TSTP Solution File: SET666+3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET666+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 15:35:07 EDT 2009
% Result : Theorem 7.9s
% Output : Refutation 7.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 201 ( 93 ~; 96 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 72 ( 10 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(p24,plain,
! [A] : ilf_type(A,set_type),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165855032,plain,
ilf_type(A,set_type),
inference(rewrite,[status(thm)],[p24]),
[] ).
fof(p1,plain,
! [C,A,B,D] :
( ( ~ ilf_type(C,subset_type(cross_product(A,B)))
| ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ~ ilf_type(D,relation_type(A,B))
| ilf_type(D,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165323520,plain,
( ~ ilf_type(C,subset_type(cross_product(A,B)))
| ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p1]),
[] ).
cnf(189154584,plain,
( ~ ilf_type(C,subset_type(cross_product(A,B)))
| ilf_type(C,relation_type(A,B)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165323520,165855032]),
[] ).
fof(p6,plain,
! [B,A] :
( ( ~ ilf_type(B,identity_relation_of_type(A))
| ilf_type(B,relation_type(A,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(B,identity_relation_of_type(A))
| ~ ilf_type(B,relation_type(A,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165447184,plain,
( ilf_type(B,identity_relation_of_type(A))
| ~ ilf_type(B,relation_type(A,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p6]),
[] ).
fof(prove_relset_1_29,plain,
( ilf_type(b,set_type)
& ~ ilf_type(identity_relation_of(b),identity_relation_of_type(b)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165898952,plain,
~ ilf_type(identity_relation_of(b),identity_relation_of_type(b)),
inference(rewrite,[status(thm)],[prove_relset_1_29]),
[] ).
cnf(173886984,plain,
~ ilf_type(identity_relation_of(b),relation_type(b,b)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165447184,165898952]),
[] ).
cnf(189222504,plain,
~ ilf_type(identity_relation_of(b),subset_type(cross_product(b,b))),
inference(resolution,[status(thm)],[189154584,173886984]),
[] ).
fof(p18,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/SET666+3.tptp',unknown),
[] ).
cnf(165696120,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)],[p18]),
[] ).
cnf(175073296,plain,
( ilf_type(A,member_type(B))
| ~ member(A,B)
| empty(B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165696120,165855032]),
[] ).
fof(p17,plain,
! [A] :
( ( ilf_type(power_set(A),set_type)
| ~ ilf_type(A,set_type) )
& ( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165674472,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p17]),
[] ).
cnf(173926064,plain,
~ empty(power_set(A)),
inference(resolution,[status(thm)],[165674472,165855032]),
[] ).
cnf(175080672,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ member(A,power_set(B)) ),
inference(resolution,[status(thm)],[175073296,173926064]),
[] ).
fof(p12,plain,
! [B,A] :
( ( ~ ilf_type(B,subset_type(A))
| ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(B,subset_type(A))
| ~ ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165535912,plain,
( ilf_type(B,subset_type(A))
| ~ ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p12]),
[] ).
cnf(174593832,plain,
( ilf_type(B,subset_type(A))
| ~ ilf_type(B,member_type(power_set(A))) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165535912,165855032]),
[] ).
cnf(175763328,plain,
( ~ member(A,power_set(B))
| ilf_type(A,subset_type(B)) ),
inference(resolution,[status(thm)],[175080672,174593832]),
[] ).
fof(p16,plain,
! [A,B,C] :
( ( ~ member(A,power_set(B))
| ~ ilf_type(C,set_type)
| ~ member(C,A)
| member(C,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( member(d(A,B,C),A)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ~ member(d(A,B,C),B)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(d(A,B,C),set_type)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165646616,plain,
( member(d(A,B,C),A)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p16]),
[] ).
cnf(174922344,plain,
( member(d(A,B,C),A)
| member(A,power_set(B)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165646616,165855032]),
[] ).
cnf(175880952,plain,
( ilf_type(A,subset_type(B))
| member(d(A,B,C),A) ),
inference(resolution,[status(thm)],[175763328,174922344]),
[] ).
cnf(190072360,plain,
member(d(identity_relation_of(b),cross_product(b,b),A),identity_relation_of(b)),
inference(resolution,[status(thm)],[189222504,175880952]),
[] ).
fof(p3,plain,
! [A] :
( ~ ilf_type(A,set_type)
| subset(identity_relation_of(A),cross_product(A,A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165339944,plain,
( ~ ilf_type(A,set_type)
| subset(identity_relation_of(A),cross_product(A,A)) ),
inference(rewrite,[status(thm)],[p3]),
[] ).
cnf(173966624,plain,
subset(identity_relation_of(A),cross_product(A,A)),
inference(resolution,[status(thm)],[165339944,165855032]),
[] ).
fof(p14,plain,
! [A,B,C] :
( ( ~ subset(A,B)
| ~ ilf_type(C,set_type)
| ~ member(C,A)
| member(C,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( member(d(A,B,C),A)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ~ member(d(A,B,C),B)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(d(A,B,C),set_type)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),
[] ).
cnf(165608872,plain,
( ~ subset(A,B)
| ~ ilf_type(C,set_type)
| ~ member(C,A)
| member(C,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p14]),
[] ).
cnf(190911392,plain,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165608872,165855032]),
[] ).
cnf(191487256,plain,
( ~ member(B,identity_relation_of(A))
| member(B,cross_product(A,A)) ),
inference(resolution,[status(thm)],[173966624,190911392]),
[] ).
cnf(165636712,plain,
( ~ member(d(A,B,C),B)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p16]),
[] ).
cnf(181695392,plain,
( ~ member(d(A,B,C),B)
| member(A,power_set(B)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165636712,165855032]),
[] ).
cnf(181804880,plain,
( ~ member(d(A,B,C),B)
| ilf_type(A,subset_type(B)) ),
inference(resolution,[status(thm)],[181695392,175763328]),
[] ).
cnf(190117160,plain,
~ member(d(identity_relation_of(b),cross_product(b,b),A),cross_product(b,b)),
inference(resolution,[status(thm)],[189222504,181804880]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[190072360,191487256,190117160]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 8 seconds
% START OF PROOF SEQUENCE
% fof(p24,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165855032,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p24]),[]).
%
% fof(p1,plain,(((~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(~ilf_type(D,relation_type(A,B))|ilf_type(D,subset_type(cross_product(A,B)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165323520,plain,(~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p1]),[]).
%
% cnf(189154584,plain,(~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))),inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165323520,165855032]),[]).
%
% fof(p6,plain,(((~ilf_type(B,identity_relation_of_type(A))|ilf_type(B,relation_type(A,A))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(B,identity_relation_of_type(A))|~ilf_type(B,relation_type(A,A))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165447184,plain,(ilf_type(B,identity_relation_of_type(A))|~ilf_type(B,relation_type(A,A))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p6]),[]).
%
% fof(prove_relset_1_29,plain,((ilf_type(b,set_type)&~ilf_type(identity_relation_of(b),identity_relation_of_type(b)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165898952,plain,(~ilf_type(identity_relation_of(b),identity_relation_of_type(b))),inference(rewrite,[status(thm)],[prove_relset_1_29]),[]).
%
% cnf(173886984,plain,(~ilf_type(identity_relation_of(b),relation_type(b,b))),inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165447184,165898952]),[]).
%
% cnf(189222504,plain,(~ilf_type(identity_relation_of(b),subset_type(cross_product(b,b)))),inference(resolution,[status(thm)],[189154584,173886984]),[]).
%
% fof(p18,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/SET666+3.tptp',unknown),[]).
%
% cnf(165696120,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)],[p18]),[]).
%
% cnf(175073296,plain,(ilf_type(A,member_type(B))|~member(A,B)|empty(B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165696120,165855032]),[]).
%
% fof(p17,plain,(((ilf_type(power_set(A),set_type)|~ilf_type(A,set_type))&(~empty(power_set(A))|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165674472,plain,(~empty(power_set(A))|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p17]),[]).
%
% cnf(173926064,plain,(~empty(power_set(A))),inference(resolution,[status(thm)],[165674472,165855032]),[]).
%
% cnf(175080672,plain,(ilf_type(A,member_type(power_set(B)))|~member(A,power_set(B))),inference(resolution,[status(thm)],[175073296,173926064]),[]).
%
% fof(p12,plain,(((~ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A)))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(B,subset_type(A))|~ilf_type(B,member_type(power_set(A)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165535912,plain,(ilf_type(B,subset_type(A))|~ilf_type(B,member_type(power_set(A)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p12]),[]).
%
% cnf(174593832,plain,(ilf_type(B,subset_type(A))|~ilf_type(B,member_type(power_set(A)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165535912,165855032]),[]).
%
% cnf(175763328,plain,(~member(A,power_set(B))|ilf_type(A,subset_type(B))),inference(resolution,[status(thm)],[175080672,174593832]),[]).
%
% fof(p16,plain,(((~member(A,power_set(B))|~ilf_type(C,set_type)|~member(C,A)|member(C,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(member(d(A,B,C),A)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(~member(d(A,B,C),B)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(d(A,B,C),set_type)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165646616,plain,(member(d(A,B,C),A)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p16]),[]).
%
% cnf(174922344,plain,(member(d(A,B,C),A)|member(A,power_set(B))),inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165646616,165855032]),[]).
%
% cnf(175880952,plain,(ilf_type(A,subset_type(B))|member(d(A,B,C),A)),inference(resolution,[status(thm)],[175763328,174922344]),[]).
%
% cnf(190072360,plain,(member(d(identity_relation_of(b),cross_product(b,b),A),identity_relation_of(b))),inference(resolution,[status(thm)],[189222504,175880952]),[]).
%
% fof(p3,plain,(~ilf_type(A,set_type)|subset(identity_relation_of(A),cross_product(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165339944,plain,(~ilf_type(A,set_type)|subset(identity_relation_of(A),cross_product(A,A))),inference(rewrite,[status(thm)],[p3]),[]).
%
% cnf(173966624,plain,(subset(identity_relation_of(A),cross_product(A,A))),inference(resolution,[status(thm)],[165339944,165855032]),[]).
%
% fof(p14,plain,(((~subset(A,B)|~ilf_type(C,set_type)|~member(C,A)|member(C,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(member(d(A,B,C),A)|subset(A,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(~member(d(A,B,C),B)|subset(A,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(d(A,B,C),set_type)|subset(A,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET666+3.tptp',unknown),[]).
%
% cnf(165608872,plain,(~subset(A,B)|~ilf_type(C,set_type)|~member(C,A)|member(C,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p14]),[]).
%
% cnf(190911392,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165608872,165855032]),[]).
%
% cnf(191487256,plain,(~member(B,identity_relation_of(A))|member(B,cross_product(A,A))),inference(resolution,[status(thm)],[173966624,190911392]),[]).
%
% cnf(165636712,plain,(~member(d(A,B,C),B)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p16]),[]).
%
% cnf(181695392,plain,(~member(d(A,B,C),B)|member(A,power_set(B))),inference(forward_subsumption_resolution__resolution,[status(thm)],[165855032,165636712,165855032]),[]).
%
% cnf(181804880,plain,(~member(d(A,B,C),B)|ilf_type(A,subset_type(B))),inference(resolution,[status(thm)],[181695392,175763328]),[]).
%
% cnf(190117160,plain,(~member(d(identity_relation_of(b),cross_product(b,b),A),cross_product(b,b))),inference(resolution,[status(thm)],[189222504,181804880]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[190072360,191487256,190117160]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------