TPTP Problem File: SEV219^5.p
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% File : SEV219^5 : TPTP v8.2.0. 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 unt; 5 typ; 0 def)
% Number of atoms : 25 ( 25 equ; 0 cnn)
% Maximal formula atoms : 25 ( 25 avg)
% Number of connectives : 449 ( 1 ~; 0 |; 66 &; 336 @)
% ( 1 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 32 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 87 ( 0 ^; 58 !; 29 ?; 87 :)
% 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
% Mellon University. Distributed under the Creative Commons copyleft
% license: http://creativecommons.org/licenses/by-sa/3.0/
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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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