## TPTP Problem File: SEV219^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV219^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from S-SEQ-COI-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1252 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :  499 (  25 equality; 275 variable)
%            Maximal formula depth :   32 (   8 average)
%            Number of connectives :  449 (   1   ~;   0   |;  66   &; 336   @)
%                                         (   1 <=>;  45  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5   :;   0   =)
%            Number of variables   :   87 (   0 sgn;  58   !;  29   ?;   0   ^)
%                                         (  87   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_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(cP,type,(
cP: a > a > a )).

thf(cZ,type,(
cZ: a )).

thf(cR,type,(
cR: a > a )).

thf(cL,type,(
cL: a > a )).

thf(cPU_LEM9_pme,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx )
& ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
=> ! [Xb: a] :
( ! [X: a > \$o] :
( ( ( X @ cZ )
& ! [Xx: a] :
( ( X @ Xx )
=> ( ( X @ ( cP @ Xx @ cZ ) )
& ( X @ ( cP @ Xx @ ( cP @ cZ @ cZ ) ) ) ) ) )
=> ( X @ Xb ) )
=> ! [D: a > \$o] :
( ( ! [Xx: a] :
( ( D @ Xx )
=> ! [X: a > \$o] :
( ( ( X @ cZ )
& ! [Xx0: a,Xy: a] :
( ( ( X @ Xx0 )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx0 @ Xy ) ) ) )
=> ( X @ Xx ) ) )
& ( D @ cZ )
& ! [Xx: a] :
( ( D @ Xx )
=> ! [Xy: a] :
( ? [X: a > \$o] :
( ( X @ ( cP @ Xy @ Xx ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ( D @ Xy ) ) )
& ! [Xx: a,Xy: a] :
( ( ( D @ Xx )
& ( D @ Xy ) )
=> ? [Xz: a] :
( ( D @ Xz )
=> ( ? [X: a > \$o] :
( ( X @ ( cP @ Xx @ Xz ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
& ? [X: a > \$o] :
( ( X @ ( cP @ Xy @ Xz ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) ) ) )
=> ( ? [Xt: a] :
( ( D @ Xt )
& ? [Xb_2: a,Xu_1: a] :
( ( ( cP @ Xb @ cZ )
= ( cP @ Xb_2 @ Xu_1 ) )
& ! [X: a > \$o] :
( ( ( X @ ( cP @ cZ @ Xt ) )
& ! [Xc: a,Xv: a] :
( ( X @ ( cP @ Xc @ Xv ) )
=> ( ( X @ ( cP @ ( cP @ Xc @ cZ ) @ ( cL @ Xv ) ) )
& ( X @ ( cP @ ( cP @ Xc @ ( cP @ cZ @ cZ ) ) @ ( cR @ Xv ) ) ) ) ) )
=> ( X @ ( cP @ Xb_2 @ Xu_1 ) ) ) ) )
& ! [Xx: a] :
( ? [Xt: a] :
( ( D @ Xt )
& ? [Xb_3: a,Xu_2: a] :
( ( ( cP @ Xb @ Xx )
= ( cP @ Xb_3 @ Xu_2 ) )
& ! [X: a > \$o] :
( ( ( X @ ( cP @ cZ @ Xt ) )
& ! [Xc: a,Xv: a] :
( ( X @ ( cP @ Xc @ Xv ) )
=> ( ( X @ ( cP @ ( cP @ Xc @ cZ ) @ ( cL @ Xv ) ) )
& ( X @ ( cP @ ( cP @ Xc @ ( cP @ cZ @ cZ ) ) @ ( cR @ Xv ) ) ) ) ) )
=> ( X @ ( cP @ Xb_3 @ Xu_2 ) ) ) ) )
=> ! [Xy: a] :
( ? [X: a > \$o] :
( ( X @ ( cP @ Xy @ Xx ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ? [Xt: a] :
( ( D @ Xt )
& ? [Xb_4: a,Xu_6: a] :
( ( ( cP @ Xb @ Xy )
= ( cP @ Xb_4 @ Xu_6 ) )
& ! [X: a > \$o] :
( ( ( X @ ( cP @ cZ @ Xt ) )
& ! [Xc: a,Xv: a] :
( ( X @ ( cP @ Xc @ Xv ) )
=> ( ( X @ ( cP @ ( cP @ Xc @ cZ ) @ ( cL @ Xv ) ) )
& ( X @ ( cP @ ( cP @ Xc @ ( cP @ cZ @ cZ ) ) @ ( cR @ Xv ) ) ) ) ) )
=> ( X @ ( cP @ Xb_4 @ Xu_6 ) ) ) ) ) ) )
& ! [Xx: a,Xy: a] :
( ( ? [Xt: a] :
( ( D @ Xt )
& ? [Xb_5: a,Xu_7: a] :
( ( ( cP @ Xb @ Xx )
= ( cP @ Xb_5 @ Xu_7 ) )
& ! [X: a > \$o] :
( ( ( X @ ( cP @ cZ @ Xt ) )
& ! [Xc: a,Xv: a] :
( ( X @ ( cP @ Xc @ Xv ) )
=> ( ( X @ ( cP @ ( cP @ Xc @ cZ ) @ ( cL @ Xv ) ) )
& ( X @ ( cP @ ( cP @ Xc @ ( cP @ cZ @ cZ ) ) @ ( cR @ Xv ) ) ) ) ) )
=> ( X @ ( cP @ Xb_5 @ Xu_7 ) ) ) ) )
& ? [Xt: a] :
( ( D @ Xt )
& ? [Xb_6: a,Xu_8: a] :
( ( ( cP @ Xb @ Xy )
= ( cP @ Xb_6 @ Xu_8 ) )
& ! [X: a > \$o] :
( ( ( X @ ( cP @ cZ @ Xt ) )
& ! [Xc: a,Xv: a] :
( ( X @ ( cP @ Xc @ Xv ) )
=> ( ( X @ ( cP @ ( cP @ Xc @ cZ ) @ ( cL @ Xv ) ) )
& ( X @ ( cP @ ( cP @ Xc @ ( cP @ cZ @ cZ ) ) @ ( cR @ Xv ) ) ) ) ) )
=> ( X @ ( cP @ Xb_6 @ Xu_8 ) ) ) ) ) )
=> ? [Xz: a] :
( ? [Xt: a] :
( ( D @ Xt )
& ? [Xb_7: a,Xu_9: a] :
( ( ( cP @ Xb @ Xz )
= ( cP @ Xb_7 @ Xu_9 ) )
& ! [X: a > \$o] :
( ( ( X @ ( cP @ cZ @ Xt ) )
& ! [Xc: a,Xv: a] :
( ( X @ ( cP @ Xc @ Xv ) )
=> ( ( X @ ( cP @ ( cP @ Xc @ cZ ) @ ( cL @ Xv ) ) )
& ( X @ ( cP @ ( cP @ Xc @ ( cP @ cZ @ cZ ) ) @ ( cR @ Xv ) ) ) ) ) )
=> ( X @ ( cP @ Xb_7 @ Xu_9 ) ) ) ) )
=> ( ? [X: a > \$o] :
( ( X @ ( cP @ Xx @ Xz ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
& ? [X: a > \$o] :
( ( X @ ( cP @ Xy @ Xz ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) ) )
& ! [Xx: a] :
( ? [Xt: a] :
( ( D @ Xt )
& ? [Xb_8: a,Xu_10: a] :
( ( ( cP @ Xb @ Xx )
= ( cP @ Xb_8 @ Xu_10 ) )
& ! [X: a > \$o] :
( ( ( X @ ( cP @ cZ @ Xt ) )
& ! [Xc: a,Xv: a] :
( ( X @ ( cP @ Xc @ Xv ) )
=> ( ( X @ ( cP @ ( cP @ Xc @ cZ ) @ ( cL @ Xv ) ) )
& ( X @ ( cP @ ( cP @ Xc @ ( cP @ cZ @ cZ ) ) @ ( cR @ Xv ) ) ) ) ) )
=> ( X @ ( cP @ Xb_8 @ Xu_10 ) ) ) ) )
=> ! [X: a > \$o] :
( ( ( X @ cZ )
& ! [Xx0: a,Xy: a] :
( ( ( X @ Xx0 )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx0 @ Xy ) ) ) )
=> ( X @ Xx ) ) ) ) ) ) )).

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