TPTP Problem File: NUM690^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : NUM690^1 : TPTP v9.0.0. Released v3.7.0.
% Domain : Number Theory
% Problem : Landau theorem 22d
% Version : Especial.
% English : some (lambda v.diffprop (pl y u) (pl x z) v)
% 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 : satz22d [Lan30]
% : satz35d [Lan30]
% Status : Theorem
% : Without extensionality : Theorem
% Rating : 0.00 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.00 v4.0.0, 0.33 v3.7.0
% Syntax : Number of formulae : 15 ( 1 unt; 10 typ; 0 def)
% Number of atoms : 12 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 35 ( 0 ~; 0 |; 0 &; 32 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% SPC : TH0_THM_NEQ_NAR
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x,type,
x: nat ).
thf(y,type,
y: nat ).
thf(z,type,
z: nat ).
thf(u,type,
u: nat ).
thf(some,type,
some: ( nat > $o ) > $o ).
thf(diffprop,type,
diffprop: nat > nat > nat > $o ).
thf(l,axiom,
( some
@ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) ) ).
thf(lessis,type,
lessis: nat > nat > $o ).
thf(k,axiom,
lessis @ z @ u ).
thf(pl,type,
pl: nat > nat > nat ).
thf(moreis,type,
moreis: nat > nat > $o ).
thf(satz22b,axiom,
! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( some
@ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
=> ( ( moreis @ Xz @ Xu )
=> ( some
@ ^ [Xu_0: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) @ Xu_0 ) ) ) ) ).
thf(satz14,axiom,
! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ( moreis @ Xy @ Xx ) ) ).
thf(satz22d,conjecture,
( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) ) ).
%------------------------------------------------------------------------------