TSTP Solution File: SET976+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET976+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 15:43:09 EDT 2009
% Result : Theorem 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 4 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 112 ( 40 ~; 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(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/SET976+1.tptp',unknown),
[] ).
cnf(171793752,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
fof(t129_zfmisc_1,plain,
( ( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| in(a,c) )
& ( ~ in(a,c)
| in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| in(a,c) )
& ( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| ~ $equal(d,b)
| in(a,c) )
& ( ~ in(a,c)
| ~ $equal(d,b)
| in(a,c) )
& ( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| $equal(d,b) )
& ( ~ in(a,c)
| in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| $equal(d,b) )
& ( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| ~ $equal(d,b)
| $equal(d,b) )
& ( ~ in(a,c)
| ~ $equal(d,b)
| $equal(d,b) )
& ( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| ~ in(ordered_pair(a,b),cartesian_product2(c,singleton(d))) )
& ( ~ in(a,c)
| in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| ~ in(ordered_pair(a,b),cartesian_product2(c,singleton(d))) )
& ( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| ~ $equal(d,b)
| ~ in(ordered_pair(a,b),cartesian_product2(c,singleton(d))) )
& ( ~ in(a,c)
| ~ $equal(d,b)
| ~ in(ordered_pair(a,b),cartesian_product2(c,singleton(d))) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET976+1.tptp',unknown),
[] ).
cnf(171988712,plain,
( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| $equal(d,b) ),
inference(rewrite,[status(thm)],[t129_zfmisc_1]),
[] ).
cnf(171993544,plain,
( in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))
| in(a,c) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t129_zfmisc_1,171988712]),
[] ).
cnf(188034784,plain,
in(a,c),
inference(resolution,[status(thm)],[171793752,171993544]),
[] ).
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/SET976+1.tptp',unknown),
[] ).
cnf(171768336,plain,
( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(171756400,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(188745088,plain,
( ~ in(B,singleton(A))
| $equal(A,B) ),
inference(equality_resolution,[status(thm)],[171756400]),
[] ).
cnf(171797792,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
cnf(188372728,plain,
( in(b,singleton(d))
| $equal(d,b) ),
inference(resolution,[status(thm)],[171797792,171988712]),
[] ).
cnf(188891120,plain,
$equal(d,b),
inference(resolution,[status(thm)],[188745088,188372728]),
[] ).
cnf(189058776,plain,
( in(b,A)
| ~ $equal(singleton(d),A) ),
inference(resolution,[status(thm)],[171768336,188891120]),
[] ).
cnf(190411480,plain,
in(b,singleton(d)),
inference(equality_resolution,[status(thm)],[189058776]),
[] ).
cnf(171788680,plain,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
cnf(171970704,plain,
( ~ $equal(d,b)
| ~ in(ordered_pair(a,b),cartesian_product2(c,singleton(d))) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t129_zfmisc_1,171793752]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[188034784,190411480,188891120,171788680,171970704]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l55_zfmisc_1,plain,(((in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET976+1.tptp',unknown),[]).
%
% cnf(171793752,plain,(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% fof(t129_zfmisc_1,plain,(((in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|in(a,c))&(~in(a,c)|in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|in(a,c))&(in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|~$equal(d,b)|in(a,c))&(~in(a,c)|~$equal(d,b)|in(a,c))&(in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|$equal(d,b))&(~in(a,c)|in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|$equal(d,b))&(in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|~$equal(d,b)|$equal(d,b))&(~in(a,c)|~$equal(d,b)|$equal(d,b))&(in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|~in(ordered_pair(a,b),cartesian_product2(c,singleton(d))))&(~in(a,c)|in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|~in(ordered_pair(a,b),cartesian_product2(c,singleton(d))))&(in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|~$equal(d,b)|~in(ordered_pair(a,b),cartesian_product2(c,singleton(d))))&(~in(a,c)|~$equal(d,b)|~in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET976+1.tptp',unknown),[]).
%
% cnf(171988712,plain,(in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|$equal(d,b)),inference(rewrite,[status(thm)],[t129_zfmisc_1]),[]).
%
% cnf(171993544,plain,(in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))|in(a,c)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t129_zfmisc_1,171988712]),[]).
%
% cnf(188034784,plain,(in(a,c)),inference(resolution,[status(thm)],[171793752,171993544]),[]).
%
% 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/SET976+1.tptp',unknown),[]).
%
% cnf(171768336,plain,(in(C,B)|~$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(171756400,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(188745088,plain,(~in(B,singleton(A))|$equal(A,B)),inference(equality_resolution,[status(thm)],[171756400]),[]).
%
% cnf(171797792,plain,(in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% cnf(188372728,plain,(in(b,singleton(d))|$equal(d,b)),inference(resolution,[status(thm)],[171797792,171988712]),[]).
%
% cnf(188891120,plain,($equal(d,b)),inference(resolution,[status(thm)],[188745088,188372728]),[]).
%
% cnf(189058776,plain,(in(b,A)|~$equal(singleton(d),A)),inference(resolution,[status(thm)],[171768336,188891120]),[]).
%
% cnf(190411480,plain,(in(b,singleton(d))),inference(equality_resolution,[status(thm)],[189058776]),[]).
%
% cnf(171788680,plain,(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% cnf(171970704,plain,(~$equal(d,b)|~in(ordered_pair(a,b),cartesian_product2(c,singleton(d)))),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t129_zfmisc_1,171793752]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[188034784,190411480,188891120,171788680,171970704]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------