## TPTP Problem File: SEV168^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV168^5 : 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_0889 [Bro09]

% Status   : Theorem
% Rating   : 0.18 v7.5.0, 0.00 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    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   17 (   3 equality;   6 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :   10 (   0   ~;   0   |;   1   &;   8   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3   :;   0   =)
%            Number of variables   :   10 (   4 sgn;   0   !;   0   ?;  10   ^)
%                                         (  10   :;   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(q,type,(
q: ( a > a > a ) > a )).

thf(p,type,(
p: ( a > a > a ) > a )).

thf(cTHM188_PARTIAL_pme,conjecture,
( ( ( q
= ( ^ [Xg: a > a > a] :
( Xg
@ ( q
@ ^ [Xx: a,Xy: a] : Xx )
@ ( q
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( p
= ( ^ [Xg: a > a > a] :
( Xg
@ ( q
@ ^ [Xx: a,Xy: a] : Xx )
@ ( q
@ ^ [Xx: a,Xy: a] : Xy ) ) ) ) )
=> ( p = q ) )).

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