TSTP Solution File: SET591+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET591+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 15:32:08 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 29 ~; 25 |; 8 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 36 ( 11 sgn 11 !; 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/SET591+3.tptp',unknown),
[] ).
cnf(161656440,plain,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
fof(prove_th50,plain,
( subset(b,difference(c,b))
& ~ $equal(empty_set,b) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
[] ).
cnf(161796928,plain,
subset(b,difference(c,b)),
inference(rewrite,[status(thm)],[prove_th50]),
[] ).
cnf(172890824,plain,
( ~ member(A,b)
| member(A,difference(c,b)) ),
inference(resolution,[status(thm)],[161656440,161796928]),
[] ).
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/SET591+3.tptp',unknown),
[] ).
cnf(161692488,plain,
( ~ member(C,B)
| ~ member(C,difference(A,B)) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
cnf(176681088,plain,
~ member(A,b),
inference(resolution,[status(thm)],[172890824,161692488]),
[] ).
cnf(161630168,plain,
( member(d(A,B,C),A)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
fof(empty_set_defn,plain,
! [A] : ~ member(A,empty_set),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
[] ).
cnf(161696176,plain,
~ member(A,empty_set),
inference(rewrite,[status(thm)],[empty_set_defn]),
[] ).
cnf(172244176,plain,
subset(empty_set,A),
inference(resolution,[status(thm)],[161630168,161696176]),
[] ).
fof(equal_defn,plain,
! [B,A] :
( ( subset(B,A)
| ~ $equal(B,A) )
& ( subset(A,B)
| ~ $equal(B,A) )
& ( $equal(B,A)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
[] ).
cnf(161707656,plain,
( $equal(B,A)
| ~ subset(A,B)
| ~ subset(B,A) ),
inference(rewrite,[status(thm)],[equal_defn]),
[] ).
cnf(161789456,plain,
~ $equal(empty_set,b),
inference(rewrite,[status(thm)],[prove_th50]),
[] ).
cnf(172310072,plain,
~ subset(b,empty_set),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172244176,161707656,161789456]),
[] ).
fof(empty_defn,plain,
! [A,B] :
( ( ~ empty(A)
| ~ member(B,A) )
& ( empty(A)
| member(c(A,B),A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
[] ).
cnf(161742832,plain,
( ~ empty(A)
| ~ member(B,A) ),
inference(rewrite,[status(thm)],[empty_defn]),
[] ).
cnf(172377952,plain,
( ~ empty(A)
| subset(A,B) ),
inference(resolution,[status(thm)],[161742832,161630168]),
[] ).
cnf(161736312,plain,
( empty(A)
| member(c(A,B),A) ),
inference(rewrite,[status(thm)],[empty_defn]),
[] ).
cnf(172389112,plain,
( subset(A,B)
| member(c(A,C),A) ),
inference(resolution,[status(thm)],[172377952,161736312]),
[] ).
cnf(173614496,plain,
member(c(b,A),b),
inference(resolution,[status(thm)],[172310072,172389112]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[176681088,173614496]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(subset_defn,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(d(A,B,C),B)|subset(A,B))&(member(d(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
%
% cnf(161656440,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% fof(prove_th50,plain,((subset(b,difference(c,b))&~$equal(empty_set,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
%
% cnf(161796928,plain,(subset(b,difference(c,b))),inference(rewrite,[status(thm)],[prove_th50]),[]).
%
% cnf(172890824,plain,(~member(A,b)|member(A,difference(c,b))),inference(resolution,[status(thm)],[161656440,161796928]),[]).
%
% 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/SET591+3.tptp',unknown),[]).
%
% cnf(161692488,plain,(~member(C,B)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% cnf(176681088,plain,(~member(A,b)),inference(resolution,[status(thm)],[172890824,161692488]),[]).
%
% cnf(161630168,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% fof(empty_set_defn,plain,(~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
%
% cnf(161696176,plain,(~member(A,empty_set)),inference(rewrite,[status(thm)],[empty_set_defn]),[]).
%
% cnf(172244176,plain,(subset(empty_set,A)),inference(resolution,[status(thm)],[161630168,161696176]),[]).
%
% fof(equal_defn,plain,(((subset(B,A)|~$equal(B,A))&(subset(A,B)|~$equal(B,A))&($equal(B,A)|~subset(A,B)|~subset(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
%
% cnf(161707656,plain,($equal(B,A)|~subset(A,B)|~subset(B,A)),inference(rewrite,[status(thm)],[equal_defn]),[]).
%
% cnf(161789456,plain,(~$equal(empty_set,b)),inference(rewrite,[status(thm)],[prove_th50]),[]).
%
% cnf(172310072,plain,(~subset(b,empty_set)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172244176,161707656,161789456]),[]).
%
% fof(empty_defn,plain,(((~empty(A)|~member(B,A))&(empty(A)|member(c(A,B),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
%
% cnf(161742832,plain,(~empty(A)|~member(B,A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
%
% cnf(172377952,plain,(~empty(A)|subset(A,B)),inference(resolution,[status(thm)],[161742832,161630168]),[]).
%
% cnf(161736312,plain,(empty(A)|member(c(A,B),A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
%
% cnf(172389112,plain,(subset(A,B)|member(c(A,C),A)),inference(resolution,[status(thm)],[172377952,161736312]),[]).
%
% cnf(173614496,plain,(member(c(b,A),b)),inference(resolution,[status(thm)],[172310072,172389112]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[176681088,173614496]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------