TPTP Problem File: NUM711^1.p
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% File : NUM711^1 : TPTP v8.2.0. Released v3.7.0.
% Domain : Number Theory
% Problem : Landau theorem 30
% Version : Especial.
% English : ts x (pl y z) = pl (ts x y) (ts x z)
% 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 : satz30 [Lan30]
% Status : Theorem
% : Without extensionality : Theorem
% Rating : 1.00 v3.7.0
% Syntax : Number of formulae : 21 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 13 ( 7 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 0 ~; 0 |; 0 &; 60 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 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(ts,type,
ts: nat > nat > nat ).
thf(pl,type,
pl: nat > nat > nat ).
thf(set_type,type,
set: $tType ).
thf(esti,type,
esti: nat > set > $o ).
thf(setof,type,
setof: ( nat > $o ) > set ).
thf(estie,axiom,
! [Xp: nat > $o,Xs: nat] :
( ( esti @ Xs @ ( setof @ Xp ) )
=> ( Xp @ Xs ) ) ).
thf(n_1,type,
n_1: nat ).
thf(suc,type,
suc: nat > nat ).
thf(ax5,axiom,
! [Xs: set] :
( ( esti @ n_1 @ Xs )
=> ( ! [Xx: nat] :
( ( esti @ Xx @ Xs )
=> ( esti @ ( suc @ Xx ) @ Xs ) )
=> ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
thf(estii,axiom,
! [Xp: nat > $o,Xs: nat] :
( ( Xp @ Xs )
=> ( esti @ Xs @ ( setof @ Xp ) ) ) ).
thf(satz28e,axiom,
! [Xx: nat] :
( Xx
= ( ts @ Xx @ n_1 ) ) ).
thf(satz28b,axiom,
! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ ( suc @ Xy ) )
= ( pl @ ( ts @ Xx @ Xy ) @ Xx ) ) ).
thf(satz4a,axiom,
! [Xx: nat] :
( ( pl @ Xx @ n_1 )
= ( suc @ Xx ) ) ).
thf(satz28f,axiom,
! [Xx: nat,Xy: nat] :
( ( pl @ ( ts @ Xx @ Xy ) @ Xx )
= ( ts @ Xx @ ( suc @ Xy ) ) ) ).
thf(satz5,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
= ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) ).
thf(satz4b,axiom,
! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ ( suc @ Xy ) )
= ( suc @ ( pl @ Xx @ Xy ) ) ) ).
thf(satz30,conjecture,
( ( ts @ x @ ( pl @ y @ z ) )
= ( pl @ ( ts @ x @ y ) @ ( ts @ x @ z ) ) ) ).
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