## TPTP Problem File: SWV203+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWV203+1 : TPTP v8.0.0. Bugfixed v3.3.0.
% Domain   : Software Verification
% Problem  : Simplified proof obligation quaternion_ds1_inuse_0014
% Version  : [DFS04] axioms : Especial.
% English  : Proof obligation emerging from the inuse-safety verification for
%            the quaternion_ds1 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    : quaternion_ds1_inuse_0014 [Fis04]

% Status   : Theorem
% Rating   : 0.39 v7.5.0, 0.44 v7.4.0, 0.30 v7.3.0, 0.34 v7.2.0, 0.31 v7.1.0, 0.30 v6.4.0, 0.31 v6.3.0, 0.33 v6.2.0, 0.40 v6.0.0, 0.39 v5.5.0, 0.48 v5.4.0, 0.54 v5.3.0, 0.56 v5.2.0, 0.45 v5.1.0, 0.52 v5.0.0, 0.54 v4.1.0, 0.57 v4.0.1, 0.61 v4.0.0, 0.67 v3.7.0, 0.70 v3.5.0, 0.74 v3.4.0, 0.79 v3.3.0
% Syntax   : Number of formulae    :   92 (  56 unt;   0 def)
%            Number of atoms       :  307 ( 116 equ)
%            Maximal formula atoms :   51 (   3 avg)
%            Number of connectives :  223 (   8   ~;  17   |; 137   &)
%                                         (   5 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   4 avg)
%            Maximal term depth    :    9 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   37 (  37 usr;  19 con; 0-4 aty)
%            Number of variables   :  174 ( 174   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% 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(quaternion_ds1_inuse_0014,conjecture,
( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n998)
& gt(pv5,n0)
& ! [A,B] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n2)
& leq(B,pred(pv5)) )
=> a_select3(u_defuse,A,B) = use )
& ! [C,D] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,pred(pv5)) )
=> a_select3(z_defuse,C,D) = use ) )
=> ! [E,F] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n2)
& leq(F,pv5) )
=> ( ( ~ ( n0 = E
& pv5 = F )
& ~ ( n1 = E
& pv5 = F )
& ~ ( n2 = E
& pv5 = F ) )
=> a_select3(z_defuse,E,F) = use ) ) ) ).

%----Automatically generated axioms

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

fof(gt_998_4,axiom,
gt(n998,n4) ).

fof(gt_998_5,axiom,
gt(n998,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_998_tptp_minus_1,axiom,
gt(n998,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_998_0,axiom,
gt(n998,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_998_1,axiom,
gt(n998,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_998_2,axiom,
gt(n998,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_998_3,axiom,
gt(n998,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 ).

%------------------------------------------------------------------------------
```