%------------------------------------------------------------------------------ % 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 % Mellon University. Distributed under the Creative Commons copyleft % license: http://creativecommons.org/licenses/by-sa/3.0/ %------------------------------------------------------------------------------ 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 ) ) ) ) ) ) )). %------------------------------------------------------------------------------