TPTP Problem File: SEV254^5.p

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```%------------------------------------------------------------------------------
% File     : SEV254^5 : TPTP v7.0.0. 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_1170 [Bro09]
%          : tps_1171 [Bro09]

% Status   : Theorem
% Rating   : 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.33 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   72 (   0 equality;  72 variable)
%            Maximal formula depth :   17 (  17 average)
%            Number of connectives :   71 (   0   ~;   0   |;   9   &;  46   @)
%                                         (   1 <=>;  15  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   28 (   0 sgn;  15   !;   8   ?;   5   ^)
%                                         (  28   :;   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(cTHM2C_pme,conjecture,(
! [K: ( \$i > \$o ) > \$i > \$o] :
( ( ! [Xx: \$i > \$o] :
( ! [Xx0: \$i] :
( ( Xx @ Xx0 )
=> ? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
=> ! [Xx0: \$i] :
( ( K @ Xx @ Xx0 )
=> ( K
@ ^ [Xx1: \$i] :
? [S: \$i > \$o] :
( ! [Xx2: \$i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 ) ) )
& ( ! [Xx: \$i] :
( ? [S: \$i > \$o] :
( ! [Xx0: \$i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) )
=> ! [Xx: \$i] :
( ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ( K
@ ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
@ Xx ) ) ) )
=> ! [Xx: \$i] :
( ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
<=> ? [S: \$i > \$o] :
( ! [Xx0: \$i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) ) ) ) )).

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```