TSTP Solution File: SET909+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET909+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:41:16 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 31 ( 6 avg)
% Number of connectives : 104 ( 36 ~; 51 |; 17 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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; 0-4 aty)
% Number of variables : 24 ( 6 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(d1_xboole_0,plain,
! [A,B] :
( ( ~ $equal(empty_set,A)
| ~ in(B,A) )
& ( $equal(empty_set,A)
| in(b(A,B),A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET909+1.tptp',unknown),
[] ).
cnf(171004896,plain,
( ~ $equal(empty_set,A)
| ~ in(B,A) ),
inference(rewrite,[status(thm)],[d1_xboole_0]),
[] ).
cnf(180179288,plain,
~ in(A,empty_set),
inference(equality_resolution,[status(thm)],[171004896]),
[] ).
fof(d2_xboole_0,plain,
! [D,B,C,A] :
( ( ~ in(D,B)
| in(D,C)
| ~ $equal(set_union2(A,B),C) )
& ( ~ in(D,A)
| in(D,C)
| ~ $equal(set_union2(A,B),C) )
& ( ~ in(D,C)
| in(D,A)
| in(D,B)
| ~ $equal(set_union2(A,B),C) )
& ( in(d(A,B,C,D),A)
| in(d(A,B,C,D),B)
| ~ in(d(A,B,C,D),A)
| $equal(set_union2(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| ~ in(d(A,B,C,D),A)
| $equal(set_union2(A,B),C) )
& ( in(d(A,B,C,D),A)
| in(d(A,B,C,D),B)
| ~ in(d(A,B,C,D),B)
| $equal(set_union2(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| ~ in(d(A,B,C,D),B)
| $equal(set_union2(A,B),C) )
& ( in(d(A,B,C,D),A)
| in(d(A,B,C,D),B)
| in(d(A,B,C,D),C)
| $equal(set_union2(A,B),C) )
& ( ~ in(d(A,B,C,D),C)
| in(d(A,B,C,D),C)
| $equal(set_union2(A,B),C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET909+1.tptp',unknown),
[] ).
cnf(171107608,plain,
( ~ in(D,A)
| in(D,C)
| ~ $equal(set_union2(A,B),C) ),
inference(rewrite,[status(thm)],[d2_xboole_0]),
[] ).
fof(t50_zfmisc_1,plain,
$equal(set_union2(unordered_pair(a,b),c),empty_set),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET909+1.tptp',unknown),
[] ).
cnf(171177376,plain,
$equal(set_union2(unordered_pair(a,b),c),empty_set),
inference(rewrite,[status(thm)],[t50_zfmisc_1]),
[] ).
cnf(185549416,plain,
~ in(A,unordered_pair(a,b)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[180179288,171107608,171177376]),
[] ).
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/SET909+1.tptp',unknown),
[] ).
cnf(171058992,plain,
( ~ $equal(A,D)
| in(D,C)
| ~ $equal(unordered_pair(A,B),C) ),
inference(rewrite,[status(thm)],[d2_tarski]),
[] ).
cnf(183063960,plain,
in(A,unordered_pair(A,B)),
inference(equality_resolution,[status(thm)],[171058992]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[185549416,183063960]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d1_xboole_0,plain,(((~$equal(empty_set,A)|~in(B,A))&($equal(empty_set,A)|in(b(A,B),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET909+1.tptp',unknown),[]).
%
% cnf(171004896,plain,(~$equal(empty_set,A)|~in(B,A)),inference(rewrite,[status(thm)],[d1_xboole_0]),[]).
%
% cnf(180179288,plain,(~in(A,empty_set)),inference(equality_resolution,[status(thm)],[171004896]),[]).
%
% fof(d2_xboole_0,plain,(((~in(D,B)|in(D,C)|~$equal(set_union2(A,B),C))&(~in(D,A)|in(D,C)|~$equal(set_union2(A,B),C))&(~in(D,C)|in(D,A)|in(D,B)|~$equal(set_union2(A,B),C))&(in(d(A,B,C,D),A)|in(d(A,B,C,D),B)|~in(d(A,B,C,D),A)|$equal(set_union2(A,B),C))&(~in(d(A,B,C,D),C)|~in(d(A,B,C,D),A)|$equal(set_union2(A,B),C))&(in(d(A,B,C,D),A)|in(d(A,B,C,D),B)|~in(d(A,B,C,D),B)|$equal(set_union2(A,B),C))&(~in(d(A,B,C,D),C)|~in(d(A,B,C,D),B)|$equal(set_union2(A,B),C))&(in(d(A,B,C,D),A)|in(d(A,B,C,D),B)|in(d(A,B,C,D),C)|$equal(set_union2(A,B),C))&(~in(d(A,B,C,D),C)|in(d(A,B,C,D),C)|$equal(set_union2(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET909+1.tptp',unknown),[]).
%
% cnf(171107608,plain,(~in(D,A)|in(D,C)|~$equal(set_union2(A,B),C)),inference(rewrite,[status(thm)],[d2_xboole_0]),[]).
%
% fof(t50_zfmisc_1,plain,($equal(set_union2(unordered_pair(a,b),c),empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET909+1.tptp',unknown),[]).
%
% cnf(171177376,plain,($equal(set_union2(unordered_pair(a,b),c),empty_set)),inference(rewrite,[status(thm)],[t50_zfmisc_1]),[]).
%
% cnf(185549416,plain,(~in(A,unordered_pair(a,b))),inference(forward_subsumption_resolution__resolution,[status(thm)],[180179288,171107608,171177376]),[]).
%
% 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)|$equal(unordered_pair(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET909+1.tptp',unknown),[]).
%
% cnf(171058992,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
%
% cnf(183063960,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[171058992]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[185549416,183063960]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------