TSTP Solution File: SET900+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET900+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 15:40:57 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 51 ( 22 ~; 20 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t41_zfmisc_1,plain,
! [C] :
( ( ~ $equal(singleton(b),a)
| ~ in(C,a) )
& ( $equal(b,C)
| ~ in(C,a) )
& ( ~ $equal(empty_set,a)
| ~ in(C,a) )
& ( ~ $equal(singleton(b),a)
| ~ $equal(empty_set,a) )
& ( $equal(b,C)
| ~ $equal(empty_set,a) )
& ( ~ $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( ~ $equal(singleton(b),a)
| ~ $equal(singleton(b),a) )
& ( $equal(b,C)
| ~ $equal(singleton(b),a) )
& ( ~ $equal(empty_set,a)
| ~ $equal(singleton(b),a) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET900+1.tptp',unknown),
[] ).
cnf(172166504,plain,
~ $equal(empty_set,a),
inference(rewrite,[status(thm)],[t41_zfmisc_1]),
[] ).
cnf(172180184,plain,
( $equal(b,C)
| ~ in(C,a) ),
inference(rewrite,[status(thm)],[t41_zfmisc_1]),
[] ).
fof(l45_zfmisc_1,plain,
! [A,B] :
( ( in(c(A,B),A)
| $equal(empty_set,A)
| $equal(singleton(B),A) )
& ( ~ $equal(c(A,B),B)
| $equal(empty_set,A)
| $equal(singleton(B),A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET900+1.tptp',unknown),
[] ).
cnf(172210056,plain,
( in(c(A,B),A)
| $equal(empty_set,A)
| $equal(singleton(B),A) ),
inference(rewrite,[status(thm)],[l45_zfmisc_1]),
[] ).
cnf(190554112,plain,
( in(c(a,A),a)
| $equal(singleton(A),a) ),
inference(resolution,[status(thm)],[172210056,172166504]),
[] ).
cnf(172162672,plain,
~ $equal(singleton(b),a),
inference(rewrite,[status(thm)],[t41_zfmisc_1]),
[] ).
cnf(190584568,plain,
in(c(a,b),a),
inference(resolution,[status(thm)],[190554112,172162672]),
[] ).
cnf(190655880,plain,
$equal(b,c(a,b)),
inference(resolution,[status(thm)],[172180184,190584568]),
[] ).
cnf(190757168,plain,
( $equal(c(a,b),C)
| ~ in(C,a) ),
inference(paramodulation,[status(thm)],[190655880,172180184,theory(equality)]),
[] ).
cnf(190718264,plain,
in(b,a),
inference(paramodulation,[status(thm)],[190655880,190584568,theory(equality)]),
[] ).
cnf(191104488,plain,
$equal(c(a,b),b),
inference(resolution,[status(thm)],[190757168,190718264]),
[] ).
cnf(191185872,plain,
$equal(b,c(a,c(a,b))),
inference(paramodulation,[status(thm)],[191104488,190655880,theory(equality)]),
[] ).
cnf(191236032,plain,
$equal(c(a,c(a,b)),c(a,b)),
inference(paramodulation,[status(thm)],[191185872,190655880,theory(equality)]),
[] ).
cnf(172197624,plain,
( ~ $equal(c(A,B),B)
| $equal(empty_set,A)
| $equal(singleton(B),A) ),
inference(rewrite,[status(thm)],[l45_zfmisc_1]),
[] ).
cnf(190696240,plain,
~ $equal(singleton(c(a,b)),a),
inference(paramodulation,[status(thm)],[190655880,172162672,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[172166504,191236032,172197624,190696240]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t41_zfmisc_1,plain,(((~$equal(singleton(b),a)|~in(C,a))&($equal(b,C)|~in(C,a))&(~$equal(empty_set,a)|~in(C,a))&(~$equal(singleton(b),a)|~$equal(empty_set,a))&($equal(b,C)|~$equal(empty_set,a))&(~$equal(empty_set,a)|~$equal(empty_set,a))&(~$equal(singleton(b),a)|~$equal(singleton(b),a))&($equal(b,C)|~$equal(singleton(b),a))&(~$equal(empty_set,a)|~$equal(singleton(b),a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET900+1.tptp',unknown),[]).
%
% cnf(172166504,plain,(~$equal(empty_set,a)),inference(rewrite,[status(thm)],[t41_zfmisc_1]),[]).
%
% cnf(172180184,plain,($equal(b,C)|~in(C,a)),inference(rewrite,[status(thm)],[t41_zfmisc_1]),[]).
%
% fof(l45_zfmisc_1,plain,(((in(c(A,B),A)|$equal(empty_set,A)|$equal(singleton(B),A))&(~$equal(c(A,B),B)|$equal(empty_set,A)|$equal(singleton(B),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET900+1.tptp',unknown),[]).
%
% cnf(172210056,plain,(in(c(A,B),A)|$equal(empty_set,A)|$equal(singleton(B),A)),inference(rewrite,[status(thm)],[l45_zfmisc_1]),[]).
%
% cnf(190554112,plain,(in(c(a,A),a)|$equal(singleton(A),a)),inference(resolution,[status(thm)],[172210056,172166504]),[]).
%
% cnf(172162672,plain,(~$equal(singleton(b),a)),inference(rewrite,[status(thm)],[t41_zfmisc_1]),[]).
%
% cnf(190584568,plain,(in(c(a,b),a)),inference(resolution,[status(thm)],[190554112,172162672]),[]).
%
% cnf(190655880,plain,($equal(b,c(a,b))),inference(resolution,[status(thm)],[172180184,190584568]),[]).
%
% cnf(190757168,plain,($equal(c(a,b),C)|~in(C,a)),inference(paramodulation,[status(thm)],[190655880,172180184,theory(equality)]),[]).
%
% cnf(190718264,plain,(in(b,a)),inference(paramodulation,[status(thm)],[190655880,190584568,theory(equality)]),[]).
%
% cnf(191104488,plain,($equal(c(a,b),b)),inference(resolution,[status(thm)],[190757168,190718264]),[]).
%
% cnf(191185872,plain,($equal(b,c(a,c(a,b)))),inference(paramodulation,[status(thm)],[191104488,190655880,theory(equality)]),[]).
%
% cnf(191236032,plain,($equal(c(a,c(a,b)),c(a,b))),inference(paramodulation,[status(thm)],[191185872,190655880,theory(equality)]),[]).
%
% cnf(172197624,plain,(~$equal(c(A,B),B)|$equal(empty_set,A)|$equal(singleton(B),A)),inference(rewrite,[status(thm)],[l45_zfmisc_1]),[]).
%
% cnf(190696240,plain,(~$equal(singleton(c(a,b)),a)),inference(paramodulation,[status(thm)],[190655880,172162672,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[172166504,191236032,172197624,190696240]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------