TPTP Problem File: SWV034+1.p

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%------------------------------------------------------------------------------
% File     : SWV034+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Domain   : Software Verification
% Problem  : Unsimplified proof obligation gauss_init_0049
% Version  : [DFS04] axioms : Especial.
% English  : Proof obligation emerging from the init-safety verification for
%            the gauss 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    : gauss_init_0049 [Fis04]

% Status   : Theorem
% Rating   : 0.33 v8.2.0, 0.31 v8.1.0, 0.28 v7.5.0, 0.31 v7.4.0, 0.27 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.30 v7.0.0, 0.33 v6.4.0, 0.35 v6.3.0, 0.38 v6.2.0, 0.40 v6.1.0, 0.47 v6.0.0, 0.43 v5.5.0, 0.56 v5.4.0, 0.57 v5.3.0, 0.59 v5.2.0, 0.45 v5.1.0, 0.48 v5.0.0, 0.58 v4.1.0, 0.57 v4.0.1, 0.65 v4.0.0, 0.62 v3.7.0, 0.55 v3.5.0, 0.58 v3.4.0, 0.68 v3.3.0
% Syntax   : Number of formulae    :   92 (  56 unt;   0 def)
%            Number of atoms       :  315 ( 101 equ)
%            Maximal formula atoms :   59 (   3 avg)
%            Number of connectives :  228 (   5   ~;  17   |; 137   &)
%                                         (   5 <=>;  64  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Maximal term depth    :    9 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   45 (  45 usr;  27 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(gauss_init_0049,conjecture,
    ( ( s_best7_init = init
      & s_sworst7_init = init
      & s_worst7_init = init
      & leq(n0,s_best7)
      & leq(n0,s_sworst7)
      & leq(n0,s_worst7)
      & leq(n0,pv19)
      & leq(s_best7,n3)
      & leq(s_sworst7,n3)
      & leq(s_worst7,n3)
      & leq(pv19,minus(n410,n1))
      & ! [A] :
          ( ( leq(n0,A)
            & leq(A,n2) )
         => ! [B] :
              ( ( leq(n0,B)
                & leq(B,n3) )
             => a_select3(simplex7_init,B,A) = init ) )
      & ! [C] :
          ( ( leq(n0,C)
            & leq(C,n3) )
         => a_select2(s_values7_init,C) = init )
      & ! [D] :
          ( ( leq(n0,D)
            & leq(D,n2) )
         => a_select2(s_center7_init,D) = init )
      & ! [E] :
          ( ( leq(n0,E)
            & leq(E,minus(n3,n1)) )
         => a_select2(s_try7_init,E) = init )
      & ( gt(loopcounter,n1)
       => ( pvar1400_init = init
          & pvar1401_init = init
          & pvar1402_init = init ) ) )
   => ( init = init
      & s_best7_init = init
      & s_sworst7_init = init
      & s_worst7_init = init
      & leq(n0,s_best7)
      & leq(n0,s_sworst7)
      & leq(n0,s_worst7)
      & leq(n0,pv19)
      & leq(s_best7,n3)
      & leq(s_sworst7,n3)
      & leq(s_worst7,n3)
      & leq(pv19,minus(n410,n1))
      & ! [F] :
          ( ( leq(n0,F)
            & leq(F,n2) )
         => ! [G] :
              ( ( leq(n0,G)
                & leq(G,n3) )
             => a_select3(simplex7_init,G,F) = init ) )
      & ! [H] :
          ( ( leq(n0,H)
            & leq(H,n3) )
         => a_select2(s_values7_init,H) = init )
      & ! [I] :
          ( ( leq(n0,I)
            & leq(I,n2) )
         => a_select2(s_center7_init,I) = init )
      & ! [J] :
          ( ( leq(n0,J)
            & leq(J,minus(n3,n1)) )
         => a_select2(s_try7_init,J) = init )
      & ( gt(loopcounter,n1)
       => ( pvar1400_init = init
          & pvar1401_init = init
          & pvar1402_init = init ) ) ) ) ).

%----Automatically generated axioms

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

fof(gt_410_4,axiom,
    gt(n410,n4) ).

fof(gt_410_5,axiom,
    gt(n410,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_410_tptp_minus_1,axiom,
    gt(n410,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_410_0,axiom,
    gt(n410,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_410_1,axiom,
    gt(n410,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_410_2,axiom,
    gt(n410,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_410_3,axiom,
    gt(n410,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 ).

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