TPTP Axioms File: SWV007+0.ax


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% File     : SWV007+0 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Software Verification
% Axioms   : Priority queue checker: quasi-order set with bottom element
% Version  : [dNP05] axioms.
% English  :

% Refs     : [Pis06] Piskac (2006), Email to Geoff Sutcliffe
%          : [dNP05] de Nivelle & Piskac (2005), Verification of an Off-Lin
% Source   : [Pis06]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    5 (   2 unit)
%            Number of atoms       :   10 (   0 equality)
%            Maximal formula depth :    6 (   4 average)
%            Number of connectives :    6 (   1 ~  ;   1  |;   2  &)
%                                         (   1 <=>;   1 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :    1 (   1 constant; 0-0 arity)
%            Number of variables   :    9 (   0 singleton;   9 !;   0 ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : 

% Comments :
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fof(transitivity,axiom,(
    ! [U,V,W] :
      ( ( less_than(U,V)
        & less_than(V,W) )
     => less_than(U,W) ) )).

fof(totality,axiom,(
    ! [U,V] :
      ( less_than(U,V)
      | less_than(V,U) ) )).

fof(reflexivity,axiom,(
    ! [U] : less_than(U,U) )).

fof(stricly_smaller_definition,axiom,(
    ! [U,V] :
      ( strictly_less_than(U,V)
    <=> ( less_than(U,V)
        & ~ less_than(V,U) ) ) )).

fof(bottom_smallest,axiom,(
    ! [U] : less_than(bottom,U) )).

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