%--------------------------------------------------------------------------
% File     : ANA001-0 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Analysis (Limits)
% Axioms   : Analysis (limits) axioms for continuous functions
% Version  : [MOW76] axioms.
% English  :

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source   : [ANL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :   14 (   6 unt;   0 nHn;   9 RR)
%            Number of literals    :   27 (   5 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   27 (   0 sgn)
% SPC      : 

% Comments : No natural language descriptions are available.
%          : "Contributed by W.W. Bledsoe in a private correspondence",
%            [MOW76].
%--------------------------------------------------------------------------
%----Axiom 1
cnf(right_identity,axiom,
    add(X,n0) = X ).

cnf(left_identity,axiom,
    add(n0,X) = X ).

cnf(reflexivity_of_less_than,axiom,
    ~ less_than(X,X) ).

%----Less than transitivity
cnf(transitivity_of_less_than,axiom,
    ( ~ less_than(X,Y)
    | ~ less_than(Y,Z)
    | less_than(X,Z) ) ).

%----Axiom 2
cnf(axiom_2_1,axiom,
    ( ~ less_than(n0,X)
    | ~ less_than(n0,Y)
    | less_than(n0,minimum(X,Y)) ) ).

cnf(axiom_2_2,axiom,
    ( ~ less_than(n0,X)
    | ~ less_than(n0,Y)
    | less_than(minimum(X,Y),X) ) ).

cnf(axiom_2_3,axiom,
    ( ~ less_than(n0,X)
    | ~ less_than(n0,Y)
    | less_than(minimum(X,Y),Y) ) ).

%----Axiom 3
cnf(axiom_3,axiom,
    ( ~ less_than(X,half(Xa))
    | ~ less_than(Y,half(Xa))
    | less_than(add(X,Y),Xa) ) ).

%----Axiom 4
cnf(c_17,axiom,
    ( ~ less_than(add(absolute(X),absolute(Y)),Xa)
    | less_than(absolute(add(X,Y)),Xa) ) ).

%----Axiom 5
cnf(axiom_5,axiom,
    add(add(X,Y),Z) = add(X,add(Y,Z)) ).

%----Axiom 6
cnf(axiom_6_1,axiom,
    add(X,Y) = add(Y,X) ).

cnf(axiom_6_2,axiom,
    ( ~ less_than(n0,Xa)
    | less_than(n0,half(Xa)) ) ).

%----Axiom 7
cnf(axiom_7,axiom,
    ( ~ less_than(n0,Xa)
    | less_than(n0,half(Xa)) ) ).

%----Axiom 8
cnf(axiom_8,axiom,
    minus(add(X,Y)) = add(minus(X),minus(Y)) ).

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