%------------------------------------------------------------------------------
% File     : SWX008_1 : TPTP v9.1.0. Released v9.1.0.
% Domain   : Software Verification
% Problem  : one-duplicate-2
% Version  : Especial.
% English  :

% Refs     : [Kot17] Kotelnikov (2017), Email to Geoff Sutcliffe
% Source   : [Kot17]
% Names    : one-duplicate-2 [Kot17]

% Status   : Theorem
% Rating   : ? v9.1.0
% Syntax   : Number of formulae    :   25 (   1 unt;  12 typ;   0 def)
%            Number of atoms       :   47 (  14 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :   33 (   4   ~;   4   |;  12   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    8 (   5 fml;   3 var)
%            Number of X terms     :    4 (   0  [];   0 ite;   4 let)
%            Number arithmetic     :   50 (  20 atm;   0 fun;  11 num;  19 var)
%            Number of types       :    4 (   2 usr;   1 ari)
%            Number of type conns  :   10 (   4   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :   11 (   8 usr;   7 con; 0-3 aty)
%            Number of variables   :   29 (  29   !;   0   ?;  29   :)
% SPC      : TX0_THM_EQU_ARI

% Comments : This file was generated by Voogie.
%------------------------------------------------------------------------------
tff(array_int_int,type,
    array_int_int: $tType ).

tff(array_int_bool,type,
    array_int_bool: $tType ).

tff(select_int_int,type,
    select_int_int: ( array_int_int * $int ) > $int ).

tff(store_int_int,type,
    store_int_int: ( array_int_int * $int * $int ) > array_int_int ).

tff(select_int_bool,type,
    select_int_bool: ( array_int_bool * $int ) > $o ).

tff(store_int_bool,type,
    store_int_bool: ( array_int_bool * $int * $o ) > array_int_bool ).

tff(a,type,
    a: array_int_int ).

tff(bad,type,
    bad: $o ).

tff(d,type,
    d: $int ).

tff(i,type,
    i: $int ).

tff(n,type,
    n: $int ).

tff(occs,type,
    occs: array_int_bool ).

tff(voogie_precondition_1,axiom,
    ! [A: array_int_int,V: $int,I: $int,J: $int] :
      ( ( I = J )
     => ( select_int_int(store_int_int(A,I,V),J) = V ) ) ).

tff(voogie_precondition_2,axiom,
    ! [A: array_int_int,V: $int,I: $int,J: $int] :
      ( ( I != J )
     => ( select_int_int(store_int_int(A,I,V),J) = select_int_int(A,J) ) ) ).

tff(voogie_precondition_3,axiom,
    ! [A: array_int_int,B: array_int_int] :
      ( ! [I: $int] : ( select_int_int(A,I) = select_int_int(B,I) )
     => ( A = B ) ) ).

tff(voogie_precondition_4,axiom,
    ! [A: array_int_bool,V: $o,I: $int,J: $int] :
      ( ( I = J )
     => ( select_int_bool(store_int_bool(A,I,(V)),J) = (V) ) ) ).

tff(voogie_precondition_5,axiom,
    ! [A: array_int_bool,V: $o,I: $int,J: $int] :
      ( ( I != J )
     => ( select_int_bool(store_int_bool(A,I,(V)),J) = select_int_bool(A,J) ) ) ).

tff(voogie_precondition_6,axiom,
    ! [A: array_int_bool,B: array_int_bool] :
      ( ! [I: $int] : ( select_int_bool(A,I) = select_int_bool(A,I) )
     => ( A = B ) ) ).

tff(voogie_precondition_7,axiom,
    $greater(n,0) ).

tff(voogie_precondition_8,axiom,
    ! [I: $int] :
      ( ( $lesseq(0,I)
        & $less(I,n) )
     => $greatereq(select_int_int(a,I),0) ) ).

tff(voogie_precondition_9,axiom,
    ( $lesseq(0,i)
    & $lesseq(i,n) ) ).

tff(voogie_precondition_10,axiom,
    ( $greatereq(d,0)
   => select_int_bool(occs,select_int_int(a,i)) ) ).

tff(voogie_precondition_11,axiom,
    ! [K: $int] :
      ( ( $lesseq(0,K)
        & $less(K,i) )
     => select_int_bool(occs,select_int_int(a,K)) ) ).

tff(voogie_precondition_12,axiom,
    ! [J: $int,K: $int] :
      ( ( $lesseq(0,J)
        & $less(J,K)
        & $less(K,i) )
     => ( select_int_int(a,J) != select_int_int(a,K) ) ) ).

tff(voogie_conjecture,conjecture,
    $let(
      bad: $o,
      bad:= 
        $ite(
          ~ ( $less(i,n)
            & $less(d,0) ),
          $true,
          bad ),
      $let(
        [ d: $int,
          occs: array_int_bool,
          i: $int ],
        [d,occs,i]:= 
          $ite(
            ~ select_int_bool(occs,select_int_int(a,i)),
            $let(
              occs: array_int_bool,
              occs:= store_int_bool(occs,select_int_int(a,i),$true),
              $let(
                i: $int,
                i:= $sum(i,1),
                [d,occs,i] ) ),
            $let(
              d: $int,
              d:= select_int_int(a,i),
              [d,occs,i] ) ),
        $let(
          bad: $o,
          bad:= 
            $ite(
              ~ ( $less(i,n)
                & $less(d,0) ),
              $true,
              bad ),
          $let(
            [ d: $int,
              occs: array_int_bool,
              i: $int ],
            [d,occs,i]:= 
              $ite(
                ~ select_int_bool(occs,select_int_int(a,i)),
                $let(
                  occs: array_int_bool,
                  occs:= store_int_bool(occs,select_int_int(a,i),$true),
                  $let(
                    i: $int,
                    i:= $sum(i,1),
                    [d,occs,i] ) ),
                $let(
                  d: $int,
                  d:= select_int_int(a,i),
                  [d,occs,i] ) ),
            ( ( bad
              | ( $lesseq(0,i)
                & $lesseq(i,n) ) )
            & ( bad
              | ( $greatereq(d,0)
               => select_int_bool(occs,select_int_int(a,i)) ) )
            & ( bad
              | ! [K: $int] :
                  ( ( $lesseq(0,K)
                    & $less(K,i) )
                 => select_int_bool(occs,select_int_int(a,K)) ) )
            & ( bad
              | ! [J: $int,K: $int] :
                  ( ( $lesseq(0,J)
                    & $less(J,K)
                    & $less(K,i) )
                 => ( select_int_int(a,J) != select_int_int(a,K) ) ) ) ) ) ) ) ) ).

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