TSTP Solution File: SET591+3 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET591+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art09.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 15:32:08 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   23 (   9 unt;   0 def)
%            Number of atoms       :   56 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   62 (  29   ~;  25   |;   8   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   36 (  11 sgn  11   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(subset_defn,plain,
    ! [A,B,C] :
      ( ( ~ subset(A,B)
        | ~ member(C,A)
        | member(C,B) )
      & ( ~ member(d(A,B,C),B)
        | subset(A,B) )
      & ( member(d(A,B,C),A)
        | subset(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
    [] ).

cnf(161656440,plain,
    ( ~ subset(A,B)
    | ~ member(C,A)
    | member(C,B) ),
    inference(rewrite,[status(thm)],[subset_defn]),
    [] ).

fof(prove_th50,plain,
    ( subset(b,difference(c,b))
    & ~ $equal(empty_set,b) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
    [] ).

cnf(161796928,plain,
    subset(b,difference(c,b)),
    inference(rewrite,[status(thm)],[prove_th50]),
    [] ).

cnf(172890824,plain,
    ( ~ member(A,b)
    | member(A,difference(c,b)) ),
    inference(resolution,[status(thm)],[161656440,161796928]),
    [] ).

fof(difference_defn,plain,
    ! [C,B,A] :
      ( ( ~ member(C,B)
        | ~ member(C,difference(A,B)) )
      & ( member(C,A)
        | ~ member(C,difference(A,B)) )
      & ( member(C,difference(A,B))
        | ~ member(C,A)
        | member(C,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
    [] ).

cnf(161692488,plain,
    ( ~ member(C,B)
    | ~ member(C,difference(A,B)) ),
    inference(rewrite,[status(thm)],[difference_defn]),
    [] ).

cnf(176681088,plain,
    ~ member(A,b),
    inference(resolution,[status(thm)],[172890824,161692488]),
    [] ).

cnf(161630168,plain,
    ( member(d(A,B,C),A)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subset_defn]),
    [] ).

fof(empty_set_defn,plain,
    ! [A] : ~ member(A,empty_set),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
    [] ).

cnf(161696176,plain,
    ~ member(A,empty_set),
    inference(rewrite,[status(thm)],[empty_set_defn]),
    [] ).

cnf(172244176,plain,
    subset(empty_set,A),
    inference(resolution,[status(thm)],[161630168,161696176]),
    [] ).

fof(equal_defn,plain,
    ! [B,A] :
      ( ( subset(B,A)
        | ~ $equal(B,A) )
      & ( subset(A,B)
        | ~ $equal(B,A) )
      & ( $equal(B,A)
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
    [] ).

cnf(161707656,plain,
    ( $equal(B,A)
    | ~ subset(A,B)
    | ~ subset(B,A) ),
    inference(rewrite,[status(thm)],[equal_defn]),
    [] ).

cnf(161789456,plain,
    ~ $equal(empty_set,b),
    inference(rewrite,[status(thm)],[prove_th50]),
    [] ).

cnf(172310072,plain,
    ~ subset(b,empty_set),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[172244176,161707656,161789456]),
    [] ).

fof(empty_defn,plain,
    ! [A,B] :
      ( ( ~ empty(A)
        | ~ member(B,A) )
      & ( empty(A)
        | member(c(A,B),A) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),
    [] ).

cnf(161742832,plain,
    ( ~ empty(A)
    | ~ member(B,A) ),
    inference(rewrite,[status(thm)],[empty_defn]),
    [] ).

cnf(172377952,plain,
    ( ~ empty(A)
    | subset(A,B) ),
    inference(resolution,[status(thm)],[161742832,161630168]),
    [] ).

cnf(161736312,plain,
    ( empty(A)
    | member(c(A,B),A) ),
    inference(rewrite,[status(thm)],[empty_defn]),
    [] ).

cnf(172389112,plain,
    ( subset(A,B)
    | member(c(A,C),A) ),
    inference(resolution,[status(thm)],[172377952,161736312]),
    [] ).

cnf(173614496,plain,
    member(c(b,A),b),
    inference(resolution,[status(thm)],[172310072,172389112]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[176681088,173614496]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(subset_defn,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(d(A,B,C),B)|subset(A,B))&(member(d(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
% 
% cnf(161656440,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
% 
% fof(prove_th50,plain,((subset(b,difference(c,b))&~$equal(empty_set,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
% 
% cnf(161796928,plain,(subset(b,difference(c,b))),inference(rewrite,[status(thm)],[prove_th50]),[]).
% 
% cnf(172890824,plain,(~member(A,b)|member(A,difference(c,b))),inference(resolution,[status(thm)],[161656440,161796928]),[]).
% 
% fof(difference_defn,plain,(((~member(C,B)|~member(C,difference(A,B)))&(member(C,A)|~member(C,difference(A,B)))&(member(C,difference(A,B))|~member(C,A)|member(C,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
% 
% cnf(161692488,plain,(~member(C,B)|~member(C,difference(A,B))),inference(rewrite,[status(thm)],[difference_defn]),[]).
% 
% cnf(176681088,plain,(~member(A,b)),inference(resolution,[status(thm)],[172890824,161692488]),[]).
% 
% cnf(161630168,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
% 
% fof(empty_set_defn,plain,(~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
% 
% cnf(161696176,plain,(~member(A,empty_set)),inference(rewrite,[status(thm)],[empty_set_defn]),[]).
% 
% cnf(172244176,plain,(subset(empty_set,A)),inference(resolution,[status(thm)],[161630168,161696176]),[]).
% 
% fof(equal_defn,plain,(((subset(B,A)|~$equal(B,A))&(subset(A,B)|~$equal(B,A))&($equal(B,A)|~subset(A,B)|~subset(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
% 
% cnf(161707656,plain,($equal(B,A)|~subset(A,B)|~subset(B,A)),inference(rewrite,[status(thm)],[equal_defn]),[]).
% 
% cnf(161789456,plain,(~$equal(empty_set,b)),inference(rewrite,[status(thm)],[prove_th50]),[]).
% 
% cnf(172310072,plain,(~subset(b,empty_set)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172244176,161707656,161789456]),[]).
% 
% fof(empty_defn,plain,(((~empty(A)|~member(B,A))&(empty(A)|member(c(A,B),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET591+3.tptp',unknown),[]).
% 
% cnf(161742832,plain,(~empty(A)|~member(B,A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
% 
% cnf(172377952,plain,(~empty(A)|subset(A,B)),inference(resolution,[status(thm)],[161742832,161630168]),[]).
% 
% cnf(161736312,plain,(empty(A)|member(c(A,B),A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
% 
% cnf(172389112,plain,(subset(A,B)|member(c(A,C),A)),inference(resolution,[status(thm)],[172377952,161736312]),[]).
% 
% cnf(173614496,plain,(member(c(b,A),b)),inference(resolution,[status(thm)],[172310072,172389112]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[176681088,173614496]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------