TSTP Solution File: SET009+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET009+3 : TPTP v3.4.2. Released v2.2.0.
% 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 15:23:03 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 ( 8 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 42 ( 20 ~; 17 |; 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 : 30 ( 9 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET009+3.tptp',unknown),
[] ).
cnf(147951808,plain,
( member(C,A)
| ~ member(C,difference(A,B)) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
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/SET009+3.tptp',unknown),
[] ).
cnf(147963544,plain,
( member(d(A,B,C),A)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
fof(prove_subset_difference,plain,
( subset(b,c)
& ~ subset(difference(d,c),difference(d,b)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET009+3.tptp',unknown),
[] ).
cnf(148040760,plain,
~ subset(difference(d,c),difference(d,b)),
inference(rewrite,[status(thm)],[prove_subset_difference]),
[] ).
cnf(158463120,plain,
member(d(difference(d,c),difference(d,b),A),difference(d,c)),
inference(resolution,[status(thm)],[147963544,148040760]),
[] ).
cnf(158485488,plain,
member(d(difference(d,c),difference(d,b),A),d),
inference(resolution,[status(thm)],[147951808,158463120]),
[] ).
cnf(147958184,plain,
( ~ member(C,B)
| ~ member(C,difference(A,B)) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
cnf(158519984,plain,
~ member(d(difference(d,c),difference(d,b),A),c),
inference(resolution,[status(thm)],[147958184,158463120]),
[] ).
cnf(147981280,plain,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(148048080,plain,
subset(b,c),
inference(rewrite,[status(thm)],[prove_subset_difference]),
[] ).
cnf(158854392,plain,
( ~ member(A,b)
| member(A,c) ),
inference(resolution,[status(thm)],[147981280,148048080]),
[] ).
cnf(159431424,plain,
~ member(d(difference(d,c),difference(d,b),A),b),
inference(resolution,[status(thm)],[158519984,158854392]),
[] ).
cnf(147969248,plain,
( ~ member(d(A,B,C),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(158476024,plain,
~ member(d(difference(d,c),difference(d,b),A),difference(d,b)),
inference(resolution,[status(thm)],[147969248,148040760]),
[] ).
cnf(147941864,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)],[158485488,159431424,158476024,147941864]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/SET009+3.tptp',unknown),[]).
%
% cnf(147951808,plain,(member(C,A)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% 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/SET009+3.tptp',unknown),[]).
%
% cnf(147963544,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% fof(prove_subset_difference,plain,((subset(b,c)&~subset(difference(d,c),difference(d,b)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET009+3.tptp',unknown),[]).
%
% cnf(148040760,plain,(~subset(difference(d,c),difference(d,b))),inference(rewrite,[status(thm)],[prove_subset_difference]),[]).
%
% cnf(158463120,plain,(member(d(difference(d,c),difference(d,b),A),difference(d,c))),inference(resolution,[status(thm)],[147963544,148040760]),[]).
%
% cnf(158485488,plain,(member(d(difference(d,c),difference(d,b),A),d)),inference(resolution,[status(thm)],[147951808,158463120]),[]).
%
% cnf(147958184,plain,(~member(C,B)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% cnf(158519984,plain,(~member(d(difference(d,c),difference(d,b),A),c)),inference(resolution,[status(thm)],[147958184,158463120]),[]).
%
% cnf(147981280,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(148048080,plain,(subset(b,c)),inference(rewrite,[status(thm)],[prove_subset_difference]),[]).
%
% cnf(158854392,plain,(~member(A,b)|member(A,c)),inference(resolution,[status(thm)],[147981280,148048080]),[]).
%
% cnf(159431424,plain,(~member(d(difference(d,c),difference(d,b),A),b)),inference(resolution,[status(thm)],[158519984,158854392]),[]).
%
% cnf(147969248,plain,(~member(d(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(158476024,plain,(~member(d(difference(d,c),difference(d,b),A),difference(d,b))),inference(resolution,[status(thm)],[147969248,148040760]),[]).
%
% cnf(147941864,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)],[158485488,159431424,158476024,147941864]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------