TSTP Solution File: SET663+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET663+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 15:35:01 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 103 ( 49 ~; 45 |; 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 : 28 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(p33,plain,
! [A] : ilf_type(A,set_type),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET663+3.tptp',unknown),
[] ).
cnf(156086560,plain,
ilf_type(A,set_type),
inference(rewrite,[status(thm)],[p33]),
[] ).
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/SET663+3.tptp',unknown),
[] ).
cnf(156034136,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]),
[] ).
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/SET663+3.tptp',unknown),
[] ).
cnf(155503272,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(prove_relset_1_26,plain,
( ilf_type(b,set_type)
& ilf_type(c,set_type)
& ilf_type(d,relation_type(b,c))
& ilf_type(d,relation_type(empty_set,c))
& ~ $equal(empty_set,d) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET663+3.tptp',unknown),
[] ).
cnf(156177416,plain,
ilf_type(d,relation_type(empty_set,c)),
inference(rewrite,[status(thm)],[prove_relset_1_26]),
[] ).
cnf(170069344,plain,
ilf_type(d,subset_type(cross_product(empty_set,c))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,155503272,156177416]),
[] ).
cnf(170197168,plain,
relation_like(d),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,156034136,170069344]),
[] ).
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/SET663+3.tptp',unknown),
[] ).
cnf(155672304,plain,
( ilf_type(A,binary_relation_type)
| ~ relation_like(A)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p13]),
[] ).
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/SET663+3.tptp',unknown),
[] ).
cnf(155437320,plain,
( subset(domain_of(C),A)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p3]),
[] ).
cnf(170023648,plain,
subset(domain_of(d),empty_set),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,155437320,156177416]),
[] ).
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/SET663+3.tptp',unknown),
[] ).
cnf(155382232,plain,
( ~ ilf_type(A,set_type)
| ~ subset(A,empty_set)
| $equal(empty_set,A) ),
inference(rewrite,[status(thm)],[p1]),
[] ).
cnf(170574000,plain,
( ~ subset(A,empty_set)
| $equal(empty_set,A) ),
inference(resolution,[status(thm)],[156086560,155382232]),
[] ).
cnf(156165104,plain,
~ $equal(empty_set,d),
inference(rewrite,[status(thm)],[prove_relset_1_26]),
[] ).
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/SET663+3.tptp',unknown),
[] ).
cnf(155391528,plain,
( ~ $equal(empty_set,domain_of(A))
| $equal(empty_set,A)
| ~ ilf_type(A,binary_relation_type) ),
inference(rewrite,[status(thm)],[p2]),
[] ).
cnf(170793832,plain,
( ~ $equal(empty_set,domain_of(d))
| ~ ilf_type(d,binary_relation_type) ),
inference(resolution,[status(thm)],[156165104,155391528]),
[] ).
cnf(170862336,plain,
~ ilf_type(d,binary_relation_type),
inference(forward_subsumption_resolution__resolution,[status(thm)],[170023648,170574000,170793832]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,170197168,155672304,170862336]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(p33,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET663+3.tptp',unknown),[]).
%
% cnf(156086560,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p33]),[]).
%
% fof(p28,plain,(~ilf_type(A,set_type)|~ilf_type(B,set_type)|~ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET663+3.tptp',unknown),[]).
%
% cnf(156034136,plain,(~ilf_type(A,set_type)|~ilf_type(B,set_type)|~ilf_type(C,subset_type(cross_product(A,B)))|relation_like(C)),inference(rewrite,[status(thm)],[p28]),[]).
%
% fof(p6,plain,(((~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(~ilf_type(D,relation_type(A,B))|ilf_type(D,subset_type(cross_product(A,B)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET663+3.tptp',unknown),[]).
%
% cnf(155503272,plain,(~ilf_type(D,relation_type(A,B))|ilf_type(D,subset_type(cross_product(A,B)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p6]),[]).
%
% fof(prove_relset_1_26,plain,((ilf_type(b,set_type)&ilf_type(c,set_type)&ilf_type(d,relation_type(b,c))&ilf_type(d,relation_type(empty_set,c))&~$equal(empty_set,d))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET663+3.tptp',unknown),[]).
%
% cnf(156177416,plain,(ilf_type(d,relation_type(empty_set,c))),inference(rewrite,[status(thm)],[prove_relset_1_26]),[]).
%
% cnf(170069344,plain,(ilf_type(d,subset_type(cross_product(empty_set,c)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,155503272,156177416]),[]).
%
% cnf(170197168,plain,(relation_like(d)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,156034136,170069344]),[]).
%
% 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/SET663+3.tptp',unknown),[]).
%
% cnf(155672304,plain,(ilf_type(A,binary_relation_type)|~relation_like(A)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p13]),[]).
%
% 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/SET663+3.tptp',unknown),[]).
%
% cnf(155437320,plain,(subset(domain_of(C),A)|~ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p3]),[]).
%
% cnf(170023648,plain,(subset(domain_of(d),empty_set)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,155437320,156177416]),[]).
%
% fof(p1,plain,(~ilf_type(A,set_type)|~subset(A,empty_set)|$equal(empty_set,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET663+3.tptp',unknown),[]).
%
% cnf(155382232,plain,(~ilf_type(A,set_type)|~subset(A,empty_set)|$equal(empty_set,A)),inference(rewrite,[status(thm)],[p1]),[]).
%
% cnf(170574000,plain,(~subset(A,empty_set)|$equal(empty_set,A)),inference(resolution,[status(thm)],[156086560,155382232]),[]).
%
% cnf(156165104,plain,(~$equal(empty_set,d)),inference(rewrite,[status(thm)],[prove_relset_1_26]),[]).
%
% 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/SET663+3.tptp',unknown),[]).
%
% cnf(155391528,plain,(~$equal(empty_set,domain_of(A))|$equal(empty_set,A)|~ilf_type(A,binary_relation_type)),inference(rewrite,[status(thm)],[p2]),[]).
%
% cnf(170793832,plain,(~$equal(empty_set,domain_of(d))|~ilf_type(d,binary_relation_type)),inference(resolution,[status(thm)],[156165104,155391528]),[]).
%
% cnf(170862336,plain,(~ilf_type(d,binary_relation_type)),inference(forward_subsumption_resolution__resolution,[status(thm)],[170023648,170574000,170793832]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[156086560,170197168,155672304,170862336]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------