_join,plain,
! [B,A] : $equal(join(B,A),join(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),
[] ).
cnf(165486344,plain,
$equal(join(B,A),join(A,B)),
inference(rewrite,[status(thm)],[commutativity_of_join]),
[] ).
cnf(173725408,plain,
~ $equal(meet(join(complement(a),a),join(a,b)),join(a,b)),
inference(paramodulation,[status(thm)],[173444936,165486344,theory(equality)]),
[] ).
fof(invertability1,plain,
! [A] : $equal(join(complement(A),A),n1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),
[] ).
cnf(165513992,plain,
$equal(join(complement(A),A),n1),
inference(rewrite,[status(thm)],[invertability1]),
[] ).
cnf(174120800,plain,
~ $equal(meet(n1,join(a,b)),join(a,b)),
inference(paramodulation,[status(thm)],[173725408,165513992,theory(equality)]),
[] ).
fof(commutativity_of_meet,plain,
! [B,A] : $equal(meet(B,A),meet(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),
[] ).
cnf(165478464,plain,
$equal(meet(B,A),meet(A,B)),
inference(rewrite,[status(thm)],[commutativity_of_meet]),
[] ).
cnf(174209440,plain,
~ $equal(meet(join(a,b),n1),join(a,b)),
inference(paramodulation,[status(thm)],[174120800,165478464,theory(equality)]),
[] ).
cnf(174279896,plain,
~ $equal(meet(join(a,b),join(complement(A),A)),join(a,b)),
inference(paramodulation,[status(thm)],[174209440,165513992,theory(equality)]),
[] ).
cnf(175099464,plain,
~ $equal(meet(join(a,b),join(A,complement(A))),join(a,b)),
inference(paramodulation,[status(thm)],[174279896,165486344,theory(equality)]),
[] ).
fof(absorption1,plain,
! [A,B] : $equal(meet(A,join(A,B)),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),
[] ).
cnf(165461960,plain,
$equal(meet(A,join(A,B)),A),
inference(rewrite,[status(thm)],[absorption1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[175099464,165461960]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_orthomodular_law,plain,(~$equal(join(a,meet(complement(a),join(a,b))),join(a,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),[]).
%
% cnf(165530360,plain,(~$equal(join(a,meet(complement(a),join(a,b))),join(a,b))),inference(rewrite,[status(thm)],[prove_orthomodular_law]),[]).
%
% fof(modular_law,plain,($equal(meet(join(A,B),join(A,C)),join(A,meet(B,join(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),[]).
%
% cnf(165525744,plain,($equal(meet(join(A,B),join(A,C)),join(A,meet(B,join(A,C))))),inference(rewrite,[status(thm)],[modular_law]),[]).
%
% cnf(173444936,plain,(~$equal(meet(join(a,complement(a)),join(a,b)),join(a,b))),inference(paramodulation,[status(thm)],[165530360,165525744,theory(equality)]),[]).
%
% fof(commutativity_of_join,plain,($equal(join(B,A),join(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),[]).
%
% cnf(165486344,plain,($equal(join(B,A),join(A,B))),inference(rewrite,[status(thm)],[commutativity_of_join]),[]).
%
% cnf(173725408,plain,(~$equal(meet(join(complement(a),a),join(a,b)),join(a,b))),inference(paramodulation,[status(thm)],[173444936,165486344,theory(equality)]),[]).
%
% fof(invertability1,plain,($equal(join(complement(A),A),n1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),[]).
%
% cnf(165513992,plain,($equal(join(complement(A),A),n1)),inference(rewrite,[status(thm)],[invertability1]),[]).
%
% cnf(174120800,plain,(~$equal(meet(n1,join(a,b)),join(a,b))),inference(paramodulation,[status(thm)],[173725408,165513992,theory(equality)]),[]).
%
% fof(commutativity_of_meet,plain,($equal(meet(B,A),meet(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),[]).
%
% cnf(165478464,plain,($equal(meet(B,A),meet(A,B))),inference(rewrite,[status(thm)],[commutativity_of_meet]),[]).
%
% cnf(174209440,plain,(~$equal(meet(join(a,b),n1),join(a,b))),inference(paramodulation,[status(thm)],[174120800,165478464,theory(equality)]),[]).
%
% cnf(174279896,plain,(~$equal(meet(join(a,b),join(complement(A),A)),join(a,b))),inference(paramodulation,[status(thm)],[174209440,165513992,theory(equality)]),[]).
%
% cnf(175099464,plain,(~$equal(meet(join(a,b),join(A,complement(A))),join(a,b))),inference(paramodulation,[status(thm)],[174279896,165486344,theory(equality)]),[]).
%
% fof(absorption1,plain,($equal(meet(A,join(A,B)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT045-1.tptp',unknown),[]).
%
% cnf(165461960,plain,($equal(meet(A,join(A,B)),A)),inference(rewrite,[status(thm)],[absorption1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[175099464,165461960]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------