## TPTP Problem File: SYN995^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYN995^1 : TPTP v7.1.0. Released v3.7.0.
% Domain   : Syntactic
% Problem  : Every function has a fixed point
% Version  : Especial.
% English  :

% Refs     : [BB05]  Benzmueller & Brown (2005), A Structured Set of Higher
%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source   : [Ben09]
% Names    : Example 3 [BB05]

% Status   : CounterSatisfiable
% Rating   : 0.33 v4.1.0, 0.00 v3.7.0
% Syntax   : Number of formulae    :    3 (   0 unit;   1 type;   1 defn)
%            Number of atoms       :   10 (   1 equality;   7 variable)
%            Maximal formula depth :    7 (   6 average)
%            Number of connectives :    6 (   0   ~;   0   |;   0   &;   5   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   2   !;   1   ?;   2   ^)
%                                         (   5   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

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

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

thf(conj,conjecture,(
! [F: \$i > \$i] :
? [X: \$i] :
( leibeq @ ( F @ X ) @ X ) )).

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