TSTP Solution File: SET920+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET920+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.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 15:41:38 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   15 (   9 unt;   0 def)
%            Number of atoms       :   81 (   0 equ)
%            Maximal formula atoms :   31 (   5 avg)
%            Number of connectives :  103 (  37   ~;  49   |;  17   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-4 aty)
%            Number of variables   :   25 (   5 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(d3_xboole_0,plain,
    ! [D,C,A,B] :
      ( ( in(D,C)
        | ~ in(D,A)
        | ~ in(D,B)
        | ~ $equal(set_intersection2(A,B),C) )
      & ( in(D,B)
        | ~ in(D,C)
        | ~ $equal(set_intersection2(A,B),C) )
      & ( in(D,A)
        | ~ in(D,C)
        | ~ $equal(set_intersection2(A,B),C) )
      & ( in(d(A,B,C,D),A)
        | ~ in(d(A,B,C,D),A)
        | ~ in(d(A,B,C,D),B)
        | $equal(set_intersection2(A,B),C) )
      & ( in(d(A,B,C,D),B)
        | ~ in(d(A,B,C,D),A)
        | ~ in(d(A,B,C,D),B)
        | $equal(set_intersection2(A,B),C) )
      & ( ~ in(d(A,B,C,D),C)
        | ~ in(d(A,B,C,D),A)
        | ~ in(d(A,B,C,D),B)
        | $equal(set_intersection2(A,B),C) )
      & ( in(d(A,B,C,D),A)
        | in(d(A,B,C,D),C)
        | $equal(set_intersection2(A,B),C) )
      & ( in(d(A,B,C,D),B)
        | in(d(A,B,C,D),C)
        | $equal(set_intersection2(A,B),C) )
      & ( ~ in(d(A,B,C,D),C)
        | in(d(A,B,C,D),C)
        | $equal(set_intersection2(A,B),C) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),
    [] ).

cnf(172052128,plain,
    ( in(D,A)
    | ~ in(D,C)
    | ~ $equal(set_intersection2(A,B),C) ),
    inference(rewrite,[status(thm)],[d3_xboole_0]),
    [] ).

fof(t63_zfmisc_1,plain,
    ( $equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b))
    & ~ in(a,c) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),
    [] ).

cnf(172133440,plain,
    ~ in(a,c),
    inference(rewrite,[status(thm)],[t63_zfmisc_1]),
    [] ).

cnf(182638080,plain,
    ( ~ in(a,B)
    | ~ $equal(set_intersection2(c,A),B) ),
    inference(resolution,[status(thm)],[172052128,172133440]),
    [] ).

cnf(189675568,plain,
    ~ in(a,set_intersection2(c,A)),
    inference(equality_resolution,[status(thm)],[182638080]),
    [] ).

fof(d2_tarski,plain,
    ! [B,D,C,A] :
      ( ( ~ $equal(B,D)
        | in(D,C)
        | ~ $equal(unordered_pair(A,B),C) )
      & ( ~ $equal(A,D)
        | in(D,C)
        | ~ $equal(unordered_pair(A,B),C) )
      & ( ~ in(D,C)
        | $equal(A,D)
        | $equal(B,D)
        | ~ $equal(unordered_pair(A,B),C) )
      & ( $equal(d(A,B,C,D),A)
        | $equal(d(A,B,C,D),B)
        | ~ $equal(d(A,B,C,D),A)
        | $equal(unordered_pair(A,B),C) )
      & ( ~ in(d(A,B,C,D),C)
        | ~ $equal(d(A,B,C,D),A)
        | $equal(unordered_pair(A,B),C) )
      & ( $equal(d(A,B,C,D),A)
        | $equal(d(A,B,C,D),B)
        | ~ $equal(d(A,B,C,D),B)
        | $equal(unordered_pair(A,B),C) )
      & ( ~ in(d(A,B,C,D),C)
        | ~ $equal(d(A,B,C,D),B)
        | $equal(unordered_pair(A,B),C) )
      & ( $equal(d(A,B,C,D),A)
        | $equal(d(A,B,C,D),B)
        | in(d(A,B,C,D),C)
        | $equal(unordered_pair(A,B),C) )
      & ( ~ in(d(A,B,C,D),C)
        | in(d(A,B,C,D),C)
        | $equal(unordered_pair(A,B),C) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),
    [] ).

cnf(172007848,plain,
    ( ~ $equal(A,D)
    | in(D,C)
    | ~ $equal(unordered_pair(A,B),C) ),
    inference(rewrite,[status(thm)],[d2_tarski]),
    [] ).

cnf(183060560,plain,
    in(A,unordered_pair(A,B)),
    inference(equality_resolution,[status(thm)],[172007848]),
    [] ).

cnf(172141024,plain,
    $equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b)),
    inference(rewrite,[status(thm)],[t63_zfmisc_1]),
    [] ).

cnf(183367904,plain,
    in(a,set_intersection2(unordered_pair(a,b),c)),
    inference(paramodulation,[status(thm)],[183060560,172141024,theory(equality)]),
    [] ).

fof(commutativity_k3_xboole_0,plain,
    ! [B,A] : $equal(set_intersection2(B,A),set_intersection2(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),
    [] ).

cnf(171953280,plain,
    $equal(set_intersection2(B,A),set_intersection2(A,B)),
    inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),
    [] ).

cnf(183494248,plain,
    in(a,set_intersection2(c,unordered_pair(a,b))),
    inference(paramodulation,[status(thm)],[183367904,171953280,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[189675568,183494248]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d3_xboole_0,plain,(((in(D,C)|~in(D,A)|~in(D,B)|~$equal(set_intersection2(A,B),C))&(in(D,B)|~in(D,C)|~$equal(set_intersection2(A,B),C))&(in(D,A)|~in(D,C)|~$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),A)|~in(d(A,B,C,D),A)|~in(d(A,B,C,D),B)|$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),B)|~in(d(A,B,C,D),A)|~in(d(A,B,C,D),B)|$equal(set_intersection2(A,B),C))&(~in(d(A,B,C,D),C)|~in(d(A,B,C,D),A)|~in(d(A,B,C,D),B)|$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),A)|in(d(A,B,C,D),C)|$equal(set_intersection2(A,B),C))&(in(d(A,B,C,D),B)|in(d(A,B,C,D),C)|$equal(set_intersection2(A,B),C))&(~in(d(A,B,C,D),C)|in(d(A,B,C,D),C)|$equal(set_intersection2(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),[]).
% 
% cnf(172052128,plain,(in(D,A)|~in(D,C)|~$equal(set_intersection2(A,B),C)),inference(rewrite,[status(thm)],[d3_xboole_0]),[]).
% 
% fof(t63_zfmisc_1,plain,(($equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b))&~in(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),[]).
% 
% cnf(172133440,plain,(~in(a,c)),inference(rewrite,[status(thm)],[t63_zfmisc_1]),[]).
% 
% cnf(182638080,plain,(~in(a,B)|~$equal(set_intersection2(c,A),B)),inference(resolution,[status(thm)],[172052128,172133440]),[]).
% 
% cnf(189675568,plain,(~in(a,set_intersection2(c,A))),inference(equality_resolution,[status(thm)],[182638080]),[]).
% 
% fof(d2_tarski,plain,(((~$equal(B,D)|in(D,C)|~$equal(unordered_pair(A,B),C))&(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C))&(~in(D,C)|$equal(A,D)|$equal(B,D)|~$equal(unordered_pair(A,B),C))&($equal(d(A,B,C,D),A)|$equal(d(A,B,C,D),B)|~$equal(d(A,B,C,D),A)|$equal(unordered_pair(A,B),C))&(~in(d(A,B,C,D),C)|~$equal(d(A,B,C,D),A)|$equal(unordered_pair(A,B),C))&($equal(d(A,B,C,D),A)|$equal(d(A,B,C,D),B)|~$equal(d(A,B,C,D),B)|$equal(unordered_pair(A,B),C))&(~in(d(A,B,C,D),C)|~$equal(d(A,B,C,D),B)|$equal(unordered_pair(A,B),C))&($equal(d(A,B,C,D),A)|$equal(d(A,B,C,D),B)|in(d(A,B,C,D),C)|$equal(unordered_pair(A,B),C))&(~in(d(A,B,C,D),C)|in(d(A,B,C,D),C)|$equal(unordered_pair(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),[]).
% 
% cnf(172007848,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
% 
% cnf(183060560,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[172007848]),[]).
% 
% cnf(172141024,plain,($equal(set_intersection2(unordered_pair(a,b),c),unordered_pair(a,b))),inference(rewrite,[status(thm)],[t63_zfmisc_1]),[]).
% 
% cnf(183367904,plain,(in(a,set_intersection2(unordered_pair(a,b),c))),inference(paramodulation,[status(thm)],[183060560,172141024,theory(equality)]),[]).
% 
% fof(commutativity_k3_xboole_0,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET920+1.tptp',unknown),[]).
% 
% cnf(171953280,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),[]).
% 
% cnf(183494248,plain,(in(a,set_intersection2(c,unordered_pair(a,b)))),inference(paramodulation,[status(thm)],[183367904,171953280,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[189675568,183494248]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------