TPTP Problem File: NUM680_8.p
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% File : NUM680_8 : TPTP v9.0.0. Released v8.0.0.
% Domain : Number Theory
% Problem : Landau theorem 20a
% Version : Especial.
% English : more x y
% Refs :
% Source : [TPTP]
% Names :
% Status : Theorem
% Rating : 0.00 v8.1.0
% Syntax : Number of formulae : 14 ( 2 unt; 7 typ; 0 def)
% Number of atoms : 15 ( 5 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 0 fml; 2 var)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?; 11 :)
% SPC : TX0_THM_EQU_NAR
% Comments : Translated to TXF from the THF version.
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tff(nat_type,type,
nat: $tType ).
tff(x,type,
x: nat ).
tff(y,type,
y: nat ).
tff(z,type,
z: nat ).
tff(more,type,
more: ( nat * nat ) > $o ).
tff(pl,type,
pl: ( nat * nat ) > nat ).
tff(m,axiom,
more(pl(x,z),pl(y,z)) ).
tff(et,axiom,
! [Xa: $o] :
( ~ ~ (Xa)
=> (Xa) ) ).
tff(less,type,
less: ( nat * nat ) > $o ).
tff(satz10b,axiom,
! [Xx: nat,Xy: nat] :
~ ( ( ( Xx = Xy )
=> ~ more(Xx,Xy) )
=> ~ ~ ( ( more(Xx,Xy)
=> ~ less(Xx,Xy) )
=> ~ ( less(Xx,Xy)
=> ( Xx != Xy ) ) ) ) ).
tff(satz19b,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( Xx = Xy )
=> ( pl(Xx,Xz) = pl(Xy,Xz) ) ) ).
tff(satz19c,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( less(Xx,Xy)
=> less(pl(Xx,Xz),pl(Xy,Xz)) ) ).
tff(satz10a,axiom,
! [Xx: nat,Xy: nat] :
( ( Xx != Xy )
=> ( ~ more(Xx,Xy)
=> less(Xx,Xy) ) ) ).
tff(satz20a,conjecture,
more(x,y) ).
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