TSTP Solution File: SET879+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET879+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:40:22 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 64 ( 25 ~; 30 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 20 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t20_zfmisc_1,plain,
( ( ~ $equal(b,a)
| $equal(set_difference(singleton(a),singleton(b)),singleton(a)) )
& ( ~ $equal(set_difference(singleton(a),singleton(b)),singleton(a))
| $equal(set_difference(singleton(a),singleton(b)),singleton(a)) )
& ( ~ $equal(b,a)
| $equal(b,a) )
& ( ~ $equal(set_difference(singleton(a),singleton(b)),singleton(a))
| $equal(b,a) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),
[] ).
cnf(160061640,plain,
( ~ $equal(b,a)
| $equal(set_difference(singleton(a),singleton(b)),singleton(a)) ),
inference(rewrite,[status(thm)],[t20_zfmisc_1]),
[] ).
cnf(160055552,plain,
( ~ $equal(set_difference(singleton(a),singleton(b)),singleton(a))
| $equal(b,a) ),
inference(rewrite,[status(thm)],[t20_zfmisc_1]),
[] ).
fof(l34_zfmisc_1,plain,
! [A,B] :
( ( ~ $equal(set_difference(singleton(A),B),singleton(A))
| ~ in(A,B) )
& ( $equal(set_difference(singleton(A),B),singleton(A))
| in(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),
[] ).
cnf(159958568,plain,
( $equal(set_difference(singleton(A),B),singleton(A))
| in(A,B) ),
inference(rewrite,[status(thm)],[l34_zfmisc_1]),
[] ).
cnf(173632856,plain,
( $equal(b,a)
| in(a,singleton(b)) ),
inference(resolution,[status(thm)],[160055552,159958568]),
[] ).
fof(d1_tarski,plain,
! [C,B,A] :
( ( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) )
& ( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) )
& ( $equal(c(A,B,C),A)
| ~ $equal(c(A,B,C),A)
| $equal(singleton(A),B) )
& ( ~ in(c(A,B,C),B)
| ~ $equal(c(A,B,C),A)
| $equal(singleton(A),B) )
& ( $equal(c(A,B,C),A)
| in(c(A,B,C),B)
| $equal(singleton(A),B) )
& ( ~ in(c(A,B,C),B)
| in(c(A,B,C),B)
| $equal(singleton(A),B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),
[] ).
cnf(159941056,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(170497752,plain,
( ~ in(B,singleton(A))
| $equal(A,B) ),
inference(equality_resolution,[status(thm)],[159941056]),
[] ).
cnf(173842680,plain,
$equal(b,a),
inference(resolution,[status(thm)],[173632856,170497752]),
[] ).
cnf(174383240,plain,
$equal(set_difference(singleton(a),singleton(b)),singleton(a)),
inference(resolution,[status(thm)],[160061640,173842680]),
[] ).
cnf(159952992,plain,
( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(170610136,plain,
( in(A,B)
| ~ $equal(singleton(A),B) ),
inference(equality_resolution,[status(thm)],[159952992]),
[] ).
cnf(174578024,plain,
( in(a,A)
| ~ $equal(set_difference(singleton(a),singleton(b)),A) ),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[173842680,160061640,170610136,theory(equality)]),
[] ).
cnf(174892712,plain,
in(a,singleton(b)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174578024,173632856,160061640,173632856,theory(equality)]),
[] ).
cnf(159965200,plain,
( ~ $equal(set_difference(singleton(A),B),singleton(A))
| ~ in(A,B) ),
inference(rewrite,[status(thm)],[l34_zfmisc_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[174383240,174892712,159965200]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t20_zfmisc_1,plain,(((~$equal(b,a)|$equal(set_difference(singleton(a),singleton(b)),singleton(a)))&(~$equal(set_difference(singleton(a),singleton(b)),singleton(a))|$equal(set_difference(singleton(a),singleton(b)),singleton(a)))&(~$equal(b,a)|$equal(b,a))&(~$equal(set_difference(singleton(a),singleton(b)),singleton(a))|$equal(b,a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),[]).
%
% cnf(160061640,plain,(~$equal(b,a)|$equal(set_difference(singleton(a),singleton(b)),singleton(a))),inference(rewrite,[status(thm)],[t20_zfmisc_1]),[]).
%
% cnf(160055552,plain,(~$equal(set_difference(singleton(a),singleton(b)),singleton(a))|$equal(b,a)),inference(rewrite,[status(thm)],[t20_zfmisc_1]),[]).
%
% fof(l34_zfmisc_1,plain,(((~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B))&($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),[]).
%
% cnf(159958568,plain,($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
%
% cnf(173632856,plain,($equal(b,a)|in(a,singleton(b))),inference(resolution,[status(thm)],[160055552,159958568]),[]).
%
% fof(d1_tarski,plain,(((in(C,B)|~$equal(A,C)|~$equal(singleton(A),B))&(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B))&($equal(c(A,B,C),A)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&($equal(c(A,B,C),A)|in(c(A,B,C),B)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|in(c(A,B,C),B)|$equal(singleton(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),[]).
%
% cnf(159941056,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(170497752,plain,(~in(B,singleton(A))|$equal(A,B)),inference(equality_resolution,[status(thm)],[159941056]),[]).
%
% cnf(173842680,plain,($equal(b,a)),inference(resolution,[status(thm)],[173632856,170497752]),[]).
%
% cnf(174383240,plain,($equal(set_difference(singleton(a),singleton(b)),singleton(a))),inference(resolution,[status(thm)],[160061640,173842680]),[]).
%
% cnf(159952992,plain,(in(C,B)|~$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(170610136,plain,(in(A,B)|~$equal(singleton(A),B)),inference(equality_resolution,[status(thm)],[159952992]),[]).
%
% cnf(174578024,plain,(in(a,A)|~$equal(set_difference(singleton(a),singleton(b)),A)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[173842680,160061640,170610136,theory(equality)]),[]).
%
% cnf(174892712,plain,(in(a,singleton(b))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174578024,173632856,160061640,173632856,theory(equality)]),[]).
%
% cnf(159965200,plain,(~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[174383240,174892712,159965200]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------