## TPTP Problem File: SEU875^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU875^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory (Finite sets)
% Problem  : TPS problem from SET-TOPOLOGY-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1044 [Bro09]

% 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, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   38 (   1 equality;  28 variable)
%            Maximal formula depth :   17 (   6 average)
%            Number of connectives :   35 (   0   ~;   1   |;   8   &;  18   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3   :;   0   =)
%            Number of variables   :   11 (   1 sgn;   8   !;   1   ?;   2   ^)
%                                         (  11   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          :
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(t,type,(
t: a )).

thf(cA,type,(
cA: ( a > \$o ) > \$o )).

thf(cDOMLEMMA5_pme,conjecture,
( ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ( Xx @ t ) )
=> ( cA @ Xx ) )
& ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ( Xx @ t ) )
=> ? [Xe: a > \$o] :
( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: a] : \$false )
& ! [Xx0: a > \$o] :
( ( X @ Xx0 )
=> ! [Xt0: a] :
( ( Xe @ Xt0 )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt0 = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > \$o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cA @ Xy )
& ( Xy @ t ) ) ) ) ) )).

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