%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET907+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.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 15:41:11 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   11 (   5 unt;   0 def)
%            Number of atoms       :   24 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   24 (  11   ~;   9   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   11 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t38_zfmisc_1,plain,
    ! [B,C,A] :
      ( ( in(B,C)
        | ~ subset(unordered_pair(A,B),C) )
      & ( in(A,C)
        | ~ subset(unordered_pair(A,B),C) )
      & ( subset(unordered_pair(A,B),C)
        | ~ in(A,C)
        | ~ in(B,C) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET907+1.tptp',unknown),
    [] ).

cnf(149801008,plain,
    ( subset(unordered_pair(A,B),C)
    | ~ in(A,C)
    | ~ in(B,C) ),
    inference(rewrite,[status(thm)],[t38_zfmisc_1]),
    [] ).

fof(t48_zfmisc_1,plain,
    ( in(a,b)
    & in(c,b)
    & ~ $equal(set_union2(unordered_pair(a,c),b),b) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET907+1.tptp',unknown),
    [] ).

cnf(149886512,plain,
    in(c,b),
    inference(rewrite,[status(thm)],[t48_zfmisc_1]),
    [] ).

cnf(163095016,plain,
    ( subset(unordered_pair(A,c),b)
    | ~ in(A,b) ),
    inference(resolution,[status(thm)],[149801008,149886512]),
    [] ).

cnf(149897928,plain,
    in(a,b),
    inference(rewrite,[status(thm)],[t48_zfmisc_1]),
    [] ).

cnf(163103640,plain,
    subset(unordered_pair(a,c),b),
    inference(resolution,[status(thm)],[163095016,149897928]),
    [] ).

fof(t12_xboole_1,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | $equal(set_union2(A,B),B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET907+1.tptp',unknown),
    [] ).

cnf(149728768,plain,
    ( ~ subset(A,B)
    | $equal(set_union2(A,B),B) ),
    inference(rewrite,[status(thm)],[t12_xboole_1]),
    [] ).

cnf(149878984,plain,
    ~ $equal(set_union2(unordered_pair(a,c),b),b),
    inference(rewrite,[status(thm)],[t48_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[163103640,149728768,149878984]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t38_zfmisc_1,plain,(((in(B,C)|~subset(unordered_pair(A,B),C))&(in(A,C)|~subset(unordered_pair(A,B),C))&(subset(unordered_pair(A,B),C)|~in(A,C)|~in(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET907+1.tptp',unknown),[]).
% 
% cnf(149801008,plain,(subset(unordered_pair(A,B),C)|~in(A,C)|~in(B,C)),inference(rewrite,[status(thm)],[t38_zfmisc_1]),[]).
% 
% fof(t48_zfmisc_1,plain,((in(a,b)&in(c,b)&~$equal(set_union2(unordered_pair(a,c),b),b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET907+1.tptp',unknown),[]).
% 
% cnf(149886512,plain,(in(c,b)),inference(rewrite,[status(thm)],[t48_zfmisc_1]),[]).
% 
% cnf(163095016,plain,(subset(unordered_pair(A,c),b)|~in(A,b)),inference(resolution,[status(thm)],[149801008,149886512]),[]).
% 
% cnf(149897928,plain,(in(a,b)),inference(rewrite,[status(thm)],[t48_zfmisc_1]),[]).
% 
% cnf(163103640,plain,(subset(unordered_pair(a,c),b)),inference(resolution,[status(thm)],[163095016,149897928]),[]).
% 
% fof(t12_xboole_1,plain,(~subset(A,B)|$equal(set_union2(A,B),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET907+1.tptp',unknown),[]).
% 
% cnf(149728768,plain,(~subset(A,B)|$equal(set_union2(A,B),B)),inference(rewrite,[status(thm)],[t12_xboole_1]),[]).
% 
% cnf(149878984,plain,(~$equal(set_union2(unordered_pair(a,c),b),b)),inference(rewrite,[status(thm)],[t48_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[163103640,149728768,149878984]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------