TPTP Problem File: SWW990_1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW990_1 : TPTP v9.2.1. Released v9.1.0.
% Domain : Software Verification
% Problem : insertion-sort-4
% Version : Especial.
% English :
% Refs : [Kot17] Kotelnikov (2017), Email to Geoff Sutcliffe
% Source : [Kot17]
% Names : insertion-sort-4 [Kot17]
% Status : Theorem
% Rating : ? v9.1.0
% Syntax : Number of formulae : 22 ( 1 unt; 9 typ; 0 def)
% Number of atoms : 55 ( 6 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 43 ( 1 ~; 5 |; 26 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of X terms : 12 ( 0 []; 0 ite; 12 let)
% Number arithmetic : 104 ( 44 atm; 14 fun; 24 num; 22 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 5 ( 2 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 7 usr; 7 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?; 26 :)
% SPC : TX0_THM_EQU_ARI
% Comments : This file was generated by Voogie.
%------------------------------------------------------------------------------
tff(array_int_int,type,
array_int_int: $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(a,type,
a: array_int_int ).
tff(bad,type,
bad: $o ).
tff(n,type,
n: $int ).
tff(sortedFrom,type,
sortedFrom: $int ).
tff(sortedUntil,type,
sortedUntil: $int ).
tff(t,type,
t: $int ).
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,
$greater(n,0) ).
tff(voogie_precondition_5,axiom,
( $less(0,sortedUntil)
& $lesseq(sortedUntil,n) ) ).
tff(voogie_precondition_6,axiom,
! [K: $int,M: $int] :
( ( $lesseq(0,K)
& $less(K,M)
& $less(M,sortedUntil) )
=> $lesseq(select_int_int(a,K),select_int_int(a,M)) ) ).
tff(voogie_precondition_7,axiom,
! [K: $int] :
( ( $lesseq(0,K)
& $less(K,$difference(sortedUntil,1)) )
=> $lesseq(select_int_int(a,K),select_int_int(a,$difference(sortedUntil,1))) ) ).
tff(voogie_precondition_8,axiom,
( $less(0,sortedUntil)
& $lesseq(sortedUntil,n) ) ).
tff(voogie_precondition_9,axiom,
( $lesseq($uminus(1),sortedFrom)
& $lesseq(sortedFrom,$difference(sortedUntil,1)) ) ).
tff(voogie_precondition_10,axiom,
! [K: $int,M: $int] :
( ( $lesseq(0,K)
& $less(K,$sum(sortedFrom,1))
& $less($sum(sortedFrom,1),M)
& $lesseq(M,sortedUntil) )
=> $lesseq(select_int_int(a,K),select_int_int(a,M)) ) ).
tff(voogie_precondition_11,axiom,
! [K: $int,M: $int] :
( ( $lesseq(0,K)
& $less(K,M)
& $less(M,$sum(sortedFrom,1)) )
=> $lesseq(select_int_int(a,K),select_int_int(a,M)) ) ).
tff(voogie_precondition_12,axiom,
! [K: $int,M: $int] :
( ( $lesseq($sum(sortedFrom,1),K)
& $less(K,M)
& $lesseq(M,sortedUntil) )
=> $lesseq(select_int_int(a,K),select_int_int(a,M)) ) ).
tff(voogie_conjecture,conjecture,
$let(
bad: $o,
bad:=
$ite(~ $greatereq(sortedFrom,0),$true,bad),
$let(
[ t: $int,
a: array_int_int ],
[t,a]:=
$ite(
$greater(select_int_int(a,sortedFrom),select_int_int(a,$sum(sortedFrom,1))),
$let(
t: $int,
t:= select_int_int(a,sortedFrom),
$let(
a: array_int_int,
a:= store_int_int(a,sortedFrom,select_int_int(a,$sum(sortedFrom,1))),
$let(
a: array_int_int,
a:= store_int_int(a,$sum(sortedFrom,1),t),
[t,a] ) ) ),
[t,a] ),
$let(
sortedFrom: $int,
sortedFrom:= $difference(sortedFrom,1),
$let(
bad: $o,
bad:=
$ite(~ $greatereq(sortedFrom,0),$true,bad),
$let(
[ t: $int,
a: array_int_int ],
[t,a]:=
$ite(
$greater(select_int_int(a,sortedFrom),select_int_int(a,$sum(sortedFrom,1))),
$let(
t: $int,
t:= select_int_int(a,sortedFrom),
$let(
a: array_int_int,
a:= store_int_int(a,sortedFrom,select_int_int(a,$sum(sortedFrom,1))),
$let(
a: array_int_int,
a:= store_int_int(a,$sum(sortedFrom,1),t),
[t,a] ) ) ),
[t,a] ),
$let(
sortedFrom: $int,
sortedFrom:= $difference(sortedFrom,1),
$let(
bad: $o,
bad:=
$ite(~ $greatereq(sortedFrom,0),$true,bad),
$let(
[ t: $int,
a: array_int_int ],
[t,a]:=
$ite(
$greater(select_int_int(a,sortedFrom),select_int_int(a,$sum(sortedFrom,1))),
$let(
t: $int,
t:= select_int_int(a,sortedFrom),
$let(
a: array_int_int,
a:= store_int_int(a,sortedFrom,select_int_int(a,$sum(sortedFrom,1))),
$let(
a: array_int_int,
a:= store_int_int(a,$sum(sortedFrom,1),t),
[t,a] ) ) ),
[t,a] ),
$let(
sortedFrom: $int,
sortedFrom:= $difference(sortedFrom,1),
$let(
bad: $o,
bad:=
$ite(~ $greatereq(sortedFrom,0),$true,bad),
$let(
[ t: $int,
a: array_int_int ],
[t,a]:=
$ite(
$greater(select_int_int(a,sortedFrom),select_int_int(a,$sum(sortedFrom,1))),
$let(
t: $int,
t:= select_int_int(a,sortedFrom),
$let(
a: array_int_int,
a:= store_int_int(a,sortedFrom,select_int_int(a,$sum(sortedFrom,1))),
$let(
a: array_int_int,
a:= store_int_int(a,$sum(sortedFrom,1),t),
[t,a] ) ) ),
[t,a] ),
$let(
sortedFrom: $int,
sortedFrom:= $difference(sortedFrom,1),
( ( bad
| ( $less(0,sortedUntil)
& $lesseq(sortedUntil,n) ) )
& ( bad
| ( $lesseq($uminus(1),sortedFrom)
& $lesseq(sortedFrom,$difference(sortedUntil,1)) ) )
& ( bad
| ! [K: $int,M: $int] :
( ( $lesseq(0,K)
& $less(K,$sum(sortedFrom,1))
& $less($sum(sortedFrom,1),M)
& $lesseq(M,sortedUntil) )
=> $lesseq(select_int_int(a,K),select_int_int(a,M)) ) )
& ( bad
| ! [K: $int,M: $int] :
( ( $lesseq(0,K)
& $less(K,M)
& $less(M,$sum(sortedFrom,1)) )
=> $lesseq(select_int_int(a,K),select_int_int(a,M)) ) )
& ( bad
| ! [K: $int,M: $int] :
( ( $lesseq($sum(sortedFrom,1),K)
& $less(K,M)
& $lesseq(M,sortedUntil) )
=> $lesseq(select_int_int(a,K),select_int_int(a,M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------