## TPTP Problem File: SEV489^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV489^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : FORALL_IN_CLAUSES_
% Version  : Especial.
% English  :

% Refs     : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source   : [Kal16]
% Names    : FORALL_IN_CLAUSES_0.p [Kal16]

% Status   : Theorem
% Rating   : 0.00 v7.1.0
% Syntax   : Number of formulae    :    6 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   29 (   3 equality;  18 variable)
%            Maximal formula depth :   10 (   7 average)
%            Number of connectives :   21 (   1   ~;   1   |;   0   &;  18   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   12 (   0 sgn;   9   !;   0   ?;   0   ^)
%                                         (  12   :;   3  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
thf('thf_const_const/sets/INSERT',type,(
'const/sets/INSERT':
!>[A: \$tType] :
( A > ( A > \$o ) > A > \$o ) )).

thf('thf_const_const/sets/IN',type,(
'const/sets/IN':
!>[A: \$tType] :
( A > ( A > \$o ) > \$o ) )).

thf('thf_const_const/sets/EMPTY',type,(
'const/sets/EMPTY':
!>[A: \$tType] :
( A > \$o ) )).

thf('thm/sets/IN_INSERT_',axiom,(
! [A: \$tType,A0: A,A1: A,A2: A > \$o] :
( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ A2 ) )
= ( ( A0 = A1 )
| ( 'const/sets/IN' @ A @ A0 @ A2 ) ) ) )).

thf('thm/sets/NOT_IN_EMPTY_',axiom,(
! [A: \$tType,A0: A] :
~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) )).

thf('thm/sets/FORALL_IN_CLAUSES_0',conjecture,(
! [A: \$tType,P: A > \$o] :
( ( ! [A0: A] :
( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) )
=> ( P @ A0 ) ) )
= \$true ) )).

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