%--------------------------------------------------------------------------
% File     : ROB001-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Robbins Algebra
% Axioms   : Robbins algebra numbers axioms
% Version  : [Win90] (equality) axioms.
% English  :

% Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras
%          : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% Source   : [Win90]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    4 (   2 unt;   0 nHn;   2 RR)
%            Number of literals    :    6 (   2 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn)
% SPC      : 

% Comments : Requires ROB001-0.ax
%--------------------------------------------------------------------------
cnf(one_times_x,axiom,
    multiply(one,X) = X ).

cnf(times_by_adding,axiom,
    ( ~ positive_integer(X)
    | multiply(successor(V),X) = add(X,multiply(V,X)) ) ).

cnf(one,axiom,
    positive_integer(one) ).

cnf(next_integer,axiom,
    ( ~ positive_integer(X)
    | positive_integer(successor(X)) ) ).

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