TPTP Problem File: SEU827^1.p

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% File     : SEU827^1 : TPTP v7.2.0. Released v3.7.0.
% Domain   : Set Theory
% Problem  : About sets 2
% Version  : Especial.
% English  :

% Refs     : [BB05]  Benzmueller & Brown (2005), A Structured Set of Higher
%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source   : [Ben09]
% Names    : Example 22b [BB05]

% Status   : Theorem
%          : Without Boolean extensionality : CounterSatisfiable
%          : Without xi extensionality : CounterSatisfiable
% Rating   : 0.44 v7.2.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.0, 0.33 v3.7.0
% Syntax   : Number of formulae    :   10 (   0 unit;   6 type;   3 defn)
%            Number of atoms       :   31 (   3 equality;  12 variable)
%            Maximal formula depth :    7 (   5 average)
%            Number of connectives :   21 (   0   ~;   1   |;   1   &;  18   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   1   !;   0   ?;   8   ^)
%                                         (   9   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : 
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thf(leibeq_type,type,(
    leibeq: ( $i > $o ) > ( $i > $o ) > $o )).

thf(leibeq,definition,
    ( leibeq
    = ( ^ [X: $i > $o,Y: $i > $o] :
        ! [P: ( $i > $o ) > $o] :
          ( ( P @ X )
         => ( P @ Y ) ) ) )).

thf(u_type,type,(
    u: ( $i > $o ) > ( $i > $o ) > $i > $o )).

thf(u,definition,
    ( u
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) )).

thf(n_type,type,(
    n: ( $i > $o ) > ( $i > $o ) > $i > $o )).

thf(n,definition,
    ( n
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) )).

thf(a_type,type,(
    a: $i > $o )).

thf(b_type,type,(
    b: $i > $o )).

thf(c_type,type,(
    c: $i > $o )).

thf(conj,conjecture,
    ( leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )).

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