%--------------------------------------------------------------------------
% File     : SWV001-0 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Software Verification
% Axioms   : Program verification axioms
% Version  : [MOW76] axioms.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of clauses     :   12 (   5 unt;   1 nHn;   7 RR)
%            Number of literals    :   23 (   9 equ;  11 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    :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :   22 (   0 sgn)
% SPC      : 

% Comments : Only reflexivity is specified from equality, i.e. no symmetry
%            or transitivity.
%          : These axioms were contributed to [MOW76] in private
%            correspondance from G. Ernst.
%--------------------------------------------------------------------------
cnf(predecessor_successor,axiom,
    predecessor(successor(X)) = X ).

cnf(successor_predecessor,axiom,
    successor(predecessor(X)) = X ).

cnf(well_defined_predecessor,axiom,
    ( X = Y
    | predecessor(X) != predecessor(Y) ) ).

cnf(well_defined_successor,axiom,
    ( X = Y
    | successor(X) != successor(Y) ) ).

cnf(predecessor_less_than,axiom,
    less_than(predecessor(X),X) ).

cnf(less_than_successor,axiom,
    less_than(X,successor(X)) ).

cnf(transitivity_of_less_than,axiom,
    ( less_than(X,Z)
    | ~ less_than(X,Y)
    | ~ less_than(Y,Z) ) ).

cnf(all_related,axiom,
    ( less_than(X,Y)
    | less_than(Y,X)
    | X = Y ) ).

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

cnf(anti_symmetry_of_less_than,axiom,
    ( ~ less_than(X,Y)
    | ~ less_than(Y,X) ) ).

cnf(equal_and_less_than_transitivity1,axiom,
    ( less_than(Y,Z)
    | X != Y
    | ~ less_than(X,Z) ) ).

cnf(equal_and_less_than_transitivity2,axiom,
    ( less_than(Z,Y)
    | X != Y
    | ~ less_than(Z,X) ) ).

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