TSTP Solution File: SET912+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET912+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 15:41:23 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 24 ( 11 ~; 9 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET912+1.tptp',unknown),
[] ).
cnf(158220024,plain,
( subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ),
inference(rewrite,[status(thm)],[t38_zfmisc_1]),
[] ).
fof(t53_zfmisc_1,plain,
( in(a,b)
& in(c,b)
& ~ $equal(set_intersection2(unordered_pair(a,c),b),unordered_pair(a,c)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET912+1.tptp',unknown),
[] ).
cnf(158309728,plain,
in(c,b),
inference(rewrite,[status(thm)],[t53_zfmisc_1]),
[] ).
cnf(171470792,plain,
( subset(unordered_pair(A,c),b)
| ~ in(A,b) ),
inference(resolution,[status(thm)],[158220024,158309728]),
[] ).
cnf(158317064,plain,
in(a,b),
inference(rewrite,[status(thm)],[t53_zfmisc_1]),
[] ).
cnf(171483504,plain,
subset(unordered_pair(a,c),b),
inference(resolution,[status(thm)],[171470792,158317064]),
[] ).
cnf(158302328,plain,
~ $equal(set_intersection2(unordered_pair(a,c),b),unordered_pair(a,c)),
inference(rewrite,[status(thm)],[t53_zfmisc_1]),
[] ).
fof(t28_xboole_1,plain,
! [A,B] :
( ~ subset(A,B)
| $equal(set_intersection2(A,B),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET912+1.tptp',unknown),
[] ).
cnf(158212568,plain,
( ~ subset(A,B)
| $equal(set_intersection2(A,B),A) ),
inference(rewrite,[status(thm)],[t28_xboole_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[171483504,158302328,158212568]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(t38_zfmisc_1,plain,(((in(B,C)|~subset(unordered_pair(A,B),C))&(in(A,C)|~subset(unordered_pair(A,B),C))&(subset(unordered_pair(A,B),C)|~in(A,C)|~in(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET912+1.tptp',unknown),[]).
%
% cnf(158220024,plain,(subset(unordered_pair(A,B),C)|~in(A,C)|~in(B,C)),inference(rewrite,[status(thm)],[t38_zfmisc_1]),[]).
%
% fof(t53_zfmisc_1,plain,((in(a,b)&in(c,b)&~$equal(set_intersection2(unordered_pair(a,c),b),unordered_pair(a,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET912+1.tptp',unknown),[]).
%
% cnf(158309728,plain,(in(c,b)),inference(rewrite,[status(thm)],[t53_zfmisc_1]),[]).
%
% cnf(171470792,plain,(subset(unordered_pair(A,c),b)|~in(A,b)),inference(resolution,[status(thm)],[158220024,158309728]),[]).
%
% cnf(158317064,plain,(in(a,b)),inference(rewrite,[status(thm)],[t53_zfmisc_1]),[]).
%
% cnf(171483504,plain,(subset(unordered_pair(a,c),b)),inference(resolution,[status(thm)],[171470792,158317064]),[]).
%
% cnf(158302328,plain,(~$equal(set_intersection2(unordered_pair(a,c),b),unordered_pair(a,c))),inference(rewrite,[status(thm)],[t53_zfmisc_1]),[]).
%
% fof(t28_xboole_1,plain,(~subset(A,B)|$equal(set_intersection2(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET912+1.tptp',unknown),[]).
%
% cnf(158212568,plain,(~subset(A,B)|$equal(set_intersection2(A,B),A)),inference(rewrite,[status(thm)],[t28_xboole_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171483504,158302328,158212568]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------