TPTP Problem File: SEV212^5.p
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- Solve Problem
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% File : SEV212^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from S-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1224 [Bro09]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% Number of atoms : 28 ( 25 equ; 0 cnn)
% Maximal formula atoms : 28 ( 28 avg)
% Number of connectives : 118 ( 1 ~; 6 |; 27 &; 73 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 30 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 26 !; 18 ?; 44 :)
% SPC : TH0_THM_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(iS_type,type,
iS: $tType ).
thf(cP,type,
cP: iS > iS > iS ).
thf(c0,type,
c0: iS ).
thf(cS_LEM2_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 ) ) )
=> ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ! [R: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc ) )
| ( ( Xb = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ Xx @ Xy @ Xy ) )
& ! [R: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc ) )
| ( ( Xb = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ Xu @ Xv @ Xv ) ) )
=> ! [R: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc ) )
| ( ( Xb = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ) ).
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