TSTP Solution File: SET874+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET874+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 15:40:11 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    9 (   5 unt;   0 def)
%            Number of atoms       :   43 (   0 equ)
%            Maximal formula atoms :   31 (   4 avg)
%            Number of connectives :   54 (  20   ~;  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   :   14 (   2 sgn   6   !;   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/SET874+1.tptp',unknown),
    [] ).

cnf(144274992,plain,
    ( ~ $equal(A,D)
    | in(D,C)
    | ~ $equal(unordered_pair(A,B),C) ),
    inference(rewrite,[status(thm)],[d2_tarski]),
    [] ).

cnf(154575056,plain,
    in(A,unordered_pair(A,B)),
    inference(equality_resolution,[status(thm)],[144274992]),
    [] ).

fof(t14_zfmisc_1,plain,
    ~ $equal(set_union2(singleton(a),unordered_pair(a,b)),unordered_pair(a,b)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET874+1.tptp',unknown),
    [] ).

cnf(144349824,plain,
    ~ $equal(set_union2(singleton(a),unordered_pair(a,b)),unordered_pair(a,b)),
    inference(rewrite,[status(thm)],[t14_zfmisc_1]),
    [] ).

fof(l23_zfmisc_1,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | $equal(set_union2(singleton(A),B),B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET874+1.tptp',unknown),
    [] ).

cnf(144296808,plain,
    ( ~ in(A,B)
    | $equal(set_union2(singleton(A),B),B) ),
    inference(rewrite,[status(thm)],[l23_zfmisc_1]),
    [] ).

cnf(154452888,plain,
    ~ in(a,unordered_pair(a,b)),
    inference(resolution,[status(thm)],[144349824,144296808]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[154575056,154452888]),
    [] ).

%------------------------------------------------------------------------------
%----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)|$equal(unordered_pair(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET874+1.tptp',unknown),[]).
% 
% cnf(144274992,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
% 
% cnf(154575056,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[144274992]),[]).
% 
% fof(t14_zfmisc_1,plain,(~$equal(set_union2(singleton(a),unordered_pair(a,b)),unordered_pair(a,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET874+1.tptp',unknown),[]).
% 
% cnf(144349824,plain,(~$equal(set_union2(singleton(a),unordered_pair(a,b)),unordered_pair(a,b))),inference(rewrite,[status(thm)],[t14_zfmisc_1]),[]).
% 
% fof(l23_zfmisc_1,plain,(~in(A,B)|$equal(set_union2(singleton(A),B),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET874+1.tptp',unknown),[]).
% 
% cnf(144296808,plain,(~in(A,B)|$equal(set_union2(singleton(A),B),B)),inference(rewrite,[status(thm)],[l23_zfmisc_1]),[]).
% 
% cnf(154452888,plain,(~in(a,unordered_pair(a,b))),inference(resolution,[status(thm)],[144349824,144296808]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[154575056,154452888]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------