TPTP Problem File: SEV251^5.p

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```%------------------------------------------------------------------------------
% File     : SEV251^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SETS-OF-SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1047 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.1, 0.50 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   36 (   1 equality;  27 variable)
%            Maximal formula depth :   14 (   7 average)
%            Number of connectives :   33 (   0   ~;   2   |;   5   &;  17   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2   :;   0   =)
%            Number of variables   :   13 (   1 sgn;  10   !;   1   ?;   2   ^)
%                                         (  13   :;   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(cC,type,(
cC: ( \$i > \$o ) > \$o )).

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

thf(cTHM629_pme,conjecture,
( ( ! [X: \$i > \$o,Y: \$i > \$o] :
( ( ( cL @ X )
& ( cL @ Y ) )
=> ( ! [Xx: \$i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
| ! [Xx: \$i] :
( ( Y @ Xx )
=> ( X @ Xx ) ) ) )
& ! [Xx: \$i > \$o] :
( ( cC @ Xx )
=> ( cL @ Xx ) )
& ! [Xw: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( Xw
@ ^ [Xx: \$i > \$o] : \$false )
& ! [Xr: ( \$i > \$o ) > \$o,Xx: \$i > \$o] :
( ( Xw @ Xr )
=> ( Xw
@ ^ [Xt: \$i > \$o] :
( ( Xr @ Xt )
| ( Xt = Xx ) ) ) ) )
=> ( Xw @ cC ) ) )
=> ? [U: \$i > \$o] :
( ( cC @ U )
& ! [V: \$i > \$o] :
( ( cC @ V )
=> ! [Xx: \$i] :
( ( U @ Xx )
=> ( V @ Xx ) ) ) ) )).

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