## TPTP Problem File: SYO333^5.p

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```%------------------------------------------------------------------------------
% File     : SYO333^5 : TPTP v7.2.0. 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_1074 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    8 (   0 unit;   7 type;   0 defn)
%            Number of atoms       :   55 (   0 equality;  20 variable)
%            Maximal formula depth :   20 (   5 average)
%            Number of connectives :   54 (   0   ~;   0   |;   8   &;  40   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   9   !;   0   ?;   0   ^)
%                                         (   9   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_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(u,type,(
u: \$i )).

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

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

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

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

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

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

thf(cHALF_TO_DOUBLE_1,conjecture,
( ( ( cDOUBLE @ c0 @ c0 )
& ! [Xx: \$i,Xy: \$i] :
( ( cDOUBLE @ Xx @ Xy )
=> ( cDOUBLE @ cSx @ ( cS @ ( cS @ Xy ) ) ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ c0 @ ( cS @ c0 ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cHALF @ Xx @ Xy )
=> ( cHALF @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) )
& ! [Q: \$i > \$i > \$o,Xu0: \$i,Xv0: \$i] :
( ( ( cHALF @ Xu0 @ Xv0 )
& ( Q @ c0 @ c0 )
& ( Q @ c0 @ ( cS @ c0 ) )
& ! [Xx: \$i,Xy: \$i] :
( ( Q @ Xx @ Xy )
=> ( Q @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
=> ( Q @ Xu0 @ Xv0 ) ) )
=> ( ( cHALF @ u @ v )
=> ( cDOUBLE @ v @ u ) ) )).

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