TSTP Solution File: SET983+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET983+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 15:43:19 EDT 2009
% Result : Theorem 0.5s
% Output : Refutation 0.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 6 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 59 ( 22 ~; 27 |; 10 &)
% ( 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; 5 con; 0-4 aty)
% Number of variables : 21 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t137_zfmisc_1,plain,
( in(a,cartesian_product2(b,c))
& in(a,cartesian_product2(d,e))
& ~ in(a,cartesian_product2(set_intersection2(b,d),set_intersection2(c,e))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET983+1.tptp',unknown),
[] ).
cnf(172804656,plain,
in(a,cartesian_product2(d,e)),
inference(rewrite,[status(thm)],[t137_zfmisc_1]),
[] ).
cnf(172811880,plain,
in(a,cartesian_product2(b,c)),
inference(rewrite,[status(thm)],[t137_zfmisc_1]),
[] ).
fof(d3_xboole_0,plain,
! [D,C,A,B] :
( ( in(D,C)
| ~ in(D,A)
| ~ in(D,B)
| ~ $equal(set_intersection2(A,B),C) )
& ( in(D,B)
| ~ in(D,C)
| ~ $equal(set_intersection2(A,B),C) )
& ( in(D,A)
| ~ in(D,C)
| ~ $equal(set_intersection2(A,B),C) )
& ( in(d(A,B,C,D),A)
| ~ in(d(A,B,C,D),A)
| ~ in(d(A,B,C,D),B)
| $equal(set_intersection2(A,B),C) )
& ( in(d(A,B,C,D),B)
| ~ in(d(A,B,C,D),A)
| ~ in(d(A,B,C,D),B)
| $equal(set_intersection2(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| ~ in(d(A,B,C,D),A)
| ~ in(d(A,B,C,D),B)
| $equal(set_intersection2(A,B),C) )
& ( in(d(A,B,C,D),A)
| in(d(A,B,C,D),C)
| $equal(set_intersection2(A,B),C) )
& ( in(d(A,B,C,D),B)
| in(d(A,B,C,D),C)
| $equal(set_intersection2(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| in(d(A,B,C,D),C)
| $equal(set_intersection2(A,B),C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET983+1.tptp',unknown),
[] ).
cnf(172660880,plain,
( in(D,C)
| ~ in(D,A)
| ~ in(D,B)
| ~ $equal(set_intersection2(A,B),C) ),
inference(rewrite,[status(thm)],[d3_xboole_0]),
[] ).
fof(t123_zfmisc_1,plain,
! [A,C,B,D] : $equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET983+1.tptp',unknown),
[] ).
cnf(172709264,plain,
$equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))),
inference(rewrite,[status(thm)],[t123_zfmisc_1]),
[] ).
cnf(200464592,plain,
( in(A,cartesian_product2(set_intersection2(B,C),set_intersection2(D,E)))
| ~ in(A,cartesian_product2(B,D))
| ~ in(A,cartesian_product2(C,E)) ),
inference(resolution,[status(thm)],[172660880,172709264]),
[] ).
cnf(172792880,plain,
~ in(a,cartesian_product2(set_intersection2(b,d),set_intersection2(c,e))),
inference(rewrite,[status(thm)],[t137_zfmisc_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[172804656,172811880,200464592,172792880]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(t137_zfmisc_1,plain,((in(a,cartesian_product2(b,c))&in(a,cartesian_product2(d,e))&~in(a,cartesian_product2(set_intersection2(b,d),set_intersection2(c,e))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET983+1.tptp',unknown),[]).
%
% cnf(172804656,plain,(in(a,cartesian_product2(d,e))),inference(rewrite,[status(thm)],[t137_zfmisc_1]),[]).
%
% cnf(172811880,plain,(in(a,cartesian_product2(b,c))),inference(rewrite,[status(thm)],[t137_zfmisc_1]),[]).
%
% fof(d3_xboole_0,plain,(((in(D,C)|~in(D,A)|~in(D,B)|~$equal(set_intersection2(A,B),C))&(in(D,B)|~in(D,C)|~$equal(set_intersection2(A,B),C))&(in(D,A)|~in(D,C)|~$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),A)|~in(d(A,B,C,D),A)|~in(d(A,B,C,D),B)|$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),B)|~in(d(A,B,C,D),A)|~in(d(A,B,C,D),B)|$equal(set_intersection2(A,B),C))&(~in(d(A,B,C,D),C)|~in(d(A,B,C,D),A)|~in(d(A,B,C,D),B)|$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),A)|in(d(A,B,C,D),C)|$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),B)|in(d(A,B,C,D),C)|$equal(set_intersection2(A,B),C))&(~in(d(A,B,C,D),C)|in(d(A,B,C,D),C)|$equal(set_intersection2(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET983+1.tptp',unknown),[]).
%
% cnf(172660880,plain,(in(D,C)|~in(D,A)|~in(D,B)|~$equal(set_intersection2(A,B),C)),inference(rewrite,[status(thm)],[d3_xboole_0]),[]).
%
% fof(t123_zfmisc_1,plain,($equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET983+1.tptp',unknown),[]).
%
% cnf(172709264,plain,($equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)))),inference(rewrite,[status(thm)],[t123_zfmisc_1]),[]).
%
% cnf(200464592,plain,(in(A,cartesian_product2(set_intersection2(B,C),set_intersection2(D,E)))|~in(A,cartesian_product2(B,D))|~in(A,cartesian_product2(C,E))),inference(resolution,[status(thm)],[172660880,172709264]),[]).
%
% cnf(172792880,plain,(~in(a,cartesian_product2(set_intersection2(b,d),set_intersection2(c,e)))),inference(rewrite,[status(thm)],[t137_zfmisc_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[172804656,172811880,200464592,172792880]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------