TSTP Solution File: SET616+3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET616+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 15:33:10 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 103 ( 45 ~; 46 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 56 ( 14 sgn 11 !; 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/SET616+3.tptp',unknown),
[] ).
cnf(156562992,plain,
( member(C,difference(A,B))
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
cnf(156573000,plain,
( member(C,A)
| ~ member(C,difference(A,B)) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
fof(prove_th90,plain,
( $equal(difference(c,b),difference(b,c))
& ~ $equal(c,b) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET616+3.tptp',unknown),
[] ).
cnf(156720672,plain,
$equal(difference(c,b),difference(b,c)),
inference(rewrite,[status(thm)],[prove_th90]),
[] ).
cnf(167480464,plain,
( member(A,b)
| ~ member(A,difference(c,b)) ),
inference(paramodulation,[status(thm)],[156573000,156720672,theory(equality)]),
[] ).
cnf(168768168,plain,
( ~ member(A,c)
| member(A,b) ),
inference(resolution,[status(thm)],[156562992,167480464]),
[] ).
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/SET616+3.tptp',unknown),
[] ).
cnf(156640792,plain,
( member(d(A,B,C),A)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(168985376,plain,
( member(d(c,A,B),b)
| subset(c,A) ),
inference(resolution,[status(thm)],[168768168,156640792]),
[] ).
cnf(156646552,plain,
( ~ member(d(A,B,C),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(171557096,plain,
subset(c,b),
inference(resolution,[status(thm)],[168985376,156646552]),
[] ).
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/SET616+3.tptp',unknown),
[] ).
cnf(156590680,plain,
( $equal(B,A)
| ~ subset(A,B)
| ~ subset(B,A) ),
inference(rewrite,[status(thm)],[equal_defn]),
[] ).
cnf(156713304,plain,
~ $equal(c,b),
inference(rewrite,[status(thm)],[prove_th90]),
[] ).
cnf(167155816,plain,
( ~ subset(b,c)
| ~ subset(c,b) ),
inference(resolution,[status(thm)],[156590680,156713304]),
[] ).
cnf(171635472,plain,
~ subset(b,c),
inference(resolution,[status(thm)],[171557096,167155816]),
[] ).
cnf(171660296,plain,
member(d(b,c,A),b),
inference(resolution,[status(thm)],[171635472,156640792]),
[] ).
cnf(167366344,plain,
( member(d(difference(A,B),C,D),A)
| subset(difference(A,B),C) ),
inference(resolution,[status(thm)],[156573000,156640792]),
[] ).
cnf(156582736,plain,
( ~ member(C,B)
| ~ member(C,difference(A,B)) ),
inference(rewrite,[status(thm)],[difference_defn]),
[] ).
cnf(167699744,plain,
( ~ member(A,c)
| ~ member(A,difference(c,b)) ),
inference(paramodulation,[status(thm)],[156582736,156720672,theory(equality)]),
[] ).
cnf(169940520,plain,
subset(difference(c,b),A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167366344,167699744,156640792]),
[] ).
cnf(156654536,plain,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(170092272,plain,
( ~ member(B,difference(c,b))
| member(B,A) ),
inference(resolution,[status(thm)],[169940520,156654536]),
[] ).
cnf(167342952,plain,
( ~ member(B,difference(difference(C,D),A))
| member(B,C) ),
inference(resolution,[status(thm)],[156573000,156573000]),
[] ).
cnf(170602816,plain,
~ member(B,difference(c,b)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[170092272,167342952,167699744]),
[] ).
fof(equal_member_defn,plain,
! [C,A,B] :
( ( member(C,A)
| ~ member(C,B)
| ~ $equal(B,A) )
& ( ~ member(C,A)
| member(C,B)
| ~ $equal(B,A) )
& ( member(d(A,B,C),B)
| ~ member(d(A,B,C),B)
| $equal(B,A) )
& ( ~ member(d(A,B,C),A)
| ~ member(d(A,B,C),B)
| $equal(B,A) )
& ( member(d(A,B,C),B)
| member(d(A,B,C),A)
| $equal(B,A) )
& ( ~ member(d(A,B,C),A)
| member(d(A,B,C),A)
| $equal(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET616+3.tptp',unknown),
[] ).
cnf(156629944,plain,
( ~ member(C,A)
| member(C,B)
| ~ $equal(B,A) ),
inference(rewrite,[status(thm)],[equal_member_defn]),
[] ).
cnf(167269912,plain,
( ~ member(A,difference(b,c))
| member(A,difference(c,b)) ),
inference(resolution,[status(thm)],[156629944,156720672]),
[] ).
cnf(170747312,plain,
~ member(B,difference(b,c)),
inference(resolution,[status(thm)],[170602816,167269912]),
[] ).
cnf(170789768,plain,
( ~ member(B,b)
| member(B,c) ),
inference(resolution,[status(thm)],[170747312,156562992]),
[] ).
cnf(171707760,plain,
member(d(b,c,A),c),
inference(resolution,[status(thm)],[171660296,170789768]),
[] ).
cnf(171761112,plain,
subset(b,c),
inference(resolution,[status(thm)],[171707760,156646552]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[171761112,171635472]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(difference_defn,plain,(((~member(C,B)|~member(C,difference(A,B)))&(member(C,A)|~member(C,difference(A,B)))&(member(C,difference(A,B))|~member(C,A)|member(C,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET616+3.tptp',unknown),[]).
%
% cnf(156562992,plain,(member(C,difference(A,B))|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% cnf(156573000,plain,(member(C,A)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% fof(prove_th90,plain,(($equal(difference(c,b),difference(b,c))&~$equal(c,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET616+3.tptp',unknown),[]).
%
% cnf(156720672,plain,($equal(difference(c,b),difference(b,c))),inference(rewrite,[status(thm)],[prove_th90]),[]).
%
% cnf(167480464,plain,(member(A,b)|~member(A,difference(c,b))),inference(paramodulation,[status(thm)],[156573000,156720672,theory(equality)]),[]).
%
% cnf(168768168,plain,(~member(A,c)|member(A,b)),inference(resolution,[status(thm)],[156562992,167480464]),[]).
%
% 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/SET616+3.tptp',unknown),[]).
%
% cnf(156640792,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(168985376,plain,(member(d(c,A,B),b)|subset(c,A)),inference(resolution,[status(thm)],[168768168,156640792]),[]).
%
% cnf(156646552,plain,(~member(d(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(171557096,plain,(subset(c,b)),inference(resolution,[status(thm)],[168985376,156646552]),[]).
%
% fof(equal_defn,plain,(((subset(B,A)|~$equal(B,A))&(subset(A,B)|~$equal(B,A))&($equal(B,A)|~subset(A,B)|~subset(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET616+3.tptp',unknown),[]).
%
% cnf(156590680,plain,($equal(B,A)|~subset(A,B)|~subset(B,A)),inference(rewrite,[status(thm)],[equal_defn]),[]).
%
% cnf(156713304,plain,(~$equal(c,b)),inference(rewrite,[status(thm)],[prove_th90]),[]).
%
% cnf(167155816,plain,(~subset(b,c)|~subset(c,b)),inference(resolution,[status(thm)],[156590680,156713304]),[]).
%
% cnf(171635472,plain,(~subset(b,c)),inference(resolution,[status(thm)],[171557096,167155816]),[]).
%
% cnf(171660296,plain,(member(d(b,c,A),b)),inference(resolution,[status(thm)],[171635472,156640792]),[]).
%
% cnf(167366344,plain,(member(d(difference(A,B),C,D),A)|subset(difference(A,B),C)),inference(resolution,[status(thm)],[156573000,156640792]),[]).
%
% cnf(156582736,plain,(~member(C,B)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
%
% cnf(167699744,plain,(~member(A,c)|~member(A,difference(c,b))),inference(paramodulation,[status(thm)],[156582736,156720672,theory(equality)]),[]).
%
% cnf(169940520,plain,(subset(difference(c,b),A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167366344,167699744,156640792]),[]).
%
% cnf(156654536,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(170092272,plain,(~member(B,difference(c,b))|member(B,A)),inference(resolution,[status(thm)],[169940520,156654536]),[]).
%
% cnf(167342952,plain,(~member(B,difference(difference(C,D),A))|member(B,C)),inference(resolution,[status(thm)],[156573000,156573000]),[]).
%
% cnf(170602816,plain,(~member(B,difference(c,b))),inference(forward_subsumption_resolution__resolution,[status(thm)],[170092272,167342952,167699744]),[]).
%
% fof(equal_member_defn,plain,(((member(C,A)|~member(C,B)|~$equal(B,A))&(~member(C,A)|member(C,B)|~$equal(B,A))&(member(d(A,B,C),B)|~member(d(A,B,C),B)|$equal(B,A))&(~member(d(A,B,C),A)|~member(d(A,B,C),B)|$equal(B,A))&(member(d(A,B,C),B)|member(d(A,B,C),A)|$equal(B,A))&(~member(d(A,B,C),A)|member(d(A,B,C),A)|$equal(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET616+3.tptp',unknown),[]).
%
% cnf(156629944,plain,(~member(C,A)|member(C,B)|~$equal(B,A)),inference(rewrite,[status(thm)],[equal_member_defn]),[]).
%
% cnf(167269912,plain,(~member(A,difference(b,c))|member(A,difference(c,b))),inference(resolution,[status(thm)],[156629944,156720672]),[]).
%
% cnf(170747312,plain,(~member(B,difference(b,c))),inference(resolution,[status(thm)],[170602816,167269912]),[]).
%
% cnf(170789768,plain,(~member(B,b)|member(B,c)),inference(resolution,[status(thm)],[170747312,156562992]),[]).
%
% cnf(171707760,plain,(member(d(b,c,A),c)),inference(resolution,[status(thm)],[171660296,170789768]),[]).
%
% cnf(171761112,plain,(subset(b,c)),inference(resolution,[status(thm)],[171707760,156646552]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[171761112,171635472]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------