## TPTP Problem File: SEV061^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV061^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM176
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0331 [Bro09]
%          : THM176 [TPS]

% Status   : Theorem
% Rating   : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 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 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   24 (   4 equality;  20 variable)
%            Maximal formula depth :   13 (   6 average)
%            Number of connectives :   16 (   1   ~;   1   |;   3   &;   8   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   8   !;   0   ?;   0   ^)
%                                         (   8   :;   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(b_type,type,(
b: \$tType )).

thf(a_type,type,(
a: \$tType )).

thf(cTHM176_pme,conjecture,(
! [Xx: b,Xy: a,Xs: b > a > \$o,Xk: b > a > \$o] :
( ! [Xx_2: b,Xy_47: a] :
( ( Xk @ Xx_2 @ Xy_47 )
=> ( ( Xs @ Xx_2 @ Xy_47 )
| ( ( Xx_2 = Xx )
& ( Xy_47 = Xy ) ) ) )
=> ! [Xx_3: b,Xy_48: a] :
( ( ( Xk @ Xx_3 @ Xy_48 )
& ~ ( ( Xx_3 = Xx )
& ( Xy_48 = Xy ) ) )
=> ( Xs @ Xx_3 @ Xy_48 ) ) ) )).

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