TSTP Solution File: SET588+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET588+3 : TPTP v3.4.2. Released v2.2.0.
% 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 15:32:00 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 43 ( 20 ~; 18 |; 5 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 31 ( 9 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(subset_defn,plain,
! [A,B,C] :
( ( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) )
& ( ~ member(d(A,B,C),B)
| subset(A,B) )
& ( member(d(A,B,C),A)
| subset(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET588+3.tptp',unknown),
[] ).
cnf(159078464,plain,
( member(d(A,B,C),A)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
fof(prove_difference_subset1,plain,
( subset(b,c)
& ~ subset(difference(b,d),difference(c,d)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET588+3.tptp',unknown),
[] ).
cnf(159155680,plain,
~ subset(difference(b,d),difference(c,d)),
inference(rewrite,[status(thm)],[prove_difference_subset1]),
[] ).
cnf(169578040,plain,
member(d(difference(b,d),difference(c,d),A),difference(b,d)),
inference(resolution,[status(thm)],[159078464,159155680]),
[] ).
cnf(159096200,plain,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(159163000,plain,
subset(b,c),
inference(rewrite,[status(thm)],[prove_difference_subset1]),
[] ).
cnf(169974056,plain,
( ~ member(A,b)
| member(A,c) ),
inference(resolution,[status(thm)],[159096200,159163000]),
[] ).
fof(difference_defn,plain,
! [C,B,A] :
( ( ~ member(C,B)
| ~ member(C,difference(A,B)) )
& ( member(C,A)
| ~ member(C,difference(A,B)) )
& ( member(C,difference(A,B))
| ~ member(C,A)
| member(C,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET588+3.tptp',unknown),
[] ).
cnf(159066728,plain,
( member(C,A)
| ~ member(C,difference(A,B)) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
cnf(170071400,plain,
( member(A,c)
| ~ member(A,difference(b,B)) ),
inference(resolution,[status(thm)],[169974056,159066728]),
[] ).
cnf(170518664,plain,
member(d(difference(b,d),difference(c,d),A),c),
inference(resolution,[status(thm)],[169578040,170071400]),
[] ).
cnf(159073104,plain,
( ~ member(C,B)
| ~ member(C,difference(A,B)) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
cnf(169634904,plain,
~ member(d(difference(b,d),difference(c,d),A),d),
inference(resolution,[status(thm)],[159073104,169578040]),
[] ).
cnf(159084168,plain,
( ~ member(d(A,B,C),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(169590944,plain,
~ member(d(difference(b,d),difference(c,d),A),difference(c,d)),
inference(resolution,[status(thm)],[159084168,159155680]),
[] ).
cnf(159056784,plain,
( member(C,difference(A,B))
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[170518664,169634904,169590944,159056784]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(subset_defn,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(d(A,B,C),B)|subset(A,B))&(member(d(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET588+3.tptp',unknown),[]).
%
% cnf(159078464,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% fof(prove_difference_subset1,plain,((subset(b,c)&~subset(difference(b,d),difference(c,d)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET588+3.tptp',unknown),[]).
%
% cnf(159155680,plain,(~subset(difference(b,d),difference(c,d))),inference(rewrite,[status(thm)],[prove_difference_subset1]),[]).
%
% cnf(169578040,plain,(member(d(difference(b,d),difference(c,d),A),difference(b,d))),inference(resolution,[status(thm)],[159078464,159155680]),[]).
%
% cnf(159096200,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(159163000,plain,(subset(b,c)),inference(rewrite,[status(thm)],[prove_difference_subset1]),[]).
%
% cnf(169974056,plain,(~member(A,b)|member(A,c)),inference(resolution,[status(thm)],[159096200,159163000]),[]).
%
% fof(difference_defn,plain,(((~member(C,B)|~member(C,difference(A,B)))&(member(C,A)|~member(C,difference(A,B)))&(member(C,difference(A,B))|~member(C,A)|member(C,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET588+3.tptp',unknown),[]).
%
% cnf(159066728,plain,(member(C,A)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% cnf(170071400,plain,(member(A,c)|~member(A,difference(b,B))),inference(resolution,[status(thm)],[169974056,159066728]),[]).
%
% cnf(170518664,plain,(member(d(difference(b,d),difference(c,d),A),c)),inference(resolution,[status(thm)],[169578040,170071400]),[]).
%
% cnf(159073104,plain,(~member(C,B)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% cnf(169634904,plain,(~member(d(difference(b,d),difference(c,d),A),d)),inference(resolution,[status(thm)],[159073104,169578040]),[]).
%
% cnf(159084168,plain,(~member(d(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(169590944,plain,(~member(d(difference(b,d),difference(c,d),A),difference(c,d))),inference(resolution,[status(thm)],[159084168,159155680]),[]).
%
% cnf(159056784,plain,(member(C,difference(A,B))|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[170518664,169634904,169590944,159056784]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------