## TPTP Problem File: SEV045^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV045^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from PERS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1134 [Bro09]

% Status   : Theorem
% Rating   : 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    7 (   0 unit;   6 type;   0 defn)
%            Number of atoms       :   73 (   1 equality;  46 variable)
%            Maximal formula depth :   17 (   5 average)
%            Number of connectives :   70 (   0   ~;   0   |;   5   &;  52   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6   :;   0   =)
%            Number of variables   :   18 (   0 sgn;  18   !;   0   ?;   0   ^)
%                                         (  18   :;   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(b_type,type,(
b: \$tType )).

thf(g,type,(
g: a > b )).

thf(f,type,(
f: a > b )).

thf(cQ,type,(
cQ: a > b > b > \$o )).

thf(cP,type,(
cP: a > a > \$o )).

thf(cTHM509_pme,conjecture,
( ! [Xx: a] :
( ( cP @ Xx @ Xx )
=> ( cQ @ Xx @ ( f @ Xx ) @ ( g @ Xx ) ) )
=> ( ! [Xx: a,Xy: a] :
( ( cP @ Xx @ Xy )
=> ( cQ @ Xx @ ( f @ Xx ) @ ( f @ Xy ) ) )
=> ( ( ! [Xx: a,Xy: a] :
( ( cP @ Xx @ Xy )
=> ( cP @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( cP @ Xx @ Xy )
& ( cP @ Xy @ Xz ) )
=> ( cP @ Xx @ Xz ) ) )
=> ( ( ! [Xx: a] :
( ( cP @ Xx @ Xx )
=> ( ! [Xx0: b,Xy: b] :
( ( cQ @ Xx @ Xx0 @ Xy )
=> ( cQ @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: b,Xy: b,Xz: b] :
( ( ( cQ @ Xx @ Xx0 @ Xy )
& ( cQ @ Xx @ Xy @ Xz ) )
=> ( cQ @ Xx @ Xx0 @ Xz ) ) ) )
& ! [Xx: a,Xy: a] :
( ( cP @ Xx @ Xy )
=> ( ( cQ @ Xx )
= ( cQ @ Xy ) ) ) )
=> ! [Xx: a,Xy: a] :
( ( cP @ Xx @ Xy )
=> ( cQ @ Xx @ ( f @ Xx ) @ ( g @ Xy ) ) ) ) ) ) )).

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