TSTP Solution File: SET872+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET872+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 15:40:07 EDT 2009

% Result   : Theorem 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   16 (   8 unt;   0 def)
%            Number of atoms       :   76 (   0 equ)
%            Maximal formula atoms :   31 (   4 avg)
%            Number of connectives :   94 (  34   ~;  45   |;  15   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-4 aty)
%            Number of variables   :   30 (   7 sgn  10   !;   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/SET872+1.tptp',unknown),
    [] ).

cnf(147411544,plain,
    ( ~ $equal(A,D)
    | in(D,C)
    | ~ $equal(unordered_pair(A,B),C) ),
    inference(rewrite,[status(thm)],[d2_tarski]),
    [] ).

cnf(164210480,plain,
    in(A,unordered_pair(A,B)),
    inference(equality_resolution,[status(thm)],[147411544]),
    [] ).

fof(d3_tarski,plain,
    ! [A,B,C] :
      ( ( ~ subset(A,B)
        | ~ in(C,A)
        | in(C,B) )
      & ( ~ in(c(A,B,C),B)
        | subset(A,B) )
      & ( in(c(A,B,C),A)
        | subset(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET872+1.tptp',unknown),
    [] ).

cnf(147426616,plain,
    ( ~ in(c(A,B,C),B)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[d3_tarski]),
    [] ).

fof(t12_zfmisc_1,plain,
    ~ subset(singleton(a),unordered_pair(a,b)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET872+1.tptp',unknown),
    [] ).

cnf(147491960,plain,
    ~ subset(singleton(a),unordered_pair(a,b)),
    inference(rewrite,[status(thm)],[t12_zfmisc_1]),
    [] ).

cnf(155425392,plain,
    ~ in(c(singleton(a),unordered_pair(a,b),A),unordered_pair(a,b)),
    inference(resolution,[status(thm)],[147426616,147491960]),
    [] ).

fof(d1_tarski,plain,
    ! [C,B,A] :
      ( ( in(C,B)
        | ~ $equal(A,C)
        | ~ $equal(singleton(A),B) )
      & ( ~ in(C,B)
        | $equal(A,C)
        | ~ $equal(singleton(A),B) )
      & ( $equal(c(A,B,C),A)
        | ~ $equal(c(A,B,C),A)
        | $equal(singleton(A),B) )
      & ( ~ in(c(A,B,C),B)
        | ~ $equal(c(A,B,C),A)
        | $equal(singleton(A),B) )
      & ( $equal(c(A,B,C),A)
        | in(c(A,B,C),B)
        | $equal(singleton(A),B) )
      & ( ~ in(c(A,B,C),B)
        | in(c(A,B,C),B)
        | $equal(singleton(A),B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET872+1.tptp',unknown),
    [] ).

cnf(147353976,plain,
    ( ~ in(C,B)
    | $equal(A,C)
    | ~ $equal(singleton(A),B) ),
    inference(rewrite,[status(thm)],[d1_tarski]),
    [] ).

cnf(155936304,plain,
    ( ~ in(B,singleton(A))
    | $equal(A,B) ),
    inference(equality_resolution,[status(thm)],[147353976]),
    [] ).

cnf(147420696,plain,
    ( in(c(A,B,C),A)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[d3_tarski]),
    [] ).

cnf(155411592,plain,
    in(c(singleton(a),unordered_pair(a,b),A),singleton(a)),
    inference(resolution,[status(thm)],[147420696,147491960]),
    [] ).

cnf(156123040,plain,
    $equal(a,c(singleton(a),unordered_pair(a,b),A)),
    inference(resolution,[status(thm)],[155936304,155411592]),
    [] ).

cnf(163654608,plain,
    ~ in(a,unordered_pair(a,b)),
    inference(paramodulation,[status(thm)],[155425392,156123040,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[164210480,163654608]),
    [] ).

%------------------------------------------------------------------------------
%----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)|$equal(unordered_pair(A,B),C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET872+1.tptp',unknown),[]).
% 
% cnf(147411544,plain,(~$equal(A,D)|in(D,C)|~$equal(unordered_pair(A,B),C)),inference(rewrite,[status(thm)],[d2_tarski]),[]).
% 
% cnf(164210480,plain,(in(A,unordered_pair(A,B))),inference(equality_resolution,[status(thm)],[147411544]),[]).
% 
% fof(d3_tarski,plain,(((~subset(A,B)|~in(C,A)|in(C,B))&(~in(c(A,B,C),B)|subset(A,B))&(in(c(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET872+1.tptp',unknown),[]).
% 
% cnf(147426616,plain,(~in(c(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[d3_tarski]),[]).
% 
% fof(t12_zfmisc_1,plain,(~subset(singleton(a),unordered_pair(a,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET872+1.tptp',unknown),[]).
% 
% cnf(147491960,plain,(~subset(singleton(a),unordered_pair(a,b))),inference(rewrite,[status(thm)],[t12_zfmisc_1]),[]).
% 
% cnf(155425392,plain,(~in(c(singleton(a),unordered_pair(a,b),A),unordered_pair(a,b))),inference(resolution,[status(thm)],[147426616,147491960]),[]).
% 
% fof(d1_tarski,plain,(((in(C,B)|~$equal(A,C)|~$equal(singleton(A),B))&(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B))&($equal(c(A,B,C),A)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&($equal(c(A,B,C),A)|in(c(A,B,C),B)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|in(c(A,B,C),B)|$equal(singleton(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET872+1.tptp',unknown),[]).
% 
% cnf(147353976,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
% 
% cnf(155936304,plain,(~in(B,singleton(A))|$equal(A,B)),inference(equality_resolution,[status(thm)],[147353976]),[]).
% 
% cnf(147420696,plain,(in(c(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[d3_tarski]),[]).
% 
% cnf(155411592,plain,(in(c(singleton(a),unordered_pair(a,b),A),singleton(a))),inference(resolution,[status(thm)],[147420696,147491960]),[]).
% 
% cnf(156123040,plain,($equal(a,c(singleton(a),unordered_pair(a,b),A))),inference(resolution,[status(thm)],[155936304,155411592]),[]).
% 
% cnf(163654608,plain,(~in(a,unordered_pair(a,b))),inference(paramodulation,[status(thm)],[155425392,156123040,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[164210480,163654608]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------