TPTP Problem File: SWV100+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWV100+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Domain : Software Verification
% Problem : Unsimplified proof obligation quaternion_ds1_inuse_0012
% 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_0012 [Fis04]
% Status : Theorem
% Rating : 1.00 v3.3.0
% Syntax : Number of formulae : 92 ( 56 unt; 0 def)
% Number of atoms : 461 ( 233 equ)
% Maximal formula atoms : 205 ( 5 avg)
% Number of connectives : 377 ( 8 ~; 17 |; 280 &)
% ( 5 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 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 : 186 ( 186 !; 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(quaternion_ds1_inuse_0012,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,minus(n999,n1))
& ! [A,B] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n2)
& leq(B,minus(pv5,n1)) )
=> ( a_select3(u_defuse,A,B) = use
& a_select3(z_defuse,A,B) = use ) ) )
=> ( ( ~ gt(pv5,n0)
=> ( ( ~ gt(pv5,n0)
=> ( 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,minus(n999,n1))
& ! [C,D] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,pv5) )
=> ( a_select3(u_defuse,C,D) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),C,D) = use ) )
& ! [E,F] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n2)
& leq(F,minus(pv5,n1)) )
=> ( a_select3(u_defuse,E,F) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),E,F) = use ) ) ) )
& ( gt(pv5,n0)
=> ( 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,minus(n999,n1))
& ! [G,H] :
( ( leq(n0,G)
& leq(n0,H)
& leq(G,n2)
& leq(H,pv5) )
=> ( a_select3(u_defuse,G,H) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),G,H) = use ) )
& ! [I,J] :
( ( leq(n0,I)
& leq(n0,J)
& leq(I,n2)
& leq(J,minus(pv5,n1)) )
=> ( a_select3(u_defuse,I,J) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),I,J) = use ) ) ) ) ) )
& ( gt(pv5,n0)
=> ( ( ~ gt(pv5,n0)
=> ( 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_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
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),n0,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),n1,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),n2,n0) = use
& leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [K,L] :
( ( leq(n0,K)
& leq(n0,L)
& leq(K,n2)
& leq(L,pv5) )
=> ( a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),K,L) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),K,L) = use ) )
& ! [M,N] :
( ( leq(n0,M)
& leq(n0,N)
& leq(M,n2)
& leq(N,minus(pv5,n1)) )
=> ( a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),M,N) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),M,N) = use ) ) ) )
& ( gt(pv5,n0)
=> ( 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_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
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),n0,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),n1,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),n2,n0) = use
& leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [O,P] :
( ( leq(n0,O)
& leq(n0,P)
& leq(O,n2)
& leq(P,pv5) )
=> ( a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),O,P) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),O,P) = use ) )
& ! [Q,R] :
( ( leq(n0,Q)
& leq(n0,R)
& leq(Q,n2)
& leq(R,minus(pv5,n1)) )
=> ( a_select3(tptp_update3(tptp_update3(tptp_update3(z_defuse,n0,pv5,use),n1,pv5,use),n2,pv5,use),Q,R) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n0,pv5,use),n1,pv5,use),n0,pv5,use),n2,pv5,use),n1,pv5,use),n2,pv5,use),Q,R) = use ) ) ) ) ) ) ) ) ).
%----Automatically generated axioms
fof(gt_5_4,axiom,
gt(n5,n4) ).
fof(gt_999_4,axiom,
gt(n999,n4) ).
fof(gt_999_5,axiom,
gt(n999,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_999_tptp_minus_1,axiom,
gt(n999,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_999_0,axiom,
gt(n999,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_999_1,axiom,
gt(n999,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_999_2,axiom,
gt(n999,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_999_3,axiom,
gt(n999,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 ).
%------------------------------------------------------------------------------