TSTP Solution File: SET640+3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET640+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 15:34:16 EDT 2009
% Result : Theorem 3.0s
% Output : Refutation 3.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 12 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 193 ( 87 ~; 91 |; 15 &)
% ( 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 : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 66 ( 9 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(p19,plain,
! [A] : ilf_type(A,set_type),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET640+3.tptp',unknown),
[] ).
cnf(167929168,plain,
ilf_type(A,set_type),
inference(rewrite,[status(thm)],[p19]),
[] ).
fof(p6,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/SET640+3.tptp',unknown),
[] ).
cnf(167628440,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)],[p6]),
[] ).
cnf(181444672,plain,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167628440,167929168]),
[] ).
fof(prove_relset_1_2,plain,
( ilf_type(b,set_type)
& ilf_type(c,set_type)
& ilf_type(d,set_type)
& ilf_type(e,relation_type(c,d))
& subset(b,e)
& ~ subset(b,cross_product(c,d)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET640+3.tptp',unknown),
[] ).
cnf(168031880,plain,
subset(b,e),
inference(rewrite,[status(thm)],[prove_relset_1_2]),
[] ).
cnf(185008768,plain,
( ~ member(A,b)
| member(A,e) ),
inference(resolution,[status(thm)],[181444672,168031880]),
[] ).
cnf(167610832,plain,
( member(d(A,B,C),A)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p6]),
[] ).
cnf(181353368,plain,
( member(d(A,B,C),A)
| subset(A,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167610832,167929168]),
[] ).
cnf(168018064,plain,
~ subset(b,cross_product(c,d)),
inference(rewrite,[status(thm)],[prove_relset_1_2]),
[] ).
cnf(181632336,plain,
member(d(b,cross_product(c,d),A),b),
inference(resolution,[status(thm)],[181353368,168018064]),
[] ).
cnf(185641120,plain,
member(d(b,cross_product(c,d),A),e),
inference(resolution,[status(thm)],[185008768,181632336]),
[] ).
cnf(167601016,plain,
( ~ member(d(A,B,C),B)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p6]),
[] ).
cnf(181368680,plain,
( ~ member(d(A,B,C),B)
| subset(A,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167601016,167929168]),
[] ).
cnf(181771616,plain,
~ member(d(b,cross_product(c,d),A),cross_product(c,d)),
inference(resolution,[status(thm)],[181368680,168018064]),
[] ).
fof(p11,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/SET640+3.tptp',unknown),
[] ).
cnf(167743656,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) ),
inference(rewrite,[status(thm)],[p11]),
[] ).
cnf(181463592,plain,
( ~ member(A,power_set(B))
| ~ member(C,A)
| member(C,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167743656,167929168]),
[] ).
fof(p4,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/SET640+3.tptp',unknown),
[] ).
cnf(167555480,plain,
( ~ 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) ),
inference(rewrite,[status(thm)],[p4]),
[] ).
cnf(181408040,plain,
( ~ ilf_type(D,relation_type(A,B))
| ilf_type(D,subset_type(cross_product(A,B))) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167555480,167929168]),
[] ).
cnf(168039600,plain,
ilf_type(e,relation_type(c,d)),
inference(rewrite,[status(thm)],[prove_relset_1_2]),
[] ).
cnf(191570192,plain,
ilf_type(e,subset_type(cross_product(c,d))),
inference(resolution,[status(thm)],[181408040,168039600]),
[] ).
fof(p13,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/SET640+3.tptp',unknown),
[] ).
cnf(167787408,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)],[p13]),
[] ).
cnf(181398016,plain,
( ~ ilf_type(A,member_type(B))
| member(A,B)
| empty(B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167787408,167929168]),
[] ).
fof(p12,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/SET640+3.tptp',unknown),
[] ).
cnf(167754512,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p12]),
[] ).
cnf(181297576,plain,
~ empty(power_set(A)),
inference(resolution,[status(thm)],[167754512,167929168]),
[] ).
cnf(182430472,plain,
( ~ ilf_type(A,member_type(power_set(B)))
| member(A,power_set(B)) ),
inference(resolution,[status(thm)],[181398016,181297576]),
[] ).
fof(p8,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/SET640+3.tptp',unknown),
[] ).
cnf(167679720,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)],[p8]),
[] ).
cnf(181378560,plain,
( ~ ilf_type(B,subset_type(A))
| ilf_type(B,member_type(power_set(A))) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167679720,167929168]),
[] ).
cnf(183284720,plain,
( member(A,power_set(B))
| ~ ilf_type(A,subset_type(B)) ),
inference(resolution,[status(thm)],[182430472,181378560]),
[] ).
cnf(191723984,plain,
member(e,power_set(cross_product(c,d))),
inference(resolution,[status(thm)],[191570192,183284720]),
[] ).
cnf(195066816,plain,
( ~ member(A,e)
| member(A,cross_product(c,d)) ),
inference(resolution,[status(thm)],[181463592,191723984]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[185641120,181771616,195066816]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(p19,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET640+3.tptp',unknown),[]).
%
% cnf(167929168,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p19]),[]).
%
% fof(p6,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/SET640+3.tptp',unknown),[]).
%
% cnf(167628440,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)],[p6]),[]).
%
% cnf(181444672,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167628440,167929168]),[]).
%
% fof(prove_relset_1_2,plain,((ilf_type(b,set_type)&ilf_type(c,set_type)&ilf_type(d,set_type)&ilf_type(e,relation_type(c,d))&subset(b,e)&~subset(b,cross_product(c,d)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET640+3.tptp',unknown),[]).
%
% cnf(168031880,plain,(subset(b,e)),inference(rewrite,[status(thm)],[prove_relset_1_2]),[]).
%
% cnf(185008768,plain,(~member(A,b)|member(A,e)),inference(resolution,[status(thm)],[181444672,168031880]),[]).
%
% cnf(167610832,plain,(member(d(A,B,C),A)|subset(A,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p6]),[]).
%
% cnf(181353368,plain,(member(d(A,B,C),A)|subset(A,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167610832,167929168]),[]).
%
% cnf(168018064,plain,(~subset(b,cross_product(c,d))),inference(rewrite,[status(thm)],[prove_relset_1_2]),[]).
%
% cnf(181632336,plain,(member(d(b,cross_product(c,d),A),b)),inference(resolution,[status(thm)],[181353368,168018064]),[]).
%
% cnf(185641120,plain,(member(d(b,cross_product(c,d),A),e)),inference(resolution,[status(thm)],[185008768,181632336]),[]).
%
% cnf(167601016,plain,(~member(d(A,B,C),B)|subset(A,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p6]),[]).
%
% cnf(181368680,plain,(~member(d(A,B,C),B)|subset(A,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167601016,167929168]),[]).
%
% cnf(181771616,plain,(~member(d(b,cross_product(c,d),A),cross_product(c,d))),inference(resolution,[status(thm)],[181368680,168018064]),[]).
%
% fof(p11,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/SET640+3.tptp',unknown),[]).
%
% cnf(167743656,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)),inference(rewrite,[status(thm)],[p11]),[]).
%
% cnf(181463592,plain,(~member(A,power_set(B))|~member(C,A)|member(C,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167743656,167929168]),[]).
%
% fof(p4,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/SET640+3.tptp',unknown),[]).
%
% cnf(167555480,plain,(~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)),inference(rewrite,[status(thm)],[p4]),[]).
%
% cnf(181408040,plain,(~ilf_type(D,relation_type(A,B))|ilf_type(D,subset_type(cross_product(A,B)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167555480,167929168]),[]).
%
% cnf(168039600,plain,(ilf_type(e,relation_type(c,d))),inference(rewrite,[status(thm)],[prove_relset_1_2]),[]).
%
% cnf(191570192,plain,(ilf_type(e,subset_type(cross_product(c,d)))),inference(resolution,[status(thm)],[181408040,168039600]),[]).
%
% fof(p13,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/SET640+3.tptp',unknown),[]).
%
% cnf(167787408,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)],[p13]),[]).
%
% cnf(181398016,plain,(~ilf_type(A,member_type(B))|member(A,B)|empty(B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167787408,167929168]),[]).
%
% fof(p12,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/SET640+3.tptp',unknown),[]).
%
% cnf(167754512,plain,(~empty(power_set(A))|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p12]),[]).
%
% cnf(181297576,plain,(~empty(power_set(A))),inference(resolution,[status(thm)],[167754512,167929168]),[]).
%
% cnf(182430472,plain,(~ilf_type(A,member_type(power_set(B)))|member(A,power_set(B))),inference(resolution,[status(thm)],[181398016,181297576]),[]).
%
% fof(p8,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/SET640+3.tptp',unknown),[]).
%
% cnf(167679720,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)],[p8]),[]).
%
% cnf(181378560,plain,(~ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[167929168,167679720,167929168]),[]).
%
% cnf(183284720,plain,(member(A,power_set(B))|~ilf_type(A,subset_type(B))),inference(resolution,[status(thm)],[182430472,181378560]),[]).
%
% cnf(191723984,plain,(member(e,power_set(cross_product(c,d)))),inference(resolution,[status(thm)],[191570192,183284720]),[]).
%
% cnf(195066816,plain,(~member(A,e)|member(A,cross_product(c,d))),inference(resolution,[status(thm)],[181463592,191723984]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[185641120,181771616,195066816]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------