TPTP Problem File: SWW994_1.p
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%------------------------------------------------------------------------------
% File : SWW994_1 : TPTP v9.2.1. Released v9.1.0.
% Domain : Software Verification
% Problem : matrix-transpose-3
% Version : Especial.
% English :
% Refs : [Kot17] Kotelnikov (2017), Email to Geoff Sutcliffe
% Source : [Kot17]
% Names : matrix-transpose-3 [Kot17]
% Status : Theorem
% Rating : ? v9.1.0
% Syntax : Number of formulae : 22 ( 1 unt; 12 typ; 0 def)
% Number of atoms : 35 ( 18 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 27 ( 2 ~; 4 |; 13 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of X terms : 6 ( 0 []; 0 ite; 6 let)
% Number arithmetic : 36 ( 15 atm; 0 fun; 5 num; 16 var)
% Number of types : 4 ( 2 usr; 1 ari)
% Number of type conns : 10 ( 4 >; 6 *; 0 +; 0 <<)
% Number of predicates : 6 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 9 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_array_int_int,type,
array_int_array_int_int: $tType ).
tff(array_int_int,type,
array_int_int: $tType ).
tff(select_int_array_int_int,type,
select_int_array_int_int: ( array_int_array_int_int * $int ) > array_int_int ).
tff(store_int_array_int_int,type,
store_int_array_int_int: ( array_int_array_int_int * $int * array_int_int ) > array_int_array_int_int ).
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(bad,type,
bad: $o ).
tff(col,type,
col: $int ).
tff(matrix,type,
matrix: array_int_array_int_int ).
tff(row,type,
row: $int ).
tff(size,type,
size: $int ).
tff(transposed,type,
transposed: array_int_array_int_int ).
tff(voogie_precondition_1,axiom,
! [A: array_int_array_int_int,V: array_int_int,I: $int,J: $int] :
( ( I = J )
=> ( select_int_array_int_int(store_int_array_int_int(A,I,V),J) = V ) ) ).
tff(voogie_precondition_2,axiom,
! [A: array_int_array_int_int,V: array_int_int,I: $int,J: $int] :
( ( I != J )
=> ( select_int_array_int_int(store_int_array_int_int(A,I,V),J) = select_int_array_int_int(A,J) ) ) ).
tff(voogie_precondition_3,axiom,
! [A: array_int_array_int_int,B: array_int_array_int_int] :
( ! [I: $int] : ( select_int_array_int_int(A,I) = select_int_array_int_int(A,I) )
=> ( A = B ) ) ).
tff(voogie_precondition_4,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_5,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_6,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_7,axiom,
$greater(size,0) ).
tff(voogie_precondition_8,axiom,
( $lesseq(0,row)
& $lesseq(row,col) ) ).
tff(voogie_precondition_9,axiom,
! [I: $int,J: $int] :
( ( ( $lesseq(0,I)
& $lesseq(I,J)
& $less(J,size)
& ( ( ( I = row )
& $less(J,col) )
| $less(I,row) ) )
=> ( select_int_int(select_int_array_int_int(transposed,I),J) = select_int_int(select_int_array_int_int(matrix,J),I) ) )
& ( select_int_int(select_int_array_int_int(transposed,J),I) = select_int_int(select_int_array_int_int(matrix,I),J) ) ) ).
tff(voogie_conjecture,conjecture,
$let(
bad: $o,
bad:=
$ite(
~ ( ( row != size ) ),
$true,
bad ),
$let(
[ transposed: array_int_array_int_int,
col: $int,
row: $int ],
[transposed,col,row]:=
$ite(
$less(col,size),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,row,store_int_int(select_int_array_int_int(transposed,row),col,select_int_int(select_int_array_int_int(matrix,col),row))),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,col,store_int_int(select_int_array_int_int(transposed,col),row,select_int_int(select_int_array_int_int(matrix,row),col))),
$let(
col: $int,
col:= $sum(col,1),
[transposed,col,row] ) ) ),
$let(
row: $int,
row:= $sum(row,1),
$let(
col: $int,
col:= $sum(row,1),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,row,store_int_int(select_int_array_int_int(transposed,row),row,select_int_int(select_int_array_int_int(matrix,row),row))),
[transposed,col,row] ) ) ) ),
$let(
bad: $o,
bad:=
$ite(
~ ( ( row != size ) ),
$true,
bad ),
$let(
[ transposed: array_int_array_int_int,
col: $int,
row: $int ],
[transposed,col,row]:=
$ite(
$less(col,size),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,row,store_int_int(select_int_array_int_int(transposed,row),col,select_int_int(select_int_array_int_int(matrix,col),row))),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,col,store_int_int(select_int_array_int_int(transposed,col),row,select_int_int(select_int_array_int_int(matrix,row),col))),
$let(
col: $int,
col:= $sum(col,1),
[transposed,col,row] ) ) ),
$let(
row: $int,
row:= $sum(row,1),
$let(
col: $int,
col:= $sum(row,1),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,row,store_int_int(select_int_array_int_int(transposed,row),row,select_int_int(select_int_array_int_int(matrix,row),row))),
[transposed,col,row] ) ) ) ),
$let(
bad: $o,
bad:=
$ite(
~ ( ( row != size ) ),
$true,
bad ),
$let(
[ transposed: array_int_array_int_int,
col: $int,
row: $int ],
[transposed,col,row]:=
$ite(
$less(col,size),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,row,store_int_int(select_int_array_int_int(transposed,row),col,select_int_int(select_int_array_int_int(matrix,col),row))),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,col,store_int_int(select_int_array_int_int(transposed,col),row,select_int_int(select_int_array_int_int(matrix,row),col))),
$let(
col: $int,
col:= $sum(col,1),
[transposed,col,row] ) ) ),
$let(
row: $int,
row:= $sum(row,1),
$let(
col: $int,
col:= $sum(row,1),
$let(
transposed: array_int_array_int_int,
transposed:= store_int_array_int_int(transposed,row,store_int_int(select_int_array_int_int(transposed,row),row,select_int_int(select_int_array_int_int(matrix,row),row))),
[transposed,col,row] ) ) ) ),
( ( bad
| ( $lesseq(0,row)
& $lesseq(row,col) ) )
& ( bad
| ! [I: $int,J: $int] :
( ( ( $lesseq(0,I)
& $lesseq(I,J)
& $less(J,size)
& ( ( ( I = row )
& $less(J,col) )
| $less(I,row) ) )
=> ( select_int_int(select_int_array_int_int(transposed,I),J) = select_int_int(select_int_array_int_int(matrix,J),I) ) )
& ( select_int_int(select_int_array_int_int(transposed,J),I) = select_int_int(select_int_array_int_int(matrix,I),J) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------