TSTP Solution File: SET929+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET929+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 15:41:58 EDT 2009
% Result : Theorem 0.8s
% Output : Refutation 0.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 97 ( 37 ~; 46 |; 14 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 4 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t37_xboole_1,plain,
! [A,B] :
( ( ~ $equal(empty_set,set_difference(A,B))
| subset(A,B) )
& ( $equal(empty_set,set_difference(A,B))
| ~ subset(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),
[] ).
cnf(170117824,plain,
( ~ $equal(empty_set,set_difference(A,B))
| subset(A,B) ),
inference(rewrite,[status(thm)],[t37_xboole_1]),
[] ).
fof(t73_zfmisc_1,plain,
( ( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| $equal(set_difference(unordered_pair(a,b),c),empty_set)
| in(a,c) )
& ( ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),empty_set)
| in(a,c) )
& ( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| ~ in(b,c)
| in(a,c) )
& ( ~ in(a,c)
| ~ in(b,c)
| in(a,c) )
& ( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| $equal(set_difference(unordered_pair(a,b),c),empty_set)
| in(b,c) )
& ( ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),empty_set)
| in(b,c) )
& ( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| ~ in(b,c)
| in(b,c) )
& ( ~ in(a,c)
| ~ in(b,c)
| in(b,c) )
& ( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| $equal(set_difference(unordered_pair(a,b),c),empty_set)
| ~ $equal(set_difference(unordered_pair(a,b),c),empty_set) )
& ( ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),empty_set)
| ~ $equal(set_difference(unordered_pair(a,b),c),empty_set) )
& ( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| ~ in(b,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),empty_set) )
& ( ~ in(a,c)
| ~ in(b,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),empty_set) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),
[] ).
cnf(170306328,plain,
( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| in(b,c) ),
inference(rewrite,[status(thm)],[t73_zfmisc_1]),
[] ).
cnf(170310472,plain,
( $equal(set_difference(unordered_pair(a,b),c),empty_set)
| in(a,c) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t73_zfmisc_1,170306328]),
[] ).
cnf(186449840,plain,
( subset(unordered_pair(a,b),c)
| in(a,c) ),
inference(paramodulation,[status(thm)],[170117824,170310472,theory(equality)]),
[] ).
fof(t38_zfmisc_1,plain,
! [B,C,A] :
( ( in(B,C)
| ~ subset(unordered_pair(A,B),C) )
& ( in(A,C)
| ~ subset(unordered_pair(A,B),C) )
& ( subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),
[] ).
cnf(170131680,plain,
( in(A,C)
| ~ subset(unordered_pair(A,B),C) ),
inference(rewrite,[status(thm)],[t38_zfmisc_1]),
[] ).
cnf(186843456,plain,
in(a,c),
inference(resolution,[status(thm)],[186449840,170131680]),
[] ).
cnf(170125232,plain,
( subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ),
inference(rewrite,[status(thm)],[t38_zfmisc_1]),
[] ).
fof(reflexivity_r1_tarski,plain,
! [A] : subset(A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),
[] ).
cnf(170105528,plain,
subset(A,A),
inference(rewrite,[status(thm)],[reflexivity_r1_tarski]),
[] ).
cnf(170111312,plain,
( $equal(empty_set,set_difference(A,B))
| ~ subset(A,B) ),
inference(rewrite,[status(thm)],[t37_xboole_1]),
[] ).
cnf(186284880,plain,
$equal(empty_set,set_difference(A,A)),
inference(resolution,[status(thm)],[170111312,170105528]),
[] ).
cnf(186340784,plain,
( $equal(set_difference(A,A),set_difference(B,C))
| ~ subset(B,C) ),
inference(paramodulation,[status(thm)],[186284880,170111312,theory(equality)]),
[] ).
cnf(188843408,plain,
$equal(set_difference(A,A),empty_set),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[170105528,186340784,186284880,theory(equality)]),
[] ).
cnf(188911328,plain,
( $equal(set_difference(B,C),empty_set)
| ~ subset(B,C) ),
inference(paramodulation,[status(thm)],[188843408,186340784,theory(equality)]),
[] ).
cnf(187410176,plain,
( subset(unordered_pair(a,A),c)
| ~ in(A,c) ),
inference(resolution,[status(thm)],[170125232,186843456]),
[] ).
cnf(191697880,plain,
( $equal(set_difference(unordered_pair(a,B),c),empty_set)
| ~ in(B,c) ),
inference(resolution,[status(thm)],[188911328,187410176]),
[] ).
cnf(186425648,plain,
( subset(unordered_pair(a,b),c)
| in(b,c) ),
inference(paramodulation,[status(thm)],[170117824,170306328,theory(equality)]),
[] ).
cnf(170139880,plain,
( in(B,C)
| ~ subset(unordered_pair(A,B),C) ),
inference(rewrite,[status(thm)],[t38_zfmisc_1]),
[] ).
cnf(186709208,plain,
in(b,c),
inference(resolution,[status(thm)],[186425648,170139880]),
[] ).
cnf(170289200,plain,
( ~ in(a,c)
| ~ in(b,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),empty_set) ),
inference(rewrite,[status(thm)],[t73_zfmisc_1]),
[] ).
cnf(196995000,plain,
~ subset(unordered_pair(a,A),c),
inference(forward_subsumption_resolution__resolution,[status(thm)],[191697880,186709208,170289200,170131680]),
[] ).
cnf(197126896,plain,
~ in(A,c),
inference(forward_subsumption_resolution__resolution,[status(thm)],[186843456,170125232,196995000]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[197126896,186709208]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(t37_xboole_1,plain,(((~$equal(empty_set,set_difference(A,B))|subset(A,B))&($equal(empty_set,set_difference(A,B))|~subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),[]).
%
% cnf(170117824,plain,(~$equal(empty_set,set_difference(A,B))|subset(A,B)),inference(rewrite,[status(thm)],[t37_xboole_1]),[]).
%
% fof(t73_zfmisc_1,plain,((($equal(set_difference(unordered_pair(a,b),c),empty_set)|$equal(set_difference(unordered_pair(a,b),c),empty_set)|in(a,c))&(~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),empty_set)|in(a,c))&($equal(set_difference(unordered_pair(a,b),c),empty_set)|~in(b,c)|in(a,c))&(~in(a,c)|~in(b,c)|in(a,c))&($equal(set_difference(unordered_pair(a,b),c),empty_set)|$equal(set_difference(unordered_pair(a,b),c),empty_set)|in(b,c))&(~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),empty_set)|in(b,c))&($equal(set_difference(unordered_pair(a,b),c),empty_set)|~in(b,c)|in(b,c))&(~in(a,c)|~in(b,c)|in(b,c))&($equal(set_difference(unordered_pair(a,b),c),empty_set)|$equal(set_difference(unordered_pair(a,b),c),empty_set)|~$equal(set_difference(unordered_pair(a,b),c),empty_set))&(~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),empty_set)|~$equal(set_difference(unordered_pair(a,b),c),empty_set))&($equal(set_difference(unordered_pair(a,b),c),empty_set)|~in(b,c)|~$equal(set_difference(unordered_pair(a,b),c),empty_set))&(~in(a,c)|~in(b,c)|~$equal(set_difference(unordered_pair(a,b),c),empty_set)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),[]).
%
% cnf(170306328,plain,($equal(set_difference(unordered_pair(a,b),c),empty_set)|in(b,c)),inference(rewrite,[status(thm)],[t73_zfmisc_1]),[]).
%
% cnf(170310472,plain,($equal(set_difference(unordered_pair(a,b),c),empty_set)|in(a,c)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t73_zfmisc_1,170306328]),[]).
%
% cnf(186449840,plain,(subset(unordered_pair(a,b),c)|in(a,c)),inference(paramodulation,[status(thm)],[170117824,170310472,theory(equality)]),[]).
%
% fof(t38_zfmisc_1,plain,(((in(B,C)|~subset(unordered_pair(A,B),C))&(in(A,C)|~subset(unordered_pair(A,B),C))&(subset(unordered_pair(A,B),C)|~in(A,C)|~in(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),[]).
%
% cnf(170131680,plain,(in(A,C)|~subset(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[t38_zfmisc_1]),[]).
%
% cnf(186843456,plain,(in(a,c)),inference(resolution,[status(thm)],[186449840,170131680]),[]).
%
% cnf(170125232,plain,(subset(unordered_pair(A,B),C)|~in(A,C)|~in(B,C)),inference(rewrite,[status(thm)],[t38_zfmisc_1]),[]).
%
% fof(reflexivity_r1_tarski,plain,(subset(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET929+1.tptp',unknown),[]).
%
% cnf(170105528,plain,(subset(A,A)),inference(rewrite,[status(thm)],[reflexivity_r1_tarski]),[]).
%
% cnf(170111312,plain,($equal(empty_set,set_difference(A,B))|~subset(A,B)),inference(rewrite,[status(thm)],[t37_xboole_1]),[]).
%
% cnf(186284880,plain,($equal(empty_set,set_difference(A,A))),inference(resolution,[status(thm)],[170111312,170105528]),[]).
%
% cnf(186340784,plain,($equal(set_difference(A,A),set_difference(B,C))|~subset(B,C)),inference(paramodulation,[status(thm)],[186284880,170111312,theory(equality)]),[]).
%
% cnf(188843408,plain,($equal(set_difference(A,A),empty_set)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[170105528,186340784,186284880,theory(equality)]),[]).
%
% cnf(188911328,plain,($equal(set_difference(B,C),empty_set)|~subset(B,C)),inference(paramodulation,[status(thm)],[188843408,186340784,theory(equality)]),[]).
%
% cnf(187410176,plain,(subset(unordered_pair(a,A),c)|~in(A,c)),inference(resolution,[status(thm)],[170125232,186843456]),[]).
%
% cnf(191697880,plain,($equal(set_difference(unordered_pair(a,B),c),empty_set)|~in(B,c)),inference(resolution,[status(thm)],[188911328,187410176]),[]).
%
% cnf(186425648,plain,(subset(unordered_pair(a,b),c)|in(b,c)),inference(paramodulation,[status(thm)],[170117824,170306328,theory(equality)]),[]).
%
% cnf(170139880,plain,(in(B,C)|~subset(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[t38_zfmisc_1]),[]).
%
% cnf(186709208,plain,(in(b,c)),inference(resolution,[status(thm)],[186425648,170139880]),[]).
%
% cnf(170289200,plain,(~in(a,c)|~in(b,c)|~$equal(set_difference(unordered_pair(a,b),c),empty_set)),inference(rewrite,[status(thm)],[t73_zfmisc_1]),[]).
%
% cnf(196995000,plain,(~subset(unordered_pair(a,A),c)),inference(forward_subsumption_resolution__resolution,[status(thm)],[191697880,186709208,170289200,170131680]),[]).
%
% cnf(197126896,plain,(~in(A,c)),inference(forward_subsumption_resolution__resolution,[status(thm)],[186843456,170125232,196995000]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[197126896,186709208]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------