TSTP Solution File: SET662+3 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET662+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 15:34:58 EDT 2009

% Result   : Theorem 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   27 (   9 unt;   0 def)
%            Number of atoms       :   94 (   0 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  124 (  57   ~;  58   |;   9   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   43 (   8 sgn  14   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(p20,plain,
    ! [A] : ilf_type(A,set_type),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
    [] ).

cnf(173126024,plain,
    ilf_type(A,set_type),
    inference(rewrite,[status(thm)],[p20]),
    [] ).

fof(p12,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/SET662+3.tptp',unknown),
    [] ).

cnf(172944536,plain,
    ( member(d(A,B,C),A)
    | member(A,power_set(B))
    | ~ ilf_type(B,set_type)
    | ~ ilf_type(A,set_type) ),
    inference(rewrite,[status(thm)],[p12]),
    [] ).

cnf(181216560,plain,
    ( member(d(A,B,C),A)
    | member(A,power_set(B)) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172944536,173126024]),
    [] ).

fof(p4,plain,
    ! [A] :
      ( ~ ilf_type(A,set_type)
      | ~ member(A,empty_set) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
    [] ).

cnf(172747392,plain,
    ( ~ ilf_type(A,set_type)
    | ~ member(A,empty_set) ),
    inference(rewrite,[status(thm)],[p4]),
    [] ).

cnf(181113856,plain,
    ~ member(A,empty_set),
    inference(resolution,[status(thm)],[172747392,173126024]),
    [] ).

cnf(181951256,plain,
    member(empty_set,power_set(A)),
    inference(resolution,[status(thm)],[181216560,181113856]),
    [] ).

fof(p14,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/SET662+3.tptp',unknown),
    [] ).

cnf(172992928,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)],[p14]),
    [] ).

cnf(181225888,plain,
    ( ilf_type(A,member_type(B))
    | ~ member(A,B)
    | empty(B) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172992928,173126024]),
    [] ).

cnf(182045240,plain,
    ( ilf_type(empty_set,member_type(power_set(A)))
    | empty(power_set(A)) ),
    inference(resolution,[status(thm)],[181951256,181225888]),
    [] ).

fof(p13,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/SET662+3.tptp',unknown),
    [] ).

cnf(172971432,plain,
    ( ~ empty(power_set(A))
    | ~ ilf_type(A,set_type) ),
    inference(rewrite,[status(thm)],[p13]),
    [] ).

cnf(181123112,plain,
    ~ empty(power_set(A)),
    inference(resolution,[status(thm)],[172971432,173126024]),
    [] ).

cnf(182149760,plain,
    ilf_type(empty_set,member_type(power_set(A))),
    inference(resolution,[status(thm)],[182045240,181123112]),
    [] ).

fof(p7,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/SET662+3.tptp',unknown),
    [] ).

cnf(172800824,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)],[p7]),
    [] ).

cnf(181201632,plain,
    ( ilf_type(B,subset_type(A))
    | ~ ilf_type(B,member_type(power_set(A))) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172800824,173126024]),
    [] ).

cnf(182163360,plain,
    ilf_type(empty_set,subset_type(A)),
    inference(resolution,[status(thm)],[182149760,181201632]),
    [] ).

fof(p2,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/SET662+3.tptp',unknown),
    [] ).

cnf(172737680,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) ),
    inference(rewrite,[status(thm)],[p2]),
    [] ).

cnf(181250000,plain,
    ( ~ ilf_type(C,subset_type(cross_product(A,B)))
    | ilf_type(C,relation_type(A,B)) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172737680,173126024]),
    [] ).

fof(prove_relset_1_25,plain,
    ( ilf_type(b,set_type)
    & ilf_type(c,set_type)
    & ~ ilf_type(empty_set,relation_type(b,c)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
    [] ).

cnf(173177408,plain,
    ~ ilf_type(empty_set,relation_type(b,c)),
    inference(rewrite,[status(thm)],[prove_relset_1_25]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[182163360,181250000,173177408]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(p20,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
% 
% cnf(173126024,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p20]),[]).
% 
% fof(p12,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/SET662+3.tptp',unknown),[]).
% 
% cnf(172944536,plain,(member(d(A,B,C),A)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p12]),[]).
% 
% cnf(181216560,plain,(member(d(A,B,C),A)|member(A,power_set(B))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172944536,173126024]),[]).
% 
% fof(p4,plain,(~ilf_type(A,set_type)|~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
% 
% cnf(172747392,plain,(~ilf_type(A,set_type)|~member(A,empty_set)),inference(rewrite,[status(thm)],[p4]),[]).
% 
% cnf(181113856,plain,(~member(A,empty_set)),inference(resolution,[status(thm)],[172747392,173126024]),[]).
% 
% cnf(181951256,plain,(member(empty_set,power_set(A))),inference(resolution,[status(thm)],[181216560,181113856]),[]).
% 
% fof(p14,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/SET662+3.tptp',unknown),[]).
% 
% cnf(172992928,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)],[p14]),[]).
% 
% cnf(181225888,plain,(ilf_type(A,member_type(B))|~member(A,B)|empty(B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172992928,173126024]),[]).
% 
% cnf(182045240,plain,(ilf_type(empty_set,member_type(power_set(A)))|empty(power_set(A))),inference(resolution,[status(thm)],[181951256,181225888]),[]).
% 
% fof(p13,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/SET662+3.tptp',unknown),[]).
% 
% cnf(172971432,plain,(~empty(power_set(A))|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p13]),[]).
% 
% cnf(181123112,plain,(~empty(power_set(A))),inference(resolution,[status(thm)],[172971432,173126024]),[]).
% 
% cnf(182149760,plain,(ilf_type(empty_set,member_type(power_set(A)))),inference(resolution,[status(thm)],[182045240,181123112]),[]).
% 
% fof(p7,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/SET662+3.tptp',unknown),[]).
% 
% cnf(172800824,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)],[p7]),[]).
% 
% cnf(181201632,plain,(ilf_type(B,subset_type(A))|~ilf_type(B,member_type(power_set(A)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172800824,173126024]),[]).
% 
% cnf(182163360,plain,(ilf_type(empty_set,subset_type(A))),inference(resolution,[status(thm)],[182149760,181201632]),[]).
% 
% fof(p2,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/SET662+3.tptp',unknown),[]).
% 
% cnf(172737680,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)),inference(rewrite,[status(thm)],[p2]),[]).
% 
% cnf(181250000,plain,(~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172737680,173126024]),[]).
% 
% fof(prove_relset_1_25,plain,((ilf_type(b,set_type)&ilf_type(c,set_type)&~ilf_type(empty_set,relation_type(b,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
% 
% cnf(173177408,plain,(~ilf_type(empty_set,relation_type(b,c))),inference(rewrite,[status(thm)],[prove_relset_1_25]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182163360,181250000,173177408]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------