## TPTP Problem File: SEV169^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV169^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from PAIRS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1021 [Bro09]

% Status   : Theorem
% Rating   : 0.18 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 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       :   27 (   5 equality;  22 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   16 (   0   ~;   0   |;   3   &;  12   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1   :;   0   =)
%            Number of variables   :   20 (   8 sgn;   2   !;   0   ?;  18   ^)
%                                         (  20   :;   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(cTHM188_pme,conjecture,(
! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( Xq
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xx ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) )
=> ( Xp = Xq ) ) )).

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