TPTP Problem File: NUM696^1.p
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% File : NUM696^1 : TPTP v9.0.0. Released v3.7.0.
% Domain : Number Theory
% Problem : Landau theorem 25
% Version : Especial.
% English : ~(~(forall x_0:nat.~(y = pl (pl x n_1) x_0))) -> y = pl x n_1
% Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : satz25 [Lan30]
% Status : Theorem
% : Without extensionality : Theorem
% Rating : 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% Syntax : Number of formulae : 11 ( 2 unt; 5 typ; 0 def)
% Number of atoms : 8 ( 8 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 14 ~; 0 |; 0 &; 22 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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thf(nat_type,type,
nat: $tType ).
thf(x,type,
x: nat ).
thf(y,type,
y: nat ).
thf(pl,type,
pl: nat > nat > nat ).
thf(m,axiom,
~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) ).
thf(n_1,type,
n_1: nat ).
thf(et,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ) ).
thf(satz24,axiom,
! [Xx: nat] :
( ~ ~ ! [Xx_0: nat] :
( Xx
!= ( pl @ n_1 @ Xx_0 ) )
=> ( Xx = n_1 ) ) ).
thf(satz19a,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ~ ! [Xx_0: nat] :
( Xx
!= ( pl @ Xy @ Xx_0 ) )
=> ~ ! [Xx_0: nat] :
( ( pl @ Xx @ Xz )
!= ( pl @ ( pl @ Xy @ Xz ) @ Xx_0 ) ) ) ).
thf(satz6,axiom,
! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) ).
thf(satz25,conjecture,
( ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ) ).
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