## TPTP Problem File: SEV116^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV116^5 : TPTP v7.5.0. Bugfixed v5.2.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem STRANGE-HO-EXAMPLE
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0073 [Bro09]
%          : STRANGE-HO-EXAMPLE [TPS]

% Status   : Theorem
% Rating   : 0.00 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% Syntax   : Number of formulae    :    6 (   0 unit;   4 type;   1 defn)
%            Number of atoms       :   21 (   1 equality;   8 variable)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :   17 (   0   ~;   0   |;   2   &;  13   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   1   !;   0   ?;   3   ^)
%                                         (   4   :;   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
% Bugfixes : v5.2.0 - Added missing type declarations.
%------------------------------------------------------------------------------
thf(cS_type,type,(
cS: ( \$i > \$i > \$o ) > \$o )).

thf(x_type,type,(
x: \$i )).

thf(y_type,type,(
y: \$i )).

thf(cSTRANGE_HO_ABBR_type,type,(
cSTRANGE_HO_ABBR: ( ( \$i > \$i > \$o ) > \$o ) > \$i > \$i > \$o )).

thf(cSTRANGE_HO_ABBR_def,definition,
( cSTRANGE_HO_ABBR
= ( ^ [S: ( \$i > \$i > \$o ) > \$o,Xx: \$i,Xy: \$i] :
! [Xp: \$i > \$i > \$o] :
( ( ( S @ Xp )
& ( Xp @ Xx @ Xy ) )
=> ( Xp @ Xy @ Xx ) ) ) )).

thf(cSTRANGE_HO_EXAMPLE,conjecture,
( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) )).

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