## TPTP Problem File: SYO318^5.p

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```%------------------------------------------------------------------------------
% File     : SYO318^5 : 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_0955 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v4.1.0, 0.00 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :   34 (   0 equality;  10 variable)
%            Maximal formula depth :   14 (   5 average)
%            Number of connectives :   39 (   6   ~;   0   |;   6   &;  25   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   2   !;   1   ?;   0   ^)
%                                         (   3   :;   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(c0,type,(
c0: \$i )).

thf(c2,type,(
c2: \$i )).

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

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

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

thf(cBLEDSOE_FENG_9,conjecture,
( ( ~ ( c_less_ @ c0 @ c0 )
& ~ ( c_less_ @ ( div @ c0 @ c2 ) @ c0 )
& ~ ( c_less_ @ ( c_star @ c2 @ c0 ) @ c0 ) )
=> ? [A: \$i > \$o] :
( ! [Xx: \$i,Xy: \$i] :
( ( ( A @ Xx )
& ( A @ Xy ) )
=> ( ~ ( c_less_ @ ( div @ Xx @ c2 ) @ c0 )
& ~ ( c_less_ @ Xy @ ( div @ Xx @ c2 ) )
& ~ ( c_less_ @ ( c_star @ c2 @ Xx ) @ Xy ) ) )
& ( A @ c0 ) ) )).

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