## TPTP Problem File: SYO224^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO224^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem LING1
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0499 [Bro09]
%          : LING1 [TPS]

% Status   : Theorem
% Rating   : 0.38 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    8 (   0 unit;   7 type;   0 defn)
%            Number of atoms       :   33 (   3 equality;  11 variable)
%            Maximal formula depth :   11 (   4 average)
%            Number of connectives :   26 (   0   ~;   0   |;   8   &;  15   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   2   !;   2   ?;   0   ^)
%                                         (   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
%          :
%------------------------------------------------------------------------------
thf(cJ,type,(
cJ: \$i )).

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

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

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

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

thf(cS,type,(
cS: \$i )).

thf(cP,type,(
cP: \$i )).

thf(cLING1,conjecture,
( ( ! [X: \$i] :
( ( cUNIQUE @ X )
=> ! [Z: \$i] :
( ( ( cWRH @ Z )
& ( cW @ Z ) )
=> ( X = Z ) ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS ) )
=> ? [Xan: \$i > \$o] :
( ( ( Xan @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( Xan @ cJ )
= ( ? [X: \$i] :
( ( cUNIQUE @ X )
& ( cW @ X )
& ( cWRH @ X )
& ( cLIKE @ cJ @ X ) ) ) ) ) )).

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