TPTP Axioms File: NUM001-0.ax


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% File     : NUM001-0 : TPTP v7.5.0. Bugfixed v4.0.0.
% Domain   : Number Theory
% Axioms   : Number theory axioms
% Version  : [LS74] axioms : Incomplete.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of clauses     :    6 (   0 non-Horn;   4 unit;   2 RR)
%            Number of atoms       :    8 (   0 equality)
%            Maximal clause size   :    2 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    4 (   1 constant; 0-2 arity)
%            Number of variables   :   10 (   1 singleton)
%            Maximal term depth    :    3 (   2 average)
% SPC      : 

% Comments :
% Bugfixes : v4.0.0 - Duplicate successor_equality1 removed.
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cnf(adding_zero,axiom,
    ( equalish(add(A,n0),A) )).

cnf(addition,axiom,
    ( equalish(add(A,successor(B)),successor(add(A,B))) )).

cnf(times_zero,axiom,
    ( equalish(multiply(A,n0),n0) )).

cnf(times,axiom,
    ( equalish(multiply(A,successor(B)),add(multiply(A,B),A)) )).

cnf(successor_equality1,axiom,
    ( ~ equalish(successor(A),successor(B))
    | equalish(A,B) )).

cnf(successor_substitution,axiom,
    ( ~ equalish(A,B)
    | equalish(successor(A),successor(B)) )).

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