TSTP Solution File: SET679+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET679+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 15:35:24 EDT 2009
% Result : Theorem 48.4s
% Output : Refutation 48.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 88 ( 41 ~; 42 |; 5 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 4 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(p22,plain,
! [A] : ilf_type(A,set_type),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),
[] ).
cnf(159635144,plain,
ilf_type(A,set_type),
inference(rewrite,[status(thm)],[p22]),
[] ).
fof(p1,plain,
! [B,A] :
( ( ~ member(B,A)
| member(ordered_pair(B,B),identity_relation_of(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( member(B,A)
| ~ member(ordered_pair(B,B),identity_relation_of(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),
[] ).
cnf(159114024,plain,
( ~ member(B,A)
| member(ordered_pair(B,B),identity_relation_of(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p1]),
[] ).
cnf(170456304,plain,
( ~ member(B,A)
| member(ordered_pair(B,B),identity_relation_of(A)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159635144,159114024,159635144]),
[] ).
fof(p7,plain,
! [A,B] :
( ( ~ not_equal(A,B)
| ~ $equal(B,A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( not_equal(A,B)
| $equal(B,A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),
[] ).
cnf(159277160,plain,
( not_equal(A,B)
| $equal(B,A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p7]),
[] ).
cnf(170402480,plain,
( not_equal(A,B)
| $equal(B,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159635144,159277160,159635144]),
[] ).
fof(prove_relset_1_46,plain,
( ~ empty(b)
& ilf_type(b,set_type)
& ~ not_equal(identity_relation_of(b),empty_set) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),
[] ).
cnf(159684728,plain,
~ not_equal(identity_relation_of(b),empty_set),
inference(rewrite,[status(thm)],[prove_relset_1_46]),
[] ).
cnf(170599448,plain,
$equal(empty_set,identity_relation_of(b)),
inference(resolution,[status(thm)],[170402480,159684728]),
[] ).
fof(p2,plain,
! [A] :
( ~ ilf_type(A,set_type)
| ~ member(A,empty_set) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),
[] ).
cnf(159119872,plain,
( ~ ilf_type(A,set_type)
| ~ member(A,empty_set) ),
inference(rewrite,[status(thm)],[p2]),
[] ).
cnf(170334992,plain,
~ member(A,empty_set),
inference(resolution,[status(thm)],[159119872,159635144]),
[] ).
cnf(170638240,plain,
~ member(A,identity_relation_of(b)),
inference(paramodulation,[status(thm)],[170599448,170334992,theory(equality)]),
[] ).
cnf(425379848,plain,
~ member(A,b),
inference(resolution,[status(thm)],[170456304,170638240]),
[] ).
fof(p20,plain,
! [A,B] :
( ( ~ ilf_type(A,member_type(B))
| member(A,B)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(A,member_type(B))
| ~ member(A,B)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),
[] ).
cnf(159623520,plain,
( ~ ilf_type(A,member_type(B))
| member(A,B)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p20]),
[] ).
cnf(170488752,plain,
( ~ ilf_type(A,member_type(B))
| member(A,B)
| empty(B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159635144,159623520,159635144]),
[] ).
fof(p21,plain,
! [A] :
( empty(A)
| ~ ilf_type(A,set_type)
| ilf_type(c(A),member_type(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),
[] ).
cnf(159631112,plain,
( empty(A)
| ~ ilf_type(A,set_type)
| ilf_type(c(A),member_type(A)) ),
inference(rewrite,[status(thm)],[p21]),
[] ).
cnf(170394920,plain,
( empty(A)
| ilf_type(c(A),member_type(A)) ),
inference(resolution,[status(thm)],[159631112,159635144]),
[] ).
cnf(171695704,plain,
( member(c(A),A)
| empty(A) ),
inference(resolution,[status(thm)],[170488752,170394920]),
[] ).
cnf(159700400,plain,
~ empty(b),
inference(rewrite,[status(thm)],[prove_relset_1_46]),
[] ).
cnf(171764472,plain,
member(c(b),b),
inference(resolution,[status(thm)],[171695704,159700400]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[425379848,171764472]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 49 seconds
% START OF PROOF SEQUENCE
% fof(p22,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),[]).
%
% cnf(159635144,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p22]),[]).
%
% fof(p1,plain,(((~member(B,A)|member(ordered_pair(B,B),identity_relation_of(A))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(member(B,A)|~member(ordered_pair(B,B),identity_relation_of(A))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),[]).
%
% cnf(159114024,plain,(~member(B,A)|member(ordered_pair(B,B),identity_relation_of(A))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p1]),[]).
%
% cnf(170456304,plain,(~member(B,A)|member(ordered_pair(B,B),identity_relation_of(A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[159635144,159114024,159635144]),[]).
%
% fof(p7,plain,(((~not_equal(A,B)|~$equal(B,A)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(not_equal(A,B)|$equal(B,A)|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),[]).
%
% cnf(159277160,plain,(not_equal(A,B)|$equal(B,A)|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p7]),[]).
%
% cnf(170402480,plain,(not_equal(A,B)|$equal(B,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159635144,159277160,159635144]),[]).
%
% fof(prove_relset_1_46,plain,((~empty(b)&ilf_type(b,set_type)&~not_equal(identity_relation_of(b),empty_set))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),[]).
%
% cnf(159684728,plain,(~not_equal(identity_relation_of(b),empty_set)),inference(rewrite,[status(thm)],[prove_relset_1_46]),[]).
%
% cnf(170599448,plain,($equal(empty_set,identity_relation_of(b))),inference(resolution,[status(thm)],[170402480,159684728]),[]).
%
% fof(p2,plain,(~ilf_type(A,set_type)|~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),[]).
%
% cnf(159119872,plain,(~ilf_type(A,set_type)|~member(A,empty_set)),inference(rewrite,[status(thm)],[p2]),[]).
%
% cnf(170334992,plain,(~member(A,empty_set)),inference(resolution,[status(thm)],[159119872,159635144]),[]).
%
% cnf(170638240,plain,(~member(A,identity_relation_of(b))),inference(paramodulation,[status(thm)],[170599448,170334992,theory(equality)]),[]).
%
% cnf(425379848,plain,(~member(A,b)),inference(resolution,[status(thm)],[170456304,170638240]),[]).
%
% fof(p20,plain,(((~ilf_type(A,member_type(B))|member(A,B)|empty(B)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(A,member_type(B))|~member(A,B)|empty(B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),[]).
%
% cnf(159623520,plain,(~ilf_type(A,member_type(B))|member(A,B)|empty(B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p20]),[]).
%
% cnf(170488752,plain,(~ilf_type(A,member_type(B))|member(A,B)|empty(B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159635144,159623520,159635144]),[]).
%
% fof(p21,plain,(empty(A)|~ilf_type(A,set_type)|ilf_type(c(A),member_type(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET679+3.tptp',unknown),[]).
%
% cnf(159631112,plain,(empty(A)|~ilf_type(A,set_type)|ilf_type(c(A),member_type(A))),inference(rewrite,[status(thm)],[p21]),[]).
%
% cnf(170394920,plain,(empty(A)|ilf_type(c(A),member_type(A))),inference(resolution,[status(thm)],[159631112,159635144]),[]).
%
% cnf(171695704,plain,(member(c(A),A)|empty(A)),inference(resolution,[status(thm)],[170488752,170394920]),[]).
%
% cnf(159700400,plain,(~empty(b)),inference(rewrite,[status(thm)],[prove_relset_1_46]),[]).
%
% cnf(171764472,plain,(member(c(b),b)),inference(resolution,[status(thm)],[171695704,159700400]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[425379848,171764472]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------