%------------------------------------------------------------------------------
% File     : SWV128+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Domain   : Software Verification
% Problem  : Unsimplified proof obligation thruster_inuse_0001
% Version  : [DFS04] axioms : Especial.
% English  : Proof obligation emerging from the inuse-safety verification for
%            the thruster program. inuse-safety ensures that each sensor
%            reading passed as an input to the Kalman filter algorithm is
%            actually used during the computation of the output estimate.

% Refs     : [Fis04] Fischer (2004), Email to G. Sutcliffe
%          : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% Source   : [Fis04]
% Names    : thruster_inuse_0001 [Fis04]

% Status   : Theorem
% Rating   : 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.10 v5.0.0, 0.04 v4.0.0, 0.08 v3.7.0, 0.10 v3.5.0, 0.16 v3.4.0, 0.26 v3.3.0
% Syntax   : Number of formulae    :   92 (  56 unt;   0 def)
%            Number of atoms       :  280 (  87 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  193 (   5   ~;  17   |; 109   &)
%                                         (   5 <=>;  57  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    9 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   39 (  39 usr;  21 con; 0-4 aty)
%            Number of variables   :  176 ( 176   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
% Bugfixes : v3.3.0 - Bugfix in SWV003+0
%------------------------------------------------------------------------------
%----Include NASA software certification axioms
include('Axioms/SWV003+0.ax').
%------------------------------------------------------------------------------
%----Proof obligation generated by the AutoBayes/AutoFilter system
fof(thruster_inuse_0001,conjecture,
    ( ( t_defuse = use
      & tvar_defuse = use
      & ! [A,B] :
          ( ( leq(n0,A)
            & leq(n0,B)
            & leq(A,minus(m_measvars,n1))
            & leq(B,minus(n_steps,n1)) )
         => a_select3(rho_defuse,A,B) = use )
      & ! [C,D] :
          ( ( leq(n0,C)
            & leq(n0,D)
            & leq(C,n7)
            & leq(D,minus(n_steps,n1)) )
         => a_select3(tr_defuse,C,D) = use )
      & ! [E] :
          ( ( leq(n0,E)
            & leq(E,minus(n_statevars,n1)) )
         => a_select2(xinit_defuse,E) = use )
      & ! [F] :
          ( ( leq(n0,F)
            & leq(F,minus(n_statevars,n1)) )
         => a_select2(xinit_mean_defuse,F) = use )
      & ! [G,H] :
          ( ( leq(n0,G)
            & leq(n0,H)
            & leq(G,minus(m_measvars,n1))
            & leq(H,minus(n_steps,n1)) )
         => a_select3(z_defuse,G,H) = use ) )
   => true ) ).

%----Automatically generated axioms

fof(gt_5_4,axiom,
    gt(n5,n4) ).

fof(gt_7_4,axiom,
    gt(n7,n4) ).

fof(gt_7_5,axiom,
    gt(n7,n5) ).

fof(gt_4_tptp_minus_1,axiom,
    gt(n4,tptp_minus_1) ).

fof(gt_5_tptp_minus_1,axiom,
    gt(n5,tptp_minus_1) ).

fof(gt_7_tptp_minus_1,axiom,
    gt(n7,tptp_minus_1) ).

fof(gt_0_tptp_minus_1,axiom,
    gt(n0,tptp_minus_1) ).

fof(gt_1_tptp_minus_1,axiom,
    gt(n1,tptp_minus_1) ).

fof(gt_2_tptp_minus_1,axiom,
    gt(n2,tptp_minus_1) ).

fof(gt_3_tptp_minus_1,axiom,
    gt(n3,tptp_minus_1) ).

fof(gt_4_0,axiom,
    gt(n4,n0) ).

fof(gt_5_0,axiom,
    gt(n5,n0) ).

fof(gt_7_0,axiom,
    gt(n7,n0) ).

fof(gt_1_0,axiom,
    gt(n1,n0) ).

fof(gt_2_0,axiom,
    gt(n2,n0) ).

fof(gt_3_0,axiom,
    gt(n3,n0) ).

fof(gt_4_1,axiom,
    gt(n4,n1) ).

fof(gt_5_1,axiom,
    gt(n5,n1) ).

fof(gt_7_1,axiom,
    gt(n7,n1) ).

fof(gt_2_1,axiom,
    gt(n2,n1) ).

fof(gt_3_1,axiom,
    gt(n3,n1) ).

fof(gt_4_2,axiom,
    gt(n4,n2) ).

fof(gt_5_2,axiom,
    gt(n5,n2) ).

fof(gt_7_2,axiom,
    gt(n7,n2) ).

fof(gt_3_2,axiom,
    gt(n3,n2) ).

fof(gt_4_3,axiom,
    gt(n4,n3) ).

fof(gt_5_3,axiom,
    gt(n5,n3) ).

fof(gt_7_3,axiom,
    gt(n7,n3) ).

fof(finite_domain_4,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n4) )
     => ( X = n0
        | X = n1
        | X = n2
        | X = n3
        | X = n4 ) ) ).

fof(finite_domain_5,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n5) )
     => ( X = n0
        | X = n1
        | X = n2
        | X = n3
        | X = n4
        | X = n5 ) ) ).

fof(finite_domain_0,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n0) )
     => X = n0 ) ).

fof(finite_domain_1,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n1) )
     => ( X = n0
        | X = n1 ) ) ).

fof(finite_domain_2,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n2) )
     => ( X = n0
        | X = n1
        | X = n2 ) ) ).

fof(finite_domain_3,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n3) )
     => ( X = n0
        | X = n1
        | X = n2
        | X = n3 ) ) ).

fof(successor_4,axiom,
    succ(succ(succ(succ(n0)))) = n4 ).

fof(successor_5,axiom,
    succ(succ(succ(succ(succ(n0))))) = n5 ).

fof(successor_1,axiom,
    succ(n0) = n1 ).

fof(successor_2,axiom,
    succ(succ(n0)) = n2 ).

fof(successor_3,axiom,
    succ(succ(succ(n0))) = n3 ).

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