TSTP Solution File: SET618+3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET618+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:33:15 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 15 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 30 ( 14 ~; 12 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 26 ( 3 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET618+3.tptp',unknown),
[] ).
cnf(145626336,plain,
( subset(B,A)
| ~ $equal(B,A) ),
inference(rewrite,[status(thm)],[equal_defn]),
[] ).
fof(idempotency_of_union,plain,
! [A] : $equal(union(A,A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),
[] ).
cnf(145588072,plain,
$equal(union(A,A),A),
inference(rewrite,[status(thm)],[idempotency_of_union]),
[] ).
cnf(153696184,plain,
subset(union(A,A),A),
inference(resolution,[status(thm)],[145626336,145588072]),
[] ).
fof(symmetric_difference_defn,plain,
! [A,B] : $equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),
[] ).
cnf(145583656,plain,
$equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B)),
inference(rewrite,[status(thm)],[symmetric_difference_defn]),
[] ).
cnf(154151560,plain,
subset(symmetric_difference(A,A),difference(A,A)),
inference(paramodulation,[status(thm)],[153696184,145583656,theory(equality)]),
[] ).
fof(self_difference_is_empty_set,plain,
! [A] : $equal(empty_set,difference(A,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),
[] ).
cnf(145591904,plain,
$equal(empty_set,difference(A,A)),
inference(rewrite,[status(thm)],[self_difference_is_empty_set]),
[] ).
cnf(154232184,plain,
subset(symmetric_difference(A,A),empty_set),
inference(paramodulation,[status(thm)],[154151560,145591904,theory(equality)]),
[] ).
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/SET618+3.tptp',unknown),
[] ).
cnf(145692528,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/SET618+3.tptp',unknown),
[] ).
cnf(145596584,plain,
~ member(A,empty_set),
inference(rewrite,[status(thm)],[empty_set_defn]),
[] ).
cnf(153585744,plain,
subset(empty_set,A),
inference(resolution,[status(thm)],[145692528,145596584]),
[] ).
cnf(145611560,plain,
( $equal(B,A)
| ~ subset(A,B)
| ~ subset(B,A) ),
inference(rewrite,[status(thm)],[equal_defn]),
[] ).
fof(prove_th93,plain,
~ $equal(symmetric_difference(b,b),empty_set),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),
[] ).
cnf(145760496,plain,
~ $equal(symmetric_difference(b,b),empty_set),
inference(rewrite,[status(thm)],[prove_th93]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[154232184,153585744,145611560,145760496]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(equal_defn,plain,(((subset(B,A)|~$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/SET618+3.tptp',unknown),[]).
%
% cnf(145626336,plain,(subset(B,A)|~$equal(B,A)),inference(rewrite,[status(thm)],[equal_defn]),[]).
%
% fof(idempotency_of_union,plain,($equal(union(A,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),[]).
%
% cnf(145588072,plain,($equal(union(A,A),A)),inference(rewrite,[status(thm)],[idempotency_of_union]),[]).
%
% cnf(153696184,plain,(subset(union(A,A),A)),inference(resolution,[status(thm)],[145626336,145588072]),[]).
%
% fof(symmetric_difference_defn,plain,($equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),[]).
%
% cnf(145583656,plain,($equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B))),inference(rewrite,[status(thm)],[symmetric_difference_defn]),[]).
%
% cnf(154151560,plain,(subset(symmetric_difference(A,A),difference(A,A))),inference(paramodulation,[status(thm)],[153696184,145583656,theory(equality)]),[]).
%
% fof(self_difference_is_empty_set,plain,($equal(empty_set,difference(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),[]).
%
% cnf(145591904,plain,($equal(empty_set,difference(A,A))),inference(rewrite,[status(thm)],[self_difference_is_empty_set]),[]).
%
% cnf(154232184,plain,(subset(symmetric_difference(A,A),empty_set)),inference(paramodulation,[status(thm)],[154151560,145591904,theory(equality)]),[]).
%
% fof(subset_defn,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(d(A,B,C),B)|subset(A,B))&(member(d(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),[]).
%
% cnf(145692528,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
%
% fof(empty_set_defn,plain,(~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),[]).
%
% cnf(145596584,plain,(~member(A,empty_set)),inference(rewrite,[status(thm)],[empty_set_defn]),[]).
%
% cnf(153585744,plain,(subset(empty_set,A)),inference(resolution,[status(thm)],[145692528,145596584]),[]).
%
% cnf(145611560,plain,($equal(B,A)|~subset(A,B)|~subset(B,A)),inference(rewrite,[status(thm)],[equal_defn]),[]).
%
% fof(prove_th93,plain,(~$equal(symmetric_difference(b,b),empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET618+3.tptp',unknown),[]).
%
% cnf(145760496,plain,(~$equal(symmetric_difference(b,b),empty_set)),inference(rewrite,[status(thm)],[prove_th93]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[154232184,153585744,145611560,145760496]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------