TSTP Solution File: SET975+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET975+1 : TPTP v3.4.2. Released v3.2.0.
% 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 15:43:07 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 113 ( 41 ~; 54 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 4 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET975+1.tptp',unknown),
[] ).
cnf(163620592,plain,
( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(163608656,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(180747848,plain,
( ~ in(B,singleton(A))
| $equal(A,B) ),
inference(equality_resolution,[status(thm)],[163608656]),
[] ).
fof(l55_zfmisc_1,plain,
! [B,D,A,C] :
( ( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET975+1.tptp',unknown),
[] ).
cnf(163646008,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
fof(t128_zfmisc_1,plain,
( ( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| $equal(c,a) )
& ( ~ $equal(c,a)
| in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| $equal(c,a) )
& ( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| ~ in(b,d)
| $equal(c,a) )
& ( ~ $equal(c,a)
| ~ in(b,d)
| $equal(c,a) )
& ( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| in(b,d) )
& ( ~ $equal(c,a)
| in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| in(b,d) )
& ( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| ~ in(b,d)
| in(b,d) )
& ( ~ $equal(c,a)
| ~ in(b,d)
| in(b,d) )
& ( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| ~ in(ordered_pair(a,b),cartesian_product2(singleton(c),d)) )
& ( ~ $equal(c,a)
| in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| ~ in(ordered_pair(a,b),cartesian_product2(singleton(c),d)) )
& ( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| ~ in(b,d)
| ~ in(ordered_pair(a,b),cartesian_product2(singleton(c),d)) )
& ( ~ $equal(c,a)
| ~ in(b,d)
| ~ in(ordered_pair(a,b),cartesian_product2(singleton(c),d)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET975+1.tptp',unknown),
[] ).
cnf(163841744,plain,
( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| in(b,d) ),
inference(rewrite,[status(thm)],[t128_zfmisc_1]),
[] ).
cnf(163846512,plain,
( in(ordered_pair(a,b),cartesian_product2(singleton(c),d))
| $equal(c,a) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t128_zfmisc_1,163841744]),
[] ).
cnf(179884624,plain,
( in(a,singleton(c))
| $equal(c,a) ),
inference(resolution,[status(thm)],[163646008,163846512]),
[] ).
cnf(180899480,plain,
$equal(c,a),
inference(resolution,[status(thm)],[180747848,179884624]),
[] ).
cnf(181070224,plain,
( in(a,A)
| ~ $equal(singleton(c),A) ),
inference(resolution,[status(thm)],[163620592,180899480]),
[] ).
cnf(182437680,plain,
in(a,singleton(c)),
inference(equality_resolution,[status(thm)],[181070224]),
[] ).
cnf(163650048,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
cnf(180319080,plain,
in(b,d),
inference(resolution,[status(thm)],[163650048,163841744]),
[] ).
cnf(163640936,plain,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
cnf(163824600,plain,
( ~ $equal(c,a)
| ~ in(ordered_pair(a,b),cartesian_product2(singleton(c),d)) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t128_zfmisc_1,163650048]),
[] ).
cnf(188796056,plain,
~ in(ordered_pair(a,b),cartesian_product2(singleton(c),d)),
inference(resolution,[status(thm)],[163824600,180899480]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[182437680,180319080,163640936,188796056]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d1_tarski,plain,(((in(C,B)|~$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)|$equal(singleton(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET975+1.tptp',unknown),[]).
%
% cnf(163620592,plain,(in(C,B)|~$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(163608656,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(180747848,plain,(~in(B,singleton(A))|$equal(A,B)),inference(equality_resolution,[status(thm)],[163608656]),[]).
%
% fof(l55_zfmisc_1,plain,(((in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET975+1.tptp',unknown),[]).
%
% cnf(163646008,plain,(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% fof(t128_zfmisc_1,plain,(((in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|$equal(c,a))&(~$equal(c,a)|in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|$equal(c,a))&(in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|~in(b,d)|$equal(c,a))&(~$equal(c,a)|~in(b,d)|$equal(c,a))&(in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|in(b,d))&(~$equal(c,a)|in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|in(b,d))&(in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|~in(b,d)|in(b,d))&(~$equal(c,a)|~in(b,d)|in(b,d))&(in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|~in(ordered_pair(a,b),cartesian_product2(singleton(c),d)))&(~$equal(c,a)|in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|~in(ordered_pair(a,b),cartesian_product2(singleton(c),d)))&(in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|~in(b,d)|~in(ordered_pair(a,b),cartesian_product2(singleton(c),d)))&(~$equal(c,a)|~in(b,d)|~in(ordered_pair(a,b),cartesian_product2(singleton(c),d))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET975+1.tptp',unknown),[]).
%
% cnf(163841744,plain,(in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|in(b,d)),inference(rewrite,[status(thm)],[t128_zfmisc_1]),[]).
%
% cnf(163846512,plain,(in(ordered_pair(a,b),cartesian_product2(singleton(c),d))|$equal(c,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t128_zfmisc_1,163841744]),[]).
%
% cnf(179884624,plain,(in(a,singleton(c))|$equal(c,a)),inference(resolution,[status(thm)],[163646008,163846512]),[]).
%
% cnf(180899480,plain,($equal(c,a)),inference(resolution,[status(thm)],[180747848,179884624]),[]).
%
% cnf(181070224,plain,(in(a,A)|~$equal(singleton(c),A)),inference(resolution,[status(thm)],[163620592,180899480]),[]).
%
% cnf(182437680,plain,(in(a,singleton(c))),inference(equality_resolution,[status(thm)],[181070224]),[]).
%
% cnf(163650048,plain,(in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% cnf(180319080,plain,(in(b,d)),inference(resolution,[status(thm)],[163650048,163841744]),[]).
%
% cnf(163640936,plain,(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% cnf(163824600,plain,(~$equal(c,a)|~in(ordered_pair(a,b),cartesian_product2(singleton(c),d))),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t128_zfmisc_1,163650048]),[]).
%
% cnf(188796056,plain,(~in(ordered_pair(a,b),cartesian_product2(singleton(c),d))),inference(resolution,[status(thm)],[163824600,180899480]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182437680,180319080,163640936,188796056]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------