## TPTP Problem File: SYO327^5.p

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```%------------------------------------------------------------------------------
% File     : SYO327^5 : TPTP v8.2.0. 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_1011 [Bro09]

% Status   : Theorem
% Rating   : 0.25 v8.2.0, 0.27 v8.1.0, 0.33 v7.5.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.29 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unt;   4 typ;   0 def)
%            Number of atoms       :    7 (   0 equ;   0 cnn)
%            Maximal formula atoms :    7 (   7 avg)
%            Number of connectives :   39 (   0   ~;   0   |;   5   &;  29   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (  15 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    9 (   0   ^;   9   !;   0   ?;   9   :)
% 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(cHALF,type,
cHALF: \$i > \$i > \$o ).

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

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

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

thf(cDOUBLE_TO_HALF_6,conjecture,
( ( ! [Q: \$i > \$i > \$o,Xu: \$i,Xv: \$i] :
( ( ( cDOUBLE @ Xu @ Xv )
& ( Q @ c0 @ c0 )
& ! [Xx: \$i,Xy: \$i] :
( ( Q @ Xx @ Xy )
=> ( Q @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
=> ( Q @ Xu @ Xv ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ c0 @ ( cS @ c0 ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cHALF @ Xx @ Xy )
=> ( cHALF @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
=> ! [Xu: \$i,Xv: \$i] :
( ( cDOUBLE @ Xu @ Xv )
=> ( cHALF @ Xv @ Xu ) ) ) ).

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