TPTP Axioms File: SWV007+0.ax
%------------------------------------------------------------------------------
% File : SWV007+0 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 6 ( 1 ~; 1 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% SPC :
% Comments :
%------------------------------------------------------------------------------
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) ).
%------------------------------------------------------------------------------