TPTP Axioms File: ROB001-1.ax


%--------------------------------------------------------------------------
% File     : ROB001-1 : TPTP v7.5.0. 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 (   0 non-Horn;   2 unit;   2 RR)
%            Number of atoms      :    6 (   2 equality)
%            Maximal clause size  :    2 (   2 average)
%            Number of predicates :    2 (   0 propositional; 1-2 arity)
%            Number of functors   :    4 (   1 constant; 0-2 arity)
%            Number of variables  :    4 (   0 singleton)
%            Maximal term depth   :    3 (   2 average)
% 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)) )).

%--------------------------------------------------------------------------