TPTP Problem File: SWX018_1.p
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%------------------------------------------------------------------------------
% File : SWX018_1 : TPTP v9.1.0. Released v9.1.0.
% Domain : Software Verification
% Problem : two-way-sort-2
% Version : Especial.
% English :
% Refs : [Kot17] Kotelnikov (2017), Email to Geoff Sutcliffe
% Source : [Kot17]
% Names : two-way-sort-2 [Kot17]
% Status : Theorem
% Rating : ? v9.1.0
% Syntax : Number of formulae : 17 ( 1 unt; 9 typ; 0 def)
% Number of atoms : 33 ( 6 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 23 ( 3 ~; 3 |; 10 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 5 fml; 3 var)
% Number of X terms : 4 ( 0 []; 0 ite; 4 let)
% Number arithmetic : 37 ( 15 atm; 4 fun; 9 num; 9 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 5 ( 2 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 5 usr; 6 con; 0-3 aty)
% Number of variables : 15 ( 15 !; 0 ?; 15 :)
% SPC : TX0_THM_EQU_ARI
% Comments : This file was generated by Voogie.
%------------------------------------------------------------------------------
tff(array_int_bool,type,
array_int_bool: $tType ).
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_bool ).
tff(bad,type,
bad: $o ).
tff(i,type,
i: $int ).
tff(j,type,
j: $int ).
tff(n,type,
n: $int ).
tff(t,type,
t: $o ).
tff(voogie_precondition_1,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_2,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_3,axiom,
! [A: array_int_bool,B: array_int_bool] :
( ! [I: $int] : ( select_int_bool(A,I) = select_int_bool(B,I) )
=> ( A = B ) ) ).
tff(voogie_precondition_4,axiom,
$greater(n,0) ).
tff(voogie_precondition_5,axiom,
( $lesseq(0,i)
& $lesseq(i,$sum(j,1))
& $lesseq($sum(j,1),n) ) ).
tff(voogie_precondition_6,axiom,
! [M: $int] :
( ( $lesseq(0,M)
& $less(M,i) )
=> ~ select_int_bool(a,M) ) ).
tff(voogie_precondition_7,axiom,
! [K: $int] :
( ( $less(j,K)
& $less(K,n) )
=> select_int_bool(a,K) ) ).
tff(voogie_conjecture,conjecture,
$let(
bad: $o,
bad:=
$ite(~ $lesseq(i,j),$true,bad),
$let(
[ j: $int,
i: $int,
a: array_int_bool,
t: $o ],
[j,i,a,t]:=
$ite(
~ select_int_bool(a,i),
$let(
i: $int,
i:= $sum(i,1),
[j,i,a,t] ),
$ite(
select_int_bool(a,j),
$let(
j: $int,
j:= $difference(j,1),
[j,i,a,t] ),
$let(
t: $o,
t:= select_int_bool(a,i),
$let(
a: array_int_bool,
a:= store_int_bool(a,i,select_int_bool(a,j)),
$let(
a: array_int_bool,
a:= store_int_bool(a,j,t),
$let(
i: $int,
i:= $sum(i,1),
$let(
j: $int,
j:= $difference(j,1),
[j,i,a,t] ) ) ) ) ) ) ),
$let(
bad: $o,
bad:=
$ite(~ $lesseq(i,j),$true,bad),
$let(
[ j: $int,
i: $int,
a: array_int_bool,
t: $o ],
[j,i,a,t]:=
$ite(
~ select_int_bool(a,i),
$let(
i: $int,
i:= $sum(i,1),
[j,i,a,t] ),
$ite(
select_int_bool(a,j),
$let(
j: $int,
j:= $difference(j,1),
[j,i,a,t] ),
$let(
t: $o,
t:= select_int_bool(a,i),
$let(
a: array_int_bool,
a:= store_int_bool(a,i,select_int_bool(a,j)),
$let(
a: array_int_bool,
a:= store_int_bool(a,j,t),
$let(
i: $int,
i:= $sum(i,1),
$let(
j: $int,
j:= $difference(j,1),
[j,i,a,t] ) ) ) ) ) ) ),
( ( bad
| ( $lesseq(0,i)
& $lesseq(i,$sum(j,1))
& $lesseq($sum(j,1),n) ) )
& ( bad
| ! [M: $int] :
( ( $lesseq(0,M)
& $less(M,i) )
=> ~ select_int_bool(a,M) ) )
& ( bad
| ! [K: $int] :
( ( $less(j,K)
& $less(K,n) )
=> select_int_bool(a,K) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------