## TPTP Problem File: SEU942^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU942^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem THM15B
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0423 [Bro09]
%          : THM15B [TPS]
%          : THM15BA [TPS]
%          : THM15A-0 [TPS]

% Status   : Theorem
% Rating   : 1.00 v7.1.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   25 (   4 equality;  21 variable)
%            Maximal formula depth :   14 (  14 average)
%            Number of connectives :   16 (   0   ~;   0   |;   3   &;   9   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   4   !;   3   ?;   1   ^)
%                                         (   8   :;   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
%          : Polymorphic definitions expanded.
%          :
%------------------------------------------------------------------------------
thf(cTHM15B_pme,conjecture,(
! [Xf: \$i > \$i] :
( ? [Xg: \$i > \$i] :
( ! [Xp: ( \$i > \$i ) > \$o] :
( ( ( Xp @ Xf )
& ! [Xj: \$i > \$i] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: \$i] :
( Xf @ ( Xj @ Xx ) ) ) ) )
=> ( Xp @ Xg ) )
& ? [Xx: \$i] :
( ( ( Xg @ Xx )
= Xx )
& ! [Xz: \$i] :
( ( ( Xg @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) )
=> ? [Xy: \$i] :
( ( Xf @ Xy )
= Xy ) ) )).

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