%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET102-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.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 15:28:34 EDT 2009

% Result   : Unsatisfiable 1.3s
% Output   : Refutation 1.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   8 unt;   0 def)
%            Number of atoms       :   12 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   4   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   3 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(unordered_pairs_in_universal,plain,
    ! [A,B] : member(unordered_pair(A,B),universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),
    [] ).

cnf(157762992,plain,
    member(unordered_pair(A,B),universal_class),
    inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),
    [] ).

fof(unordered_pair3,plain,
    ! [A,B] :
      ( ~ member(A,universal_class)
      | member(A,unordered_pair(B,A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),
    [] ).

cnf(157759368,plain,
    ( ~ member(A,universal_class)
    | member(A,unordered_pair(B,A)) ),
    inference(rewrite,[status(thm)],[unordered_pair3]),
    [] ).

fof(ordered_pair,plain,
    ! [A,B] : $equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),
    [] ).

cnf(157782688,plain,
    $equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B)),
    inference(rewrite,[status(thm)],[ordered_pair]),
    [] ).

cnf(176649488,plain,
    member(unordered_pair(A,singleton(B)),ordered_pair(A,B)),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157762992,157759368,157782688,theory(equality)]),
    [] ).

fof(prove_unordered_pair_member_of_ordered_pair_1,plain,
    ~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),
    [] ).

cnf(158612680,plain,
    ~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
    inference(rewrite,[status(thm)],[prove_unordered_pair_member_of_ordered_pair_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[176649488,158612680]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(unordered_pairs_in_universal,plain,(member(unordered_pair(A,B),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),[]).
% 
% cnf(157762992,plain,(member(unordered_pair(A,B),universal_class)),inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),[]).
% 
% fof(unordered_pair3,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),[]).
% 
% cnf(157759368,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),inference(rewrite,[status(thm)],[unordered_pair3]),[]).
% 
% fof(ordered_pair,plain,($equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),[]).
% 
% cnf(157782688,plain,($equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
% 
% cnf(176649488,plain,(member(unordered_pair(A,singleton(B)),ordered_pair(A,B))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157762992,157759368,157782688,theory(equality)]),[]).
% 
% fof(prove_unordered_pair_member_of_ordered_pair_1,plain,(~member(unordered_pair(x,singleton(y)),ordered_pair(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-6.tptp',unknown),[]).
% 
% cnf(158612680,plain,(~member(unordered_pair(x,singleton(y)),ordered_pair(x,y))),inference(rewrite,[status(thm)],[prove_unordered_pair_member_of_ordered_pair_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[176649488,158612680]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------