## TPTP Problem File: SYO262^5.p

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%------------------------------------------------------------------------------
% File     : SYO262^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM19SK1
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0152 [Bro09]
%          : THM19SK1 [TPS]

% Status   : Theorem
% Rating   : 0.30 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, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   18 (   0 equality;  10 variable)
%            Maximal formula depth :   12 (   7 average)
%            Number of connectives :   21 (   4   ~;   0   |;   1   &;  16   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   2   !;   0   ?;   3   ^)
%                                         (   5   :;   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(cP,type,(
cP: \$i > \$i > \$o )).

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

thf(cTHM19SK1,conjecture,(
~ ( ! [Xx: \$i] :
( cP @ Xx
@ ( cE
@ ^ [Xy: \$i] :
( cP @ Xx @ Xy ) ) )
& ! [Xf: \$i > \$i] :
~ ( cP
@ ( cE
@ ^ [Xx: \$i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) )
@ ( Xf
@ ( cE
@ ^ [Xx: \$i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) ) )).

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