## TPTP Problem File: SEU994^5.p

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%------------------------------------------------------------------------------
% File     : SEU994^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from LATTICES
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1019 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v5.4.0, 1.00 v5.0.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   35 (   1 equality;  26 variable)
%            Maximal formula depth :   12 (   6 average)
%            Number of connectives :   32 (   0   ~;   0   |;   5   &;  20   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   12 (   0 sgn;  10   !;   2   ?;   0   ^)
%                                         (  12   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          :
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cR,type,(
cR: a > a > \$o )).

thf(cCLATTICE_pme,conjecture,
( ! [Xs: a > \$o] :
? [Xx: a] :
( ! [Xz: a] :
( ( Xs @ Xz )
=> ( cR @ Xz @ Xx ) )
& ! [Xj: a] :
( ! [Xz: a] :
( ( Xs @ Xz )
=> ( cR @ Xz @ Xj ) )
=> ( cR @ Xx @ Xj ) ) )
& ! [Xs: a > \$o] :
? [Xx: a] :
( ! [Xz: a] :
( ( Xs @ Xz )
=> ( cR @ Xx @ Xz ) )
& ! [Xj: a] :
( ! [Xz: a] :
( ( Xs @ Xz )
=> ( cR @ Xj @ Xz ) )
=> ( cR @ Xj @ Xx ) ) )
& ! [Xx: a,Xy: a] :
( ( ( cR @ Xx @ Xy )
& ( cR @ Xy @ Xx ) )
=> ( Xx = Xy ) ) )).

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