TSTP Solution File: SET903+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET903+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 15:41:04 EDT 2009
% Result : Theorem 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 32 ( 2 avg)
% Number of connectives : 56 ( 18 ~; 28 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t43_zfmisc_1,plain,
! [C,A,B] :
( ( $equal(empty_set,C)
| $equal(singleton(A),C)
| $equal(singleton(A),C)
| ~ $equal(set_union2(B,C),singleton(A)) )
& ( $equal(singleton(A),B)
| $equal(singleton(A),C)
| $equal(singleton(A),C)
| ~ $equal(set_union2(B,C),singleton(A)) )
& ( $equal(empty_set,C)
| $equal(empty_set,B)
| $equal(singleton(A),C)
| ~ $equal(set_union2(B,C),singleton(A)) )
& ( $equal(singleton(A),B)
| $equal(empty_set,B)
| $equal(singleton(A),C)
| ~ $equal(set_union2(B,C),singleton(A)) )
& ( $equal(empty_set,C)
| $equal(singleton(A),C)
| $equal(singleton(A),B)
| ~ $equal(set_union2(B,C),singleton(A)) )
& ( $equal(singleton(A),B)
| $equal(singleton(A),C)
| $equal(singleton(A),B)
| ~ $equal(set_union2(B,C),singleton(A)) )
& ( $equal(empty_set,C)
| $equal(empty_set,B)
| $equal(singleton(A),B)
| ~ $equal(set_union2(B,C),singleton(A)) )
& ( $equal(singleton(A),B)
| $equal(empty_set,B)
| $equal(singleton(A),B)
| ~ $equal(set_union2(B,C),singleton(A)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET903+1.tptp',unknown),
[] ).
cnf(160374488,plain,
( $equal(singleton(A),B)
| $equal(empty_set,B)
| ~ $equal(set_union2(B,C),singleton(A)) ),
inference(rewrite,[status(thm)],[t43_zfmisc_1]),
[] ).
fof(t44_zfmisc_1,plain,
( $equal(set_union2(b,c),singleton(a))
& ~ $equal(c,b)
& ~ $equal(empty_set,b)
& ~ $equal(empty_set,c) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET903+1.tptp',unknown),
[] ).
cnf(160497072,plain,
$equal(set_union2(b,c),singleton(a)),
inference(rewrite,[status(thm)],[t44_zfmisc_1]),
[] ).
cnf(179513880,plain,
( $equal(singleton(a),b)
| $equal(empty_set,b) ),
inference(resolution,[status(thm)],[160374488,160497072]),
[] ).
cnf(160482680,plain,
~ $equal(empty_set,b),
inference(rewrite,[status(thm)],[t44_zfmisc_1]),
[] ).
cnf(179569912,plain,
$equal(singleton(a),b),
inference(resolution,[status(thm)],[179513880,160482680]),
[] ).
cnf(179776832,plain,
$equal(set_union2(b,c),b),
inference(paramodulation,[status(thm)],[179569912,160497072,theory(equality)]),
[] ).
cnf(179927528,plain,
$equal(singleton(a),set_union2(b,c)),
inference(paramodulation,[status(thm)],[179776832,179569912,theory(equality)]),
[] ).
cnf(160471264,plain,
~ $equal(empty_set,c),
inference(rewrite,[status(thm)],[t44_zfmisc_1]),
[] ).
cnf(176199568,plain,
( $equal(singleton(A),c)
| ~ $equal(set_union2(c,B),singleton(A)) ),
inference(resolution,[status(thm)],[160374488,160471264]),
[] ).
fof(commutativity_k2_xboole_0,plain,
! [B,A] : $equal(set_union2(B,A),set_union2(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET903+1.tptp',unknown),
[] ).
cnf(160314432,plain,
$equal(set_union2(B,A),set_union2(A,B)),
inference(rewrite,[status(thm)],[commutativity_k2_xboole_0]),
[] ).
cnf(179865408,plain,
$equal(b,set_union2(c,b)),
inference(paramodulation,[status(thm)],[179776832,160314432,theory(equality)]),
[] ).
cnf(179892208,plain,
$equal(b,singleton(a)),
inference(paramodulation,[status(thm)],[179776832,160497072,theory(equality)]),
[] ).
cnf(180148528,plain,
$equal(set_union2(c,b),singleton(a)),
inference(paramodulation,[status(thm)],[179865408,179892208,theory(equality)]),
[] ).
cnf(184097384,plain,
$equal(singleton(a),c),
inference(resolution,[status(thm)],[176199568,180148528]),
[] ).
cnf(160489736,plain,
~ $equal(c,b),
inference(rewrite,[status(thm)],[t44_zfmisc_1]),
[] ).
cnf(179590632,plain,
~ $equal(c,singleton(a)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[160482680,179513880,160489736,theory(equality)]),
[] ).
cnf(179841448,plain,
~ $equal(c,set_union2(b,c)),
inference(paramodulation,[status(thm)],[179590632,160497072,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[179927528,184097384,179841448,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t43_zfmisc_1,plain,((($equal(empty_set,C)|$equal(singleton(A),C)|$equal(singleton(A),C)|~$equal(set_union2(B,C),singleton(A)))&($equal(singleton(A),B)|$equal(singleton(A),C)|$equal(singleton(A),C)|~$equal(set_union2(B,C),singleton(A)))&($equal(empty_set,C)|$equal(empty_set,B)|$equal(singleton(A),C)|~$equal(set_union2(B,C),singleton(A)))&($equal(singleton(A),B)|$equal(empty_set,B)|$equal(singleton(A),C)|~$equal(set_union2(B,C),singleton(A)))&($equal(empty_set,C)|$equal(singleton(A),C)|$equal(singleton(A),B)|~$equal(set_union2(B,C),singleton(A)))&($equal(singleton(A),B)|$equal(singleton(A),C)|$equal(singleton(A),B)|~$equal(set_union2(B,C),singleton(A)))&($equal(empty_set,C)|$equal(empty_set,B)|$equal(singleton(A),B)|~$equal(set_union2(B,C),singleton(A)))&($equal(singleton(A),B)|$equal(empty_set,B)|$equal(singleton(A),B)|~$equal(set_union2(B,C),singleton(A))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET903+1.tptp',unknown),[]).
%
% cnf(160374488,plain,($equal(singleton(A),B)|$equal(empty_set,B)|~$equal(set_union2(B,C),singleton(A))),inference(rewrite,[status(thm)],[t43_zfmisc_1]),[]).
%
% fof(t44_zfmisc_1,plain,(($equal(set_union2(b,c),singleton(a))&~$equal(c,b)&~$equal(empty_set,b)&~$equal(empty_set,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET903+1.tptp',unknown),[]).
%
% cnf(160497072,plain,($equal(set_union2(b,c),singleton(a))),inference(rewrite,[status(thm)],[t44_zfmisc_1]),[]).
%
% cnf(179513880,plain,($equal(singleton(a),b)|$equal(empty_set,b)),inference(resolution,[status(thm)],[160374488,160497072]),[]).
%
% cnf(160482680,plain,(~$equal(empty_set,b)),inference(rewrite,[status(thm)],[t44_zfmisc_1]),[]).
%
% cnf(179569912,plain,($equal(singleton(a),b)),inference(resolution,[status(thm)],[179513880,160482680]),[]).
%
% cnf(179776832,plain,($equal(set_union2(b,c),b)),inference(paramodulation,[status(thm)],[179569912,160497072,theory(equality)]),[]).
%
% cnf(179927528,plain,($equal(singleton(a),set_union2(b,c))),inference(paramodulation,[status(thm)],[179776832,179569912,theory(equality)]),[]).
%
% cnf(160471264,plain,(~$equal(empty_set,c)),inference(rewrite,[status(thm)],[t44_zfmisc_1]),[]).
%
% cnf(176199568,plain,($equal(singleton(A),c)|~$equal(set_union2(c,B),singleton(A))),inference(resolution,[status(thm)],[160374488,160471264]),[]).
%
% fof(commutativity_k2_xboole_0,plain,($equal(set_union2(B,A),set_union2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET903+1.tptp',unknown),[]).
%
% cnf(160314432,plain,($equal(set_union2(B,A),set_union2(A,B))),inference(rewrite,[status(thm)],[commutativity_k2_xboole_0]),[]).
%
% cnf(179865408,plain,($equal(b,set_union2(c,b))),inference(paramodulation,[status(thm)],[179776832,160314432,theory(equality)]),[]).
%
% cnf(179892208,plain,($equal(b,singleton(a))),inference(paramodulation,[status(thm)],[179776832,160497072,theory(equality)]),[]).
%
% cnf(180148528,plain,($equal(set_union2(c,b),singleton(a))),inference(paramodulation,[status(thm)],[179865408,179892208,theory(equality)]),[]).
%
% cnf(184097384,plain,($equal(singleton(a),c)),inference(resolution,[status(thm)],[176199568,180148528]),[]).
%
% cnf(160489736,plain,(~$equal(c,b)),inference(rewrite,[status(thm)],[t44_zfmisc_1]),[]).
%
% cnf(179590632,plain,(~$equal(c,singleton(a))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[160482680,179513880,160489736,theory(equality)]),[]).
%
% cnf(179841448,plain,(~$equal(c,set_union2(b,c))),inference(paramodulation,[status(thm)],[179590632,160497072,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[179927528,184097384,179841448,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------