TSTP Solution File: SET878+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET878+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 15:40:20 EDT 2009
% Result : Theorem 0.0s
% Output : Refutation 0.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 31 ( 3 avg)
% Number of connectives : 55 ( 21 ~; 26 |; 8 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 18 ( 2 sgn 8 !; 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/SET878+1.tptp',unknown),
[] ).
cnf(165475432,plain,
( ~ $equal(A,D)
| in(D,C)
| ~ $equal(unordered_pair(A,B),C) ),
inference(rewrite,[status(thm)],[d2_tarski]),
[] ).
cnf(174022944,plain,
in(A,unordered_pair(A,B)),
inference(equality_resolution,[status(thm)],[165475432]),
[] ).
fof(t19_zfmisc_1,plain,
~ $equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),
[] ).
cnf(165555600,plain,
~ $equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a)),
inference(rewrite,[status(thm)],[t19_zfmisc_1]),
[] ).
fof(commutativity_k3_xboole_0,plain,
! [B,A] : $equal(set_intersection2(B,A),set_intersection2(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),
[] ).
cnf(165420864,plain,
$equal(set_intersection2(B,A),set_intersection2(A,B)),
inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),
[] ).
cnf(173740072,plain,
~ $equal(set_intersection2(unordered_pair(a,b),singleton(a)),singleton(a)),
inference(paramodulation,[status(thm)],[165555600,165420864,theory(equality)]),
[] ).
fof(l32_zfmisc_1,plain,
! [A,B] :
( ~ in(A,B)
| $equal(set_intersection2(B,singleton(A)),singleton(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),
[] ).
cnf(165501800,plain,
( ~ in(A,B)
| $equal(set_intersection2(B,singleton(A)),singleton(A)) ),
inference(rewrite,[status(thm)],[l32_zfmisc_1]),
[] ).
cnf(173903016,plain,
~ in(a,unordered_pair(a,b)),
inference(resolution,[status(thm)],[173740072,165501800]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[174022944,173903016]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d2_tarski,plain,(((~$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/SET878+1.tptp',unknown),[]).
%
% cnf(165475432,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
%
% cnf(174022944,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[165475432]),[]).
%
% fof(t19_zfmisc_1,plain,(~$equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),[]).
%
% cnf(165555600,plain,(~$equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a))),inference(rewrite,[status(thm)],[t19_zfmisc_1]),[]).
%
% fof(commutativity_k3_xboole_0,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),[]).
%
% cnf(165420864,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),[]).
%
% cnf(173740072,plain,(~$equal(set_intersection2(unordered_pair(a,b),singleton(a)),singleton(a))),inference(paramodulation,[status(thm)],[165555600,165420864,theory(equality)]),[]).
%
% fof(l32_zfmisc_1,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),[]).
%
% cnf(165501800,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),inference(rewrite,[status(thm)],[l32_zfmisc_1]),[]).
%
% cnf(173903016,plain,(~in(a,unordered_pair(a,b))),inference(resolution,[status(thm)],[173740072,165501800]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[174022944,173903016]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------