TPTP Problem File: SWV167+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV167+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Domain : Software Verification
% Problem : Simplified proof obligation cl5_nebula_init_0011
% Version : [DFS04] axioms : Especial.
% English : Proof obligation emerging from the init-safety verification for
% the cl5_nebula program. init-safety ensures that each variable or
% individual array element has been assigned a defined value before
% it is used.
% Refs : [Fis04] Fischer (2004), Email to G. Sutcliffe
% : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% Source : [Fis04]
% Names : cl5_nebula_init_0011 [Fis04]
% Status : Theorem
% Rating : 0.27 v9.0.0, 0.31 v8.2.0, 0.25 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.20 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.32 v6.1.0, 0.40 v6.0.0, 0.26 v5.5.0, 0.44 v5.4.0, 0.46 v5.3.0, 0.48 v5.2.0, 0.35 v5.1.0, 0.43 v5.0.0, 0.46 v4.1.0, 0.43 v4.0.0, 0.50 v3.5.0, 0.53 v3.4.0, 0.63 v3.3.0
% Syntax : Number of formulae : 92 ( 56 unt; 0 def)
% Number of atoms : 292 ( 91 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 205 ( 5 ~; 17 |; 113 &)
% ( 5 <=>; 65 =>; 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 : 40 ( 40 usr; 22 con; 0-4 aty)
% Number of variables : 178 ( 178 !; 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(cl5_nebula_init_0011,conjecture,
( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n4) )
=> a_select3(q_init,A,B) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n4) )
=> a_select2(rho_init,C) = init )
& ! [D] :
( ( leq(n0,D)
& leq(D,pred(pv40)) )
=> a_select2(mu_init,D) = init )
& ! [E] :
( ( leq(n0,E)
& leq(E,pred(pv40)) )
=> a_select2(sigma_init,E) = init )
& ! [F] :
( ( leq(n0,F)
& leq(F,n4) )
=> a_select3(center_init,F,n0) = init )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(n0,G)
& leq(G,n4) )
=> a_select2(muold_init,G) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(n0,H)
& leq(H,n4) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(n0,I)
& leq(I,n4) )
=> a_select2(sigmaold_init,I) = init ) ) )
=> ! [J] :
( ( leq(n0,J)
& leq(J,pv40) )
=> a_select2(mu_init,J) = init ) ) ).
%----Automatically generated axioms
fof(gt_5_4,axiom,
gt(n5,n4) ).
fof(gt_135299_4,axiom,
gt(n135299,n4) ).
fof(gt_135299_5,axiom,
gt(n135299,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_135299_tptp_minus_1,axiom,
gt(n135299,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_135299_0,axiom,
gt(n135299,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_135299_1,axiom,
gt(n135299,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_135299_2,axiom,
gt(n135299,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_135299_3,axiom,
gt(n135299,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 ).
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