## TPTP Problem File: SYO543^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO543^1 : TPTP v7.1.0. Released v5.2.0.
% Domain   : Syntactic
% Problem  : If-then-else on \$i>\$i defined from choice on \$i>\$i
% Version  : Especial.
% English  : A choice operator on (\$i>\$i) is used to define an if-then-else
%            operator at (\$i>\$i). Check that if the then-part and else-part
%            are both X, then it returns X.

% Refs     : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% Source   : [Bro11]
% Names    : CHOICE16c [Bro11]

% Status   : Theorem
% Rating   : 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% Syntax   : Number of formulae    :    5 (   0 unit;   2 type;   1 defn)
%            Number of atoms       :   22 (   4 equality;  14 variable)
%            Maximal formula depth :   10 (   7 average)
%            Number of connectives :   12 (   1   ~;   1   |;   2   &;   7   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   3   !;   1   ?;   4   ^)
%                                         (   8   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

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

thf(choiceaxii,axiom,(
! [P: ( \$i > \$i ) > \$o] :
( ? [X: \$i > \$i] :
( P @ X )
=> ( P @ ( epsii @ P ) ) ) )).

thf(if,type,(
if: \$o > ( \$i > \$i ) > ( \$i > \$i ) > \$i > \$i )).

thf(ifd,definition,
( if
= ( ^ [B: \$o,X: \$i > \$i,Y: \$i > \$i] :
( epsii
@ ^ [Z: \$i > \$i] :
( ( B
& ( Z = X ) )
| ( ~ ( B )
& ( Z = Y ) ) ) ) ) )).

thf(conj,conjecture,(
! [B: \$o,X: \$i > \$i] :
( ( if @ B @ X @ X )
= X ) )).

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