## TPTP Problem File: SYO105^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO105^5 : TPTP v7.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem X2201TEST
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0395 [Bro09]
%          : X2201TEST [TPS]

% Status   : Theorem
% Rating   : 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.2.0, 0.25 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   18 (   0 equality;   8 variable)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :   23 (   6   ~;   0   |;   0   &;  12   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   4   !;   4   ?;   0   ^)
%                                         (   8   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          :
%------------------------------------------------------------------------------
thf(cR,type,(
cR: \$i > \$o )).

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

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

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

thf(cX2201TEST,conjecture,
( ~ ( ? [Xx: \$i] :
( cQ @ Xx @ y )
=> ~ ( ! [Xz: \$i] :
( ! [Xu: \$i] :
( cP @ Xu @ y @ Xz )
=> ~ ( ? [Xv: \$i] :
( cR @ Xv ) ) ) ) )
<=> ? [Xx: \$i] :
! [Xz: \$i] :
? [Xu: \$i] :
! [Xv: \$i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) ) )).

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