## TPTP Problem File: SEU957^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU957^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem from FUNCTION-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0895 [Bro09]

% Status   : Theorem
% Rating   : 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.86 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   17 (   3 equality;  14 variable)
%            Maximal formula depth :    9 (   4 average)
%            Number of connectives :   10 (   0   ~;   0   |;   0   &;   6   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   4   !;   5   ?;   0   ^)
%                                         (   9   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%          :
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(b_type,type,(
b: \$tType )).

thf(cTHM607_pme,conjecture,
( ? [Xc: ( a > \$o ) > a] :
! [X: a > \$o] :
( ? [Xt: a] :
( X @ Xt )
=> ( X @ ( Xc @ X ) ) )
=> ( ? [Xg: a > b] :
! [Y: b] :
? [X: a] :
( ( Xg @ X )
= Y )
=> ? [Xf: b > a] :
! [Xx: b,Xy: b] :
( ( ( Xf @ Xx )
= ( Xf @ Xy ) )
=> ( Xx = Xy ) ) ) )).

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