%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET078-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:27:26 EDT 2009
% Result : Unsatisfiable 0.4s
% Output : Refutation 0.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 8 unt; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 3 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(unordered_pair2,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),
[] ).
cnf(148476440,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(rewrite,[status(thm)],[unordered_pair2]),
[] ).
fof(singletons_are_sets,plain,
! [A] : member(singleton(A),universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),
[] ).
cnf(149561184,plain,
member(singleton(A),universal_class),
inference(rewrite,[status(thm)],[singletons_are_sets]),
[] ).
cnf(158478240,plain,
member(singleton(B),unordered_pair(singleton(B),A)),
inference(resolution,[status(thm)],[148476440,149561184]),
[] ).
fof(prove_corollary_1_to_singletons_are_sets_1,plain,
~ member(singleton(y),unordered_pair(x,singleton(y))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),
[] ).
cnf(149569184,plain,
~ member(singleton(y),unordered_pair(x,singleton(y))),
inference(rewrite,[status(thm)],[prove_corollary_1_to_singletons_are_sets_1]),
[] ).
fof(commutativity_of_unordered_pair,plain,
! [B,A] : $equal(unordered_pair(B,A),unordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),
[] ).
cnf(149451056,plain,
$equal(unordered_pair(B,A),unordered_pair(A,B)),
inference(rewrite,[status(thm)],[commutativity_of_unordered_pair]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158478240,149569184,149451056,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(unordered_pair2,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),[]).
%
% cnf(148476440,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair2]),[]).
%
% fof(singletons_are_sets,plain,(member(singleton(A),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),[]).
%
% cnf(149561184,plain,(member(singleton(A),universal_class)),inference(rewrite,[status(thm)],[singletons_are_sets]),[]).
%
% cnf(158478240,plain,(member(singleton(B),unordered_pair(singleton(B),A))),inference(resolution,[status(thm)],[148476440,149561184]),[]).
%
% fof(prove_corollary_1_to_singletons_are_sets_1,plain,(~member(singleton(y),unordered_pair(x,singleton(y)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),[]).
%
% cnf(149569184,plain,(~member(singleton(y),unordered_pair(x,singleton(y)))),inference(rewrite,[status(thm)],[prove_corollary_1_to_singletons_are_sets_1]),[]).
%
% fof(commutativity_of_unordered_pair,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET078-7.tptp',unknown),[]).
%
% cnf(149451056,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),inference(rewrite,[status(thm)],[commutativity_of_unordered_pair]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158478240,149569184,149451056,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------