TSTP Solution File: SET094-7 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET094-7 : 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 15:28:12 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(equal_implies_subclass2,plain,
! [B,A] :
( ~ $equal(B,A)
| subclass(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),
[] ).
cnf(171571192,plain,
( ~ $equal(B,A)
| subclass(B,A) ),
inference(rewrite,[status(thm)],[equal_implies_subclass2]),
[] ).
fof(prove_property_of_singletons1_1,plain,
$equal(singleton(member_of(x)),x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),
[] ).
cnf(172844016,plain,
$equal(singleton(member_of(x)),x),
inference(rewrite,[status(thm)],[prove_property_of_singletons1_1]),
[] ).
cnf(188625128,plain,
subclass(singleton(member_of(x)),x),
inference(resolution,[status(thm)],[171571192,172844016]),
[] ).
fof(subclass_implies_equal,plain,
! [A,B] :
( ~ subclass(A,B)
| ~ subclass(B,A)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),
[] ).
cnf(171577224,plain,
( ~ subclass(A,B)
| ~ subclass(B,A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[subclass_implies_equal]),
[] ).
fof(equal_implies_subclass1,plain,
! [B,A] :
( ~ $equal(B,A)
| subclass(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),
[] ).
cnf(171561320,plain,
( ~ $equal(B,A)
| subclass(A,B) ),
inference(rewrite,[status(thm)],[equal_implies_subclass1]),
[] ).
cnf(188612504,plain,
subclass(x,singleton(member_of(x))),
inference(resolution,[status(thm)],[171561320,172844016]),
[] ).
cnf(191339424,plain,
$equal(x,singleton(member_of(x))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[188625128,171577224,188612504]),
[] ).
fof(prove_property_of_singletons1_2,plain,
member(y,x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),
[] ).
cnf(172848512,plain,
member(y,x),
inference(rewrite,[status(thm)],[prove_property_of_singletons1_2]),
[] ).
cnf(202610744,plain,
member(y,singleton(member_of(x))),
inference(paramodulation,[status(thm)],[191339424,172848512,theory(equality)]),
[] ).
fof(only_member_in_singleton,plain,
! [A,B] :
( ~ member(A,singleton(B))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),
[] ).
cnf(172725880,plain,
( ~ member(A,singleton(B))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[only_member_in_singleton]),
[] ).
cnf(202893952,plain,
$equal(member_of(x),y),
inference(resolution,[status(thm)],[202610744,172725880]),
[] ).
fof(prove_property_of_singletons1_3,plain,
~ $equal(member_of(x),y),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),
[] ).
cnf(172852328,plain,
~ $equal(member_of(x),y),
inference(rewrite,[status(thm)],[prove_property_of_singletons1_3]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[202893952,172852328]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(equal_implies_subclass2,plain,(~$equal(B,A)|subclass(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),[]).
%
% cnf(171571192,plain,(~$equal(B,A)|subclass(B,A)),inference(rewrite,[status(thm)],[equal_implies_subclass2]),[]).
%
% fof(prove_property_of_singletons1_1,plain,($equal(singleton(member_of(x)),x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),[]).
%
% cnf(172844016,plain,($equal(singleton(member_of(x)),x)),inference(rewrite,[status(thm)],[prove_property_of_singletons1_1]),[]).
%
% cnf(188625128,plain,(subclass(singleton(member_of(x)),x)),inference(resolution,[status(thm)],[171571192,172844016]),[]).
%
% fof(subclass_implies_equal,plain,(~subclass(A,B)|~subclass(B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),[]).
%
% cnf(171577224,plain,(~subclass(A,B)|~subclass(B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[subclass_implies_equal]),[]).
%
% fof(equal_implies_subclass1,plain,(~$equal(B,A)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),[]).
%
% cnf(171561320,plain,(~$equal(B,A)|subclass(A,B)),inference(rewrite,[status(thm)],[equal_implies_subclass1]),[]).
%
% cnf(188612504,plain,(subclass(x,singleton(member_of(x)))),inference(resolution,[status(thm)],[171561320,172844016]),[]).
%
% cnf(191339424,plain,($equal(x,singleton(member_of(x)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[188625128,171577224,188612504]),[]).
%
% fof(prove_property_of_singletons1_2,plain,(member(y,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),[]).
%
% cnf(172848512,plain,(member(y,x)),inference(rewrite,[status(thm)],[prove_property_of_singletons1_2]),[]).
%
% cnf(202610744,plain,(member(y,singleton(member_of(x)))),inference(paramodulation,[status(thm)],[191339424,172848512,theory(equality)]),[]).
%
% fof(only_member_in_singleton,plain,(~member(A,singleton(B))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),[]).
%
% cnf(172725880,plain,(~member(A,singleton(B))|$equal(B,A)),inference(rewrite,[status(thm)],[only_member_in_singleton]),[]).
%
% cnf(202893952,plain,($equal(member_of(x),y)),inference(resolution,[status(thm)],[202610744,172725880]),[]).
%
% fof(prove_property_of_singletons1_3,plain,(~$equal(member_of(x),y)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET094-7.tptp',unknown),[]).
%
% cnf(172852328,plain,(~$equal(member_of(x),y)),inference(rewrite,[status(thm)],[prove_property_of_singletons1_3]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[202893952,172852328]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------