%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET885+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 15:40:39 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 31 ( 5 avg)
% Number of connectives : 98 ( 36 ~; 46 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 24 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(d2_tarski,plain,
! [B,D,C,A] :
( ( ~ $equal(B,D)
| in(D,C)
| ~ $equal(unordered_pair(A,B),C) )
& ( ~ $equal(A,D)
| in(D,C)
| ~ $equal(unordered_pair(A,B),C) )
& ( ~ in(D,C)
| $equal(A,D)
| $equal(B,D)
| ~ $equal(unordered_pair(A,B),C) )
& ( $equal(d(A,B,C,D),A)
| $equal(d(A,B,C,D),B)
| ~ $equal(d(A,B,C,D),A)
| $equal(unordered_pair(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| ~ $equal(d(A,B,C,D),A)
| $equal(unordered_pair(A,B),C) )
& ( $equal(d(A,B,C,D),A)
| $equal(d(A,B,C,D),B)
| ~ $equal(d(A,B,C,D),B)
| $equal(unordered_pair(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| ~ $equal(d(A,B,C,D),B)
| $equal(unordered_pair(A,B),C) )
& ( $equal(d(A,B,C,D),A)
| $equal(d(A,B,C,D),B)
| in(d(A,B,C,D),C)
| $equal(unordered_pair(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| in(d(A,B,C,D),C)
| $equal(unordered_pair(A,B),C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET885+1.tptp',unknown),
[] ).
cnf(169399912,plain,
( ~ $equal(A,D)
| in(D,C)
| ~ $equal(unordered_pair(A,B),C) ),
inference(rewrite,[status(thm)],[d2_tarski]),
[] ).
cnf(187878840,plain,
in(A,unordered_pair(A,B)),
inference(equality_resolution,[status(thm)],[169399912]),
[] ).
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/SET885+1.tptp',unknown),
[] ).
cnf(169342344,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
fof(t26_zfmisc_1,plain,
( subset(unordered_pair(a,b),singleton(c))
& ~ $equal(c,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET885+1.tptp',unknown),
[] ).
cnf(169499376,plain,
~ $equal(c,a),
inference(rewrite,[status(thm)],[t26_zfmisc_1]),
[] ).
cnf(179992840,plain,
( ~ in(a,A)
| ~ $equal(singleton(c),A) ),
inference(resolution,[status(thm)],[169342344,169499376]),
[] ).
fof(d3_tarski,plain,
! [A,B,C] :
( ( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) )
& ( ~ in(c(A,B,C),B)
| subset(A,B) )
& ( in(c(A,B,C),A)
| subset(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET885+1.tptp',unknown),
[] ).
cnf(169427152,plain,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
inference(rewrite,[status(thm)],[d3_tarski]),
[] ).
cnf(169506840,plain,
subset(unordered_pair(a,b),singleton(c)),
inference(rewrite,[status(thm)],[t26_zfmisc_1]),
[] ).
cnf(180190104,plain,
( ~ in(A,unordered_pair(a,b))
| in(A,singleton(c)) ),
inference(resolution,[status(thm)],[169427152,169506840]),
[] ).
cnf(180847560,plain,
~ in(a,unordered_pair(a,b)),
inference(resolution,[status(thm)],[179992840,180190104]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[187878840,180847560]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d2_tarski,plain,(((~$equal(B,D)|in(D,C)|~$equal(unordered_pair(A,B),C))&(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C))&(~in(D,C)|$equal(A,D)|$equal(B,D)|~$equal(unordered_pair(A,B),C))&($equal(d(A,B,C,D),A)|$equal(d(A,B,C,D),B)|~$equal(d(A,B,C,D),A)|$equal(unordered_pair(A,B),C))&(~in(d(A,B,C,D),C)|~$equal(d(A,B,C,D),A)|$equal(unordered_pair(A,B),C))&($equal(d(A,B,C,D),A)|$equal(d(A,B,C,D),B)|~$equal(d(A,B,C,D),B)|$equal(unordered_pair(A,B),C))&(~in(d(A,B,C,D),C)|~$equal(d(A,B,C,D),B)|$equal(unordered_pair(A,B),C))&($equal(d(A,B,C,D),A)|$equal(d(A,B,C,D),B)|in(d(A,B,C,D),C)|$equal(unordered_pair(A,B),C))&(~in(d(A,B,C,D),C)|in(d(A,B,C,D),C)|$equal(unordered_pair(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET885+1.tptp',unknown),[]).
%
% cnf(169399912,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
%
% cnf(187878840,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[169399912]),[]).
%
% 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/SET885+1.tptp',unknown),[]).
%
% cnf(169342344,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% fof(t26_zfmisc_1,plain,((subset(unordered_pair(a,b),singleton(c))&~$equal(c,a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET885+1.tptp',unknown),[]).
%
% cnf(169499376,plain,(~$equal(c,a)),inference(rewrite,[status(thm)],[t26_zfmisc_1]),[]).
%
% cnf(179992840,plain,(~in(a,A)|~$equal(singleton(c),A)),inference(resolution,[status(thm)],[169342344,169499376]),[]).
%
% fof(d3_tarski,plain,(((~subset(A,B)|~in(C,A)|in(C,B))&(~in(c(A,B,C),B)|subset(A,B))&(in(c(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET885+1.tptp',unknown),[]).
%
% cnf(169427152,plain,(~subset(A,B)|~in(C,A)|in(C,B)),inference(rewrite,[status(thm)],[d3_tarski]),[]).
%
% cnf(169506840,plain,(subset(unordered_pair(a,b),singleton(c))),inference(rewrite,[status(thm)],[t26_zfmisc_1]),[]).
%
% cnf(180190104,plain,(~in(A,unordered_pair(a,b))|in(A,singleton(c))),inference(resolution,[status(thm)],[169427152,169506840]),[]).
%
% cnf(180847560,plain,(~in(a,unordered_pair(a,b))),inference(resolution,[status(thm)],[179992840,180190104]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[187878840,180847560]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------