## TPTP Problem File: SYO016^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO016^1 : TPTP v7.1.0. Released v3.7.0.
% Domain   : Syntactic
% Problem  : Formula valid in MBb, but not in model classes not requiring b
% Version  : Especial.
% English  :

% Refs     : [BB05]  Benzmueller & Brown (2005), A Structured Set of Higher
%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source   : [Ben09]
% Names    : Example 18a [BB05]

% Status   : Theorem
%          : Without Boolean extensionality : CounterSatisfiable
% Rating   : 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.60 v5.1.0, 0.80 v4.1.0, 1.00 v4.0.1, 0.67 v3.7.0
% Syntax   : Number of formulae    :    4 (   0 unit;   2 type;   1 defn)
%            Number of atoms       :   15 (   1 equality;   4 variable)
%            Maximal formula depth :    7 (   5 average)
%            Number of connectives :   11 (   0   ~;   0   |;   0   &;  10   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   1   !;   0   ?;   2   ^)
%                                         (   3   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
thf(leibeq_decl,type,(
leibeq: \$o > \$o > \$o )).

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

thf(h,type,(
h: \$o > \$o )).

thf(conj,conjecture,
( leibeq @ ( h @ ( leibeq @ ( h @ \$true ) @ ( h @ \$false ) ) ) @ ( h @ \$false ) )).

%------------------------------------------------------------------------------
```