TPTP Axioms File: NUM001-1.ax


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% File     : NUM001-1 : TPTP v7.5.0. 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 non-Horn;   0 unit;   3 RR)
%            Number of atoms      :    7 (   0 equality)
%            Maximal clause size  :    3 (   2 average)
%            Number of predicates :    2 (   0 propositional; 2-2 arity)
%            Number of functors   :    3 (   0 constant; 1-2 arity)
%            Number of variables  :    8 (   1 singleton)
%            Maximal term depth   :    4 (   1 average)
% SPC      : 

% Comments : Requires NUM001-0.ax
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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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