## TPTP Problem File: MSC021^5.p

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```%------------------------------------------------------------------------------
% File     : MSC021^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Miscellaneous
% Problem  : TPS problem THM300
% Version  : Especial.
% English  : Relation between HALF and DOUBLE functions.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0473 [Bro09]
%          : THM300 [TPS]

% Status   : Theorem
% Rating   : 0.92 v7.4.0, 0.89 v7.3.0, 0.90 v7.2.0, 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 :   18 (   6 average)
%            Number of connectives :   44 (   0   ~;   1   |;   5   &;  33   @)
%                                         (   0 <=>;   5  =>;   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
%          :
%------------------------------------------------------------------------------
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(cTHM300,conjecture,
( ( ( cDOUBLE @ c0 @ c0 )
& ! [Xx: \$i,Xy: \$i] :
( ( cDOUBLE @ Xx @ Xy )
=> ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) )
& ! [Q: \$i > \$i > \$o,Xu: \$i,Xv: \$i] :
( ( ( cHALF @ Xu @ Xv )
& ( Q @ c0 @ c0 )
& ( Q @ ( cS @ c0 ) @ c0 )
& ! [Xx: \$i,Xy: \$i] :
( ( Q @ Xx @ Xy )
=> ( Q @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
=> ( Q @ Xu @ Xv ) ) )
=> ! [Xu: \$i,Xv: \$i] :
( ( cHALF @ Xu @ Xv )
=> ( ( cDOUBLE @ Xv @ Xu )
| ( cDOUBLE @ ( cS @ Xv ) @ ( cS @ Xu ) ) ) ) )).

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