## TPTP Problem File: SEU927^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU927^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem THM92
% Version  : Especial.
% English  : Trivial theorem which gives nice simple example of an expansion
%            proof.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0233 [Bro09]
%          : THM92 [TPS]

% Status   : Theorem
% Rating   : 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   12 (   0 equality;  12 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :   11 (   0   ~;   0   |;   1   &;   8   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   3   !;   0   ?;   3   ^)
%                                         (   6   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_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(a_type,type,(
a: \$tType )).

thf(cTHM92_pme,conjecture,(
! [Xf: a > a,Xp: ( a > a ) > \$o] :
( ( ( Xp
@ ^ [Xu: a] : Xu )
& ! [Xj: a > a] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: a] :
( Xf @ ( Xj @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: a] :
( Xf @ ( Xf @ Xx ) ) ) ) )).

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