TSTP Solution File: SET664+3 by Faust---1.0

View Problem - 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.
% 
%------------------------------------------------------------------------------