TSTP Solution File: SET878+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET878+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 15:40:20 EDT 2009

% Result   : Theorem 0.0s
% Output   : Refutation 0.0s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   12 (   8 unt;   0 def)
%            Number of atoms       :   46 (   0 equ)
%            Maximal formula atoms :   31 (   3 avg)
%            Number of connectives :   55 (  21   ~;  26   |;   8   &)
%                                         (   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;   2 con; 0-4 aty)
%            Number of variables   :   18 (   2 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET878+1.tptp',unknown),
    [] ).

cnf(165475432,plain,
    ( ~ $equal(A,D)
    | in(D,C)
    | ~ $equal(unordered_pair(A,B),C) ),
    inference(rewrite,[status(thm)],[d2_tarski]),
    [] ).

cnf(174022944,plain,
    in(A,unordered_pair(A,B)),
    inference(equality_resolution,[status(thm)],[165475432]),
    [] ).

fof(t19_zfmisc_1,plain,
    ~ $equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),
    [] ).

cnf(165555600,plain,
    ~ $equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a)),
    inference(rewrite,[status(thm)],[t19_zfmisc_1]),
    [] ).

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/SET878+1.tptp',unknown),
    [] ).

cnf(165420864,plain,
    $equal(set_intersection2(B,A),set_intersection2(A,B)),
    inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),
    [] ).

cnf(173740072,plain,
    ~ $equal(set_intersection2(unordered_pair(a,b),singleton(a)),singleton(a)),
    inference(paramodulation,[status(thm)],[165555600,165420864,theory(equality)]),
    [] ).

fof(l32_zfmisc_1,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | $equal(set_intersection2(B,singleton(A)),singleton(A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),
    [] ).

cnf(165501800,plain,
    ( ~ in(A,B)
    | $equal(set_intersection2(B,singleton(A)),singleton(A)) ),
    inference(rewrite,[status(thm)],[l32_zfmisc_1]),
    [] ).

cnf(173903016,plain,
    ~ in(a,unordered_pair(a,b)),
    inference(resolution,[status(thm)],[173740072,165501800]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[174022944,173903016]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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)|$equal(unordered_pair(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),[]).
% 
% cnf(165475432,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
% 
% cnf(174022944,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[165475432]),[]).
% 
% fof(t19_zfmisc_1,plain,(~$equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),[]).
% 
% cnf(165555600,plain,(~$equal(set_intersection2(singleton(a),unordered_pair(a,b)),singleton(a))),inference(rewrite,[status(thm)],[t19_zfmisc_1]),[]).
% 
% fof(commutativity_k3_xboole_0,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),[]).
% 
% cnf(165420864,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),[]).
% 
% cnf(173740072,plain,(~$equal(set_intersection2(unordered_pair(a,b),singleton(a)),singleton(a))),inference(paramodulation,[status(thm)],[165555600,165420864,theory(equality)]),[]).
% 
% fof(l32_zfmisc_1,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET878+1.tptp',unknown),[]).
% 
% cnf(165501800,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),inference(rewrite,[status(thm)],[l32_zfmisc_1]),[]).
% 
% cnf(173903016,plain,(~in(a,unordered_pair(a,b))),inference(resolution,[status(thm)],[173740072,165501800]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[174022944,173903016]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------