## TPTP Problem File: SYN985^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYN985^1 : TPTP v7.1.0. Bugfixed v3.7.0.
% Domain   : Syntactic
% Problem  : Factoring application over conjunction with abstraction
% Version  : Especial.
% English  : Variation of BB-1 with functional extensionality

% Refs     : [BB05]  Benzmueller & Brown (2005), A Structured Set of Higher-Ord
%          : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% Source   : [Ben08]
% Names    : BB-3 [Ben08]

% Status   : CounterSatisfiable
% Rating   : 0.33 v4.1.0, 0.00 v4.0.1, 0.50 v4.0.0, 0.00 v3.7.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   11 (   0 equality;  11 variable)
%            Maximal formula depth :   10 (  10 average)
%            Number of connectives :   11 (   1   ~;   0   |;   2   &;   7   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   3   !;   0   ?;   3   ^)
%                                         (   6   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_NEQ_NAR

% Bugfixes : v3.7.0 - Fixed thm to universally quantify over the sets
%------------------------------------------------------------------------------
thf(thm,conjecture,(
~ ( ! [P: ( \$i > \$o ) > \$o,A: \$i > \$o,B: \$i > \$o] :
( ( ( P
@ ^ [X: \$i] :
( A @ X ) )
& ( P
@ ^ [X: \$i] :
( B @ X ) ) )
=> ( P
@ ^ [X: \$i] :
( ( A @ X )
& ( B @ X ) ) ) ) ) )).

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