TSTP Solution File: SET664+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET664+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:35:03 EDT 2009
% Result : Theorem 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 114 ( 55 ~; 50 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_relset_1_27,plain,
( ilf_type(b,set_type)
& ilf_type(c,set_type)
& ilf_type(d,relation_type(c,b))
& ilf_type(d,relation_type(c,empty_set))
& ~ $equal(empty_set,d) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),
[] ).
cnf(147662704,plain,
ilf_type(d,relation_type(c,empty_set)),
inference(rewrite,[status(thm)],[prove_relset_1_27]),
[] ).
fof(p33,plain,
! [A] : ilf_type(A,set_type),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),
[] ).
cnf(147571848,plain,
ilf_type(A,set_type),
inference(rewrite,[status(thm)],[p33]),
[] ).
fof(p6,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/SET664+3.tptp',unknown),
[] ).
cnf(146988544,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)],[p6]),
[] ).
fof(p28,plain,
! [A,B,C] :
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| relation_like(C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),
[] ).
cnf(147519424,plain,
( ~ ilf_type(A,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| relation_like(C) ),
inference(rewrite,[status(thm)],[p28]),
[] ).
cnf(169729024,plain,
( ~ ilf_type(C,subset_type(cross_product(A,B)))
| relation_like(C) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[147571848,147571848,147519424]),
[] ).
cnf(169774768,plain,
( ~ ilf_type(D,relation_type(A,B))
| relation_like(D) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[147571848,146988544,169729024]),
[] ).
cnf(169861760,plain,
relation_like(d),
inference(resolution,[status(thm)],[147662704,169774768]),
[] ).
fof(p2,plain,
! [A] :
( ( ~ $equal(empty_set,range_of(A))
| $equal(empty_set,A)
| ~ ilf_type(A,binary_relation_type) )
& ( ~ $equal(empty_set,domain_of(A))
| $equal(empty_set,A)
| ~ ilf_type(A,binary_relation_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),
[] ).
cnf(146893416,plain,
( ~ $equal(empty_set,range_of(A))
| $equal(empty_set,A)
| ~ ilf_type(A,binary_relation_type) ),
inference(rewrite,[status(thm)],[p2]),
[] ).
cnf(147650392,plain,
~ $equal(empty_set,d),
inference(rewrite,[status(thm)],[prove_relset_1_27]),
[] ).
cnf(163372984,plain,
( ~ $equal(empty_set,range_of(d))
| ~ ilf_type(d,binary_relation_type) ),
inference(resolution,[status(thm)],[146893416,147650392]),
[] ).
fof(p1,plain,
! [A] :
( ~ ilf_type(A,set_type)
| ~ subset(A,empty_set)
| $equal(empty_set,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),
[] ).
cnf(146867504,plain,
( ~ ilf_type(A,set_type)
| ~ subset(A,empty_set)
| $equal(empty_set,A) ),
inference(rewrite,[status(thm)],[p1]),
[] ).
cnf(161951144,plain,
( ~ subset(A,empty_set)
| $equal(empty_set,A) ),
inference(resolution,[status(thm)],[146867504,147571848]),
[] ).
cnf(164285240,plain,
( ~ ilf_type(d,binary_relation_type)
| ~ subset(range_of(d),empty_set) ),
inference(resolution,[status(thm)],[163372984,161951144]),
[] ).
fof(p3,plain,
! [C,B,A] :
( ( subset(range_of(C),B)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( subset(domain_of(C),A)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),
[] ).
cnf(146941720,plain,
( subset(range_of(C),B)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p3]),
[] ).
cnf(170764400,plain,
( subset(range_of(C),A)
| ~ ilf_type(C,relation_type(B,A)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[147571848,147571848,146941720]),
[] ).
cnf(170771432,plain,
subset(range_of(d),empty_set),
inference(resolution,[status(thm)],[147662704,170764400]),
[] ).
cnf(170875392,plain,
~ ilf_type(d,binary_relation_type),
inference(resolution,[status(thm)],[164285240,170771432]),
[] ).
fof(p13,plain,
! [A] :
( ( ilf_type(A,binary_relation_type)
| ~ relation_like(A)
| ~ ilf_type(A,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(A,set_type)
| ~ ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) )
& ( relation_like(A)
| ~ ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),
[] ).
cnf(147157592,plain,
( ilf_type(A,binary_relation_type)
| ~ relation_like(A)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p13]),
[] ).
cnf(161916256,plain,
( ilf_type(A,binary_relation_type)
| ~ relation_like(A) ),
inference(resolution,[status(thm)],[147157592,147571848]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[169861760,170875392,161916256]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_relset_1_27,plain,((ilf_type(b,set_type)&ilf_type(c,set_type)&ilf_type(d,relation_type(c,b))&ilf_type(d,relation_type(c,empty_set))&~$equal(empty_set,d))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),[]).
%
% cnf(147662704,plain,(ilf_type(d,relation_type(c,empty_set))),inference(rewrite,[status(thm)],[prove_relset_1_27]),[]).
%
% fof(p33,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),[]).
%
% cnf(147571848,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p33]),[]).
%
% fof(p6,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/SET664+3.tptp',unknown),[]).
%
% cnf(146988544,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)],[p6]),[]).
%
% fof(p28,plain,(~ilf_type(A,set_type)|~ilf_type(B,set_type)|~ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),[]).
%
% cnf(147519424,plain,(~ilf_type(A,set_type)|~ilf_type(B,set_type)|~ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C)),inference(rewrite,[status(thm)],[p28]),[]).
%
% cnf(169729024,plain,(~ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C)),inference(forward_subsumption_resolution__resolution,[status(thm)],[147571848,147571848,147519424]),[]).
%
% cnf(169774768,plain,(~ilf_type(D,relation_type(A,B))|relation_like(D)),inference(forward_subsumption_resolution__resolution,[status(thm)],[147571848,146988544,169729024]),[]).
%
% cnf(169861760,plain,(relation_like(d)),inference(resolution,[status(thm)],[147662704,169774768]),[]).
%
% fof(p2,plain,(((~$equal(empty_set,range_of(A))|$equal(empty_set,A)|~ilf_type(A,binary_relation_type))&(~$equal(empty_set,domain_of(A))|$equal(empty_set,A)|~ilf_type(A,binary_relation_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),[]).
%
% cnf(146893416,plain,(~$equal(empty_set,range_of(A))|$equal(empty_set,A)|~ilf_type(A,binary_relation_type)),inference(rewrite,[status(thm)],[p2]),[]).
%
% cnf(147650392,plain,(~$equal(empty_set,d)),inference(rewrite,[status(thm)],[prove_relset_1_27]),[]).
%
% cnf(163372984,plain,(~$equal(empty_set,range_of(d))|~ilf_type(d,binary_relation_type)),inference(resolution,[status(thm)],[146893416,147650392]),[]).
%
% fof(p1,plain,(~ilf_type(A,set_type)|~subset(A,empty_set)|$equal(empty_set,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),[]).
%
% cnf(146867504,plain,(~ilf_type(A,set_type)|~subset(A,empty_set)|$equal(empty_set,A)),inference(rewrite,[status(thm)],[p1]),[]).
%
% cnf(161951144,plain,(~subset(A,empty_set)|$equal(empty_set,A)),inference(resolution,[status(thm)],[146867504,147571848]),[]).
%
% cnf(164285240,plain,(~ilf_type(d,binary_relation_type)|~subset(range_of(d),empty_set)),inference(resolution,[status(thm)],[163372984,161951144]),[]).
%
% fof(p3,plain,(((subset(range_of(C),B)|~ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(subset(domain_of(C),A)|~ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),[]).
%
% cnf(146941720,plain,(subset(range_of(C),B)|~ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p3]),[]).
%
% cnf(170764400,plain,(subset(range_of(C),A)|~ilf_type(C,relation_type(B,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[147571848,147571848,146941720]),[]).
%
% cnf(170771432,plain,(subset(range_of(d),empty_set)),inference(resolution,[status(thm)],[147662704,170764400]),[]).
%
% cnf(170875392,plain,(~ilf_type(d,binary_relation_type)),inference(resolution,[status(thm)],[164285240,170771432]),[]).
%
% fof(p13,plain,(((ilf_type(A,binary_relation_type)|~relation_like(A)|~ilf_type(A,set_type)|~ilf_type(A,set_type))&(ilf_type(A,set_type)|~ilf_type(A,binary_relation_type)|~ilf_type(A,set_type))&(relation_like(A)|~ilf_type(A,binary_relation_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET664+3.tptp',unknown),[]).
%
% cnf(147157592,plain,(ilf_type(A,binary_relation_type)|~relation_like(A)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p13]),[]).
%
% cnf(161916256,plain,(ilf_type(A,binary_relation_type)|~relation_like(A)),inference(resolution,[status(thm)],[147157592,147571848]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[169861760,170875392,161916256]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------