## TPTP Problem File: SEV163^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV163^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM187
% Version  : Especial.
% English  : Basic theorem about pairing.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0155 [Bro09]
%          : THM187 [TPS]

% Status   : Theorem
% Rating   : 0.09 v7.5.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   14 (   2 equality;  12 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :    9 (   0   ~;   0   |;   0   &;   8   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1   :;   0   =)
%            Number of variables   :   11 (   4 sgn;   1   !;   0   ?;  10   ^)
%                                         (  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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM187_pme,conjecture,(
! [Xp: ( a > a > a ) > a] :
( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
=> ( ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= Xp ) ) )).

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