%------------------------------------------------------------------------------
% File     : SYO329^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1027 [Bro09]

% Status   : Theorem
% Rating   : 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   45 (   0 equality;  23 variable)
%            Maximal formula depth :   17 (   6 average)
%            Number of connectives :   44 (   0   ~;   1   |;   4   &;  33   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   9   !;   0   ?;   0   ^)
%                                         (   9   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%          : 
%------------------------------------------------------------------------------
thf(cS,type,(
    cS: $i > $i )).

thf(cDOUBLE,type,(
    cDOUBLE: $i > $i > $o )).

thf(cHALF,type,(
    cHALF: $i > $i > $o )).

thf(c0,type,(
    c0: $i )).

thf(cTHM300B,conjecture,
    ( ( ! [Xu: $i,Xv: $i] :
          ( ( cHALF @ Xu @ Xv )
         => ! [Q: $i > $i > $o] :
              ( ( ( Q @ c0 @ c0 )
                & ( Q @ ( cS @ c0 ) @ c0 )
                & ! [Xx: $i,Xy: $i] :
                    ( ( Q @ Xx @ Xy )
                   => ( Q @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
             => ( Q @ Xu @ Xv ) ) )
      & ( cDOUBLE @ c0 @ c0 )
      & ! [Xx: $i,Xy: $i] :
          ( ( cDOUBLE @ Xx @ Xy )
         => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
   => ! [Xu: $i,Xv: $i] :
        ( ( cHALF @ Xu @ Xv )
       => ( ( cDOUBLE @ Xv @ Xu )
          | ( cDOUBLE @ ( cS @ Xv ) @ ( cS @ Xu ) ) ) ) )).

%------------------------------------------------------------------------------