TPTP Problem File: NUM663_8.p
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% File : NUM663_8 : TPTP v9.0.0. Released v8.0.0.
% Domain : Number Theory
% Problem : Landau theorem 16a
% Version : Especial.
% English : less x z
% Refs :
% Source : [TPTP]
% Names :
% Status : Theorem
% Rating : 0.00 v8.1.0
% Syntax : Number of formulae : 10 ( 2 unt; 5 typ; 0 def)
% Number of atoms : 7 ( 1 equ)
% Maximal formula atoms : 3 ( 0 avg)
% Number of connectives : 7 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 0 fml; 2 var)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 4 ( 4 !; 0 ?; 4 :)
% 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(less,type,
less: ( nat * nat ) > $o ).
tff(l,axiom,
( ~ less(x,y)
=> ( x = y ) ) ).
tff(k,axiom,
less(y,z) ).
tff(et,axiom,
! [Xa: $o] :
( ~ ~ (Xa)
=> (Xa) ) ).
tff(satz15,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( less(Xx,Xy)
=> ( less(Xy,Xz)
=> less(Xx,Xz) ) ) ).
tff(satz16a,conjecture,
less(x,z) ).
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