TSTP Solution File: SET663+3 by Faust---1.0

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