TPTP Problem File: SEV215^5.p
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- Solve Problem
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% File : SEV215^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from S-T-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1248 [Bro09]
% Status : Unknown
% Rating : 1.00 v4.0.0
% Syntax : Number of formulae : 9 ( 0 unt; 8 typ; 0 def)
% Number of atoms : 56 ( 47 equ; 0 cnn)
% Maximal formula atoms : 50 ( 56 avg)
% Number of connectives : 230 ( 2 ~; 12 |; 53 &; 142 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 40 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 6 ^; 45 !; 29 ?; 80 :)
% 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(c_type,type,
c: $tType ).
thf(iS_type,type,
iS: $tType ).
thf(cR,type,
cR: c > c ).
thf(cP,type,
cP: iS > iS > iS ).
thf(c0,type,
c0: iS ).
thf(cL,type,
cL: c > c ).
thf(cX0,type,
cX0: c > $o ).
thf(cX1,type,
cX1: c > $o ).
thf(cTHM_S_CHAR_T_pme,conjecture,
( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) )
& ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) )
& ! [Xz: c] :
( ( cX0 @ Xz )
<=> ~ ( cX1 @ Xz ) )
& ! [Xz: c] :
( ( cX0 @ Xz )
=> ( ( ( cL @ Xz )
= Xz )
& ( ( cR @ Xz )
= Xz ) ) ) )
=> ? [Xf: c > iS > $o] :
( ! [Xb: c] :
( ( Xf @ Xb @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( Xf @ Xb @ Xy )
& ! [R0: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xy ) ) )
=> ( Xf @ Xb @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( Xf @ Xb @ Xx )
& ( Xf @ Xb @ Xy )
& ! [R0: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xz ) ) )
=> ( Xf @ Xb @ Xz ) ) )
& ! [Xc: c] :
( ( cX0 @ Xc )
<=> ( ( Xf @ Xc )
= ( ^ [Xy: iS] : c0 = Xy ) ) )
& ! [Xb: c] :
( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] : ( Xf @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xf @ ( cL @ Xb ) ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] : ( Xf @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xf @ ( cR @ Xb ) ) ) )
& ! [Xg: c > iS > $o] :
( ( ! [Xb: c] :
( ( Xg @ Xb @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( Xg @ Xb @ Xy )
& ! [R0: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xy ) ) )
=> ( Xg @ Xb @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( Xg @ Xb @ Xx )
& ( Xg @ Xb @ Xy )
& ! [R0: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xz ) ) )
=> ( Xg @ Xb @ Xz ) ) )
& ! [Xc: c] :
( ( cX0 @ Xc )
<=> ( ( Xg @ Xc )
= ( ^ [Xy: iS] : c0 = Xy ) ) )
& ! [Xb: c] :
( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] : ( Xg @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xg @ ( cL @ Xb ) ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] : ( Xg @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xg @ ( cR @ Xb ) ) ) ) )
=> ( Xf = Xg ) ) ) ) ).
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