TPTP Problem File: NUM713^1.p
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% File : NUM713^1 : TPTP v8.2.0. Released v3.7.0.
% Domain : Number Theory
% Problem : Landau theorem 32a
% Version : Especial.
% English : ~(forall x_0:nat.~(ts x z = pl (ts y z) x_0))
% 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 : satz32a [Lan30]
% Status : Theorem
% : Without extensionality : Theorem
% Rating : 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% Syntax : Number of formulae : 11 ( 4 unt; 6 typ; 0 def)
% Number of atoms : 4 ( 4 equ; 0 cnn)
% Maximal formula atoms : 1 ( 0 avg)
% Number of connectives : 29 ( 6 ~; 0 |; 0 &; 22 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 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(z,type,
z: nat ).
thf(pl,type,
pl: nat > nat > nat ).
thf(m,axiom,
~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) ) ).
thf(ts,type,
ts: nat > nat > nat ).
thf(et,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ) ).
thf(satz29,axiom,
! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) ).
thf(satz30,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( ts @ Xx @ ( pl @ Xy @ Xz ) )
= ( pl @ ( ts @ Xx @ Xy ) @ ( ts @ Xx @ Xz ) ) ) ).
thf(satz32a,conjecture,
~ ! [Xx_0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ Xx_0 ) ) ).
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