TSTP Solution File: SET920+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET920+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 15:41:38 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 31 ( 5 avg)
% Number of connectives : 103 ( 37 ~; 49 |; 17 &)
% ( 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; 3 con; 0-4 aty)
% Number of variables : 25 ( 5 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET920+1.tptp',unknown),
[] ).
cnf(172052128,plain,
( in(D,A)
| ~ in(D,C)
| ~ $equal(set_intersection2(A,B),C) ),
inference(rewrite,[status(thm)],[d3_xboole_0]),
[] ).
fof(t63_zfmisc_1,plain,
( $equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b))
& ~ in(a,c) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),
[] ).
cnf(172133440,plain,
~ in(a,c),
inference(rewrite,[status(thm)],[t63_zfmisc_1]),
[] ).
cnf(182638080,plain,
( ~ in(a,B)
| ~ $equal(set_intersection2(c,A),B) ),
inference(resolution,[status(thm)],[172052128,172133440]),
[] ).
cnf(189675568,plain,
~ in(a,set_intersection2(c,A)),
inference(equality_resolution,[status(thm)],[182638080]),
[] ).
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/SET920+1.tptp',unknown),
[] ).
cnf(172007848,plain,
( ~ $equal(A,D)
| in(D,C)
| ~ $equal(unordered_pair(A,B),C) ),
inference(rewrite,[status(thm)],[d2_tarski]),
[] ).
cnf(183060560,plain,
in(A,unordered_pair(A,B)),
inference(equality_resolution,[status(thm)],[172007848]),
[] ).
cnf(172141024,plain,
$equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b)),
inference(rewrite,[status(thm)],[t63_zfmisc_1]),
[] ).
cnf(183367904,plain,
in(a,set_intersection2(unordered_pair(a,b),c)),
inference(paramodulation,[status(thm)],[183060560,172141024,theory(equality)]),
[] ).
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/SET920+1.tptp',unknown),
[] ).
cnf(171953280,plain,
$equal(set_intersection2(B,A),set_intersection2(A,B)),
inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),
[] ).
cnf(183494248,plain,
in(a,set_intersection2(c,unordered_pair(a,b))),
inference(paramodulation,[status(thm)],[183367904,171953280,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[189675568,183494248]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d3_xboole_0,plain,(((in(D,C)|~in(D,A)|~in(D,B)|~$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/SET920+1.tptp',unknown),[]).
%
% cnf(172052128,plain,(in(D,A)|~in(D,C)|~$equal(set_intersection2(A,B),C)),inference(rewrite,[status(thm)],[d3_xboole_0]),[]).
%
% fof(t63_zfmisc_1,plain,(($equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b))&~in(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),[]).
%
% cnf(172133440,plain,(~in(a,c)),inference(rewrite,[status(thm)],[t63_zfmisc_1]),[]).
%
% cnf(182638080,plain,(~in(a,B)|~$equal(set_intersection2(c,A),B)),inference(resolution,[status(thm)],[172052128,172133440]),[]).
%
% cnf(189675568,plain,(~in(a,set_intersection2(c,A))),inference(equality_resolution,[status(thm)],[182638080]),[]).
%
% fof(d2_tarski,plain,(((~$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/SET920+1.tptp',unknown),[]).
%
% cnf(172007848,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
%
% cnf(183060560,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[172007848]),[]).
%
% cnf(172141024,plain,($equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b))),inference(rewrite,[status(thm)],[t63_zfmisc_1]),[]).
%
% cnf(183367904,plain,(in(a,set_intersection2(unordered_pair(a,b),c))),inference(paramodulation,[status(thm)],[183060560,172141024,theory(equality)]),[]).
%
% fof(commutativity_k3_xboole_0,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),[]).
%
% cnf(171953280,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),[]).
%
% cnf(183494248,plain,(in(a,set_intersection2(c,unordered_pair(a,b)))),inference(paramodulation,[status(thm)],[183367904,171953280,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[189675568,183494248]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------