## TPTP Problem File: SYO114^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO114^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM119
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0536 [Bro09]
%          : THM119 [TPS]

% Status   : Theorem
% Rating   : 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    8 (   0 unit;   7 type;   0 defn)
%            Number of atoms       :   20 (   0 equality;   6 variable)
%            Maximal formula depth :   12 (   4 average)
%            Number of connectives :   26 (   7   ~;   6   |;   3   &;  10   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   2   !;   1   ?;   0   ^)
%                                         (   3   :;   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(b,type,(
b: \$i )).

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

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

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

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

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

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

thf(cTHM119,conjecture,(
~ ( ! [Xz: \$i] :
( ( ( cP @ Xz )
| ( cR @ Xz ) )
& ( cQ @ Xz ) )
& ! [Xx: \$i] :
? [Xy: \$i] :
( ( cP @ Xx )
| ~ ( cQ @ Xx )
| ~ ( cQ @ Xy )
| ~ ( cQ @ c )
| ~ ( cQ @ d ) )
& ( ~ ( cP @ a )
| ~ ( cP @ b ) ) ) )).

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