TSTP Solution File: SET585+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET585+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 15:31:52 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 38 ( 16 ~; 16 |; 6 &)
% ( 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 9 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(union_defn,plain,
! [C,A,B] :
( ( ~ member(C,union(A,B))
| member(C,A)
| member(C,B) )
& ( ~ member(C,B)
| member(C,union(A,B)) )
& ( ~ member(C,A)
| member(C,union(A,B)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET585+3.tptp',unknown),
[] ).
cnf(170208048,plain,
( ~ member(C,A)
| member(C,union(A,B)) ),
inference(rewrite,[status(thm)],[union_defn]),
[] ).
fof(intersection_defn,plain,
! [C,B,A] :
( ( member(C,B)
| ~ member(C,intersection(A,B)) )
& ( member(C,A)
| ~ member(C,intersection(A,B)) )
& ( member(C,intersection(A,B))
| ~ member(C,A)
| ~ member(C,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET585+3.tptp',unknown),
[] ).
cnf(170253392,plain,
( member(C,A)
| ~ member(C,intersection(A,B)) ),
inference(rewrite,[status(thm)],[intersection_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/SET585+3.tptp',unknown),
[] ).
cnf(170262384,plain,
( member(d(A,B,C),A)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
fof(prove_intersection_subset_of_union,plain,
~ subset(intersection(b,c),union(b,d)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET585+3.tptp',unknown),
[] ).
cnf(170378248,plain,
~ subset(intersection(b,c),union(b,d)),
inference(rewrite,[status(thm)],[prove_intersection_subset_of_union]),
[] ).
cnf(178194896,plain,
member(d(intersection(b,c),union(b,d),A),intersection(b,c)),
inference(resolution,[status(thm)],[170262384,170378248]),
[] ).
cnf(178253736,plain,
member(d(intersection(b,c),union(b,d),A),b),
inference(resolution,[status(thm)],[170253392,178194896]),
[] ).
cnf(178331560,plain,
member(d(intersection(b,c),union(b,d),B),union(b,A)),
inference(resolution,[status(thm)],[170208048,178253736]),
[] ).
cnf(170268152,plain,
( ~ member(d(A,B,C),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset_defn]),
[] ).
cnf(178208584,plain,
~ member(d(intersection(b,c),union(b,d),A),union(b,d)),
inference(resolution,[status(thm)],[170268152,170378248]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[178331560,178208584]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(union_defn,plain,(((~member(C,union(A,B))|member(C,A)|member(C,B))&(~member(C,B)|member(C,union(A,B)))&(~member(C,A)|member(C,union(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET585+3.tptp',unknown),[]).
%
% cnf(170208048,plain,(~member(C,A)|member(C,union(A,B))),inference(rewrite,[status(thm)],[union_defn]),[]).
%
% fof(intersection_defn,plain,(((member(C,B)|~member(C,intersection(A,B)))&(member(C,A)|~member(C,intersection(A,B)))&(member(C,intersection(A,B))|~member(C,A)|~member(C,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET585+3.tptp',unknown),[]).
%
% cnf(170253392,plain,(member(C,A)|~member(C,intersection(A,B))),inference(rewrite,[status(thm)],[intersection_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/SET585+3.tptp',unknown),[]).
%
% cnf(170262384,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% fof(prove_intersection_subset_of_union,plain,(~subset(intersection(b,c),union(b,d))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET585+3.tptp',unknown),[]).
%
% cnf(170378248,plain,(~subset(intersection(b,c),union(b,d))),inference(rewrite,[status(thm)],[prove_intersection_subset_of_union]),[]).
%
% cnf(178194896,plain,(member(d(intersection(b,c),union(b,d),A),intersection(b,c))),inference(resolution,[status(thm)],[170262384,170378248]),[]).
%
% cnf(178253736,plain,(member(d(intersection(b,c),union(b,d),A),b)),inference(resolution,[status(thm)],[170253392,178194896]),[]).
%
% cnf(178331560,plain,(member(d(intersection(b,c),union(b,d),B),union(b,A))),inference(resolution,[status(thm)],[170208048,178253736]),[]).
%
% cnf(170268152,plain,(~member(d(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% cnf(178208584,plain,(~member(d(intersection(b,c),union(b,d),A),union(b,d))),inference(resolution,[status(thm)],[170268152,170378248]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[178331560,178208584]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------