%--------------------------------------------------------------------------
% File     : NUM001-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Number Theory
% Axioms   : Number theory less axioms
% Version  : [LS74] axioms.
% English  :

% Refs     : [LS74]  Lawrence & Starkey (1974), Experimental Tests of Resol
% Source   : [SPRFN]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    3 (   0 unt;   0 nHn;   3 RR)
%            Number of literals    :    7 (   0 equ;   4 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    3 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :    8 (   1 sgn)
% SPC      : 

% Comments : Requires NUM001-0.ax
%--------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
    ( ~ less(A,B)
    | ~ less(C,A)
    | less(C,B) ) ).

cnf(smaller_number,axiom,
    ( ~ equalish(add(successor(A),B),C)
    | less(B,C) ) ).

cnf(less_lemma,axiom,
    ( ~ less(A,B)
    | equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ) ).

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