TPTP Problem File: SWW639_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW639_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Resizable array-T-WP parameter test2
% Version : Especial : Let and conditional terms encoded away.
% English :
% Refs : [Fil14] Filliatre (2014), Email to Geoff Sutcliffe
% : [BF+] Bobot et al. (URL), Toccata: Certified Programs and Cert
% Source : [Fil14]
% Names : resizable_array-T-WP_parameter_test2 [Fil14]
% Status : Theorem
% Rating : 0.12 v7.5.0, 0.30 v7.4.0, 0.12 v7.3.0, 0.00 v7.1.0, 0.17 v7.0.0, 0.29 v6.4.0, 0.00 v6.3.0, 0.43 v6.2.0, 0.50 v6.1.0
% Syntax : Number of formulae : 108 ( 41 unt; 47 typ; 0 def)
% Number of atoms : 151 ( 71 equ)
% Maximal formula atoms : 68 ( 1 avg)
% Number of connectives : 92 ( 2 ~; 3 |; 56 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 263 ( 52 atm; 4 fun; 139 num; 68 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 72 ( 32 >; 40 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 47 ( 39 usr; 13 con; 0-5 aty)
% Number of variables : 187 ( 162 !; 25 ?; 187 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
%------------------------------------------------------------------------------
tff(uni,type,
uni: $tType ).
tff(ty,type,
ty: $tType ).
tff(sort,type,
sort1: ( ty * uni ) > $o ).
tff(witness,type,
witness1: ty > uni ).
tff(witness_sort1,axiom,
! [A: ty] : sort1(A,witness1(A)) ).
tff(int,type,
int: ty ).
tff(real,type,
real: ty ).
tff(bool,type,
bool1: $tType ).
tff(bool1,type,
bool: ty ).
tff(true,type,
true1: bool1 ).
tff(false,type,
false1: bool1 ).
tff(match_bool,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(match_bool_sort1,axiom,
! [A: ty,X: bool1,X1: uni,X2: uni] : sort1(A,match_bool1(A,X,X1,X2)) ).
tff(match_bool_True,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z)
=> ( match_bool1(A,true1,Z,Z1) = Z ) ) ).
tff(match_bool_False,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z1)
=> ( match_bool1(A,false1,Z,Z1) = Z1 ) ) ).
tff(true_False,axiom,
true1 != false1 ).
tff(bool_inversion,axiom,
! [U: bool1] :
( ( U = true1 )
| ( U = false1 ) ) ).
tff(tuple0,type,
tuple02: $tType ).
tff(tuple01,type,
tuple0: ty ).
tff(tuple02,type,
tuple03: tuple02 ).
tff(tuple0_inversion,axiom,
! [U: tuple02] : U = tuple03 ).
tff(qtmark,type,
qtmark: ty ).
tff(compatOrderMult,axiom,
! [X: $int,Y: $int,Z: $int] :
( $lesseq(X,Y)
=> ( $lesseq(0,Z)
=> $lesseq($product(X,Z),$product(Y,Z)) ) ) ).
tff(min,type,
min1: ( $int * $int ) > $int ).
tff(max,type,
max1: ( $int * $int ) > $int ).
tff(max_is_ge,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,max1(X,Y))
& $lesseq(Y,max1(X,Y)) ) ).
tff(max_is_some,axiom,
! [X: $int,Y: $int] :
( ( max1(X,Y) = X )
| ( max1(X,Y) = Y ) ) ).
tff(min_is_le,axiom,
! [X: $int,Y: $int] :
( $lesseq(min1(X,Y),X)
& $lesseq(min1(X,Y),Y) ) ).
tff(min_is_some,axiom,
! [X: $int,Y: $int] :
( ( min1(X,Y) = X )
| ( min1(X,Y) = Y ) ) ).
tff(max_x,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( max1(X,Y) = X ) ) ).
tff(max_y,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> ( max1(X,Y) = Y ) ) ).
tff(min_x,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> ( min1(X,Y) = X ) ) ).
tff(min_y,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( min1(X,Y) = Y ) ) ).
tff(max_sym,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( max1(X,Y) = max1(Y,X) ) ) ).
tff(min_sym,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( min1(X,Y) = min1(Y,X) ) ) ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(get_sort2,axiom,
! [A: ty,B: ty,X: uni,X1: uni] : sort1(B,get(B,A,X,X1)) ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(set_sort2,axiom,
! [A: ty,B: ty,X: uni,X1: uni,X2: uni] : sort1(map(A,B),set(B,A,X,X1,X2)) ).
tff(select_eq,axiom,
! [A: ty,B: ty,M: uni,A1: uni,A2: uni,B1: uni] :
( sort1(B,B1)
=> ( ( A1 = A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = B1 ) ) ) ).
tff(select_neq,axiom,
! [A: ty,B: ty,M: uni,A1: uni,A2: uni] :
( sort1(A,A1)
=> ( sort1(A,A2)
=> ! [B1: uni] :
( ( A1 != A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = get(B,A,M,A2) ) ) ) ) ).
tff(const1,type,
const: ( ty * ty * uni ) > uni ).
tff(const_sort1,axiom,
! [A: ty,B: ty,X: uni] : sort1(map(A,B),const(B,A,X)) ).
tff(const,axiom,
! [A: ty,B: ty,B1: uni,A1: uni] :
( sort1(B,B1)
=> ( get(B,A,const(B,A,B1),A1) = B1 ) ) ).
tff(array,type,
array: ty > ty ).
tff(mk_array,type,
mk_array1: ( ty * $int * uni ) > uni ).
tff(mk_array_sort1,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),mk_array1(A,X,X1)) ).
tff(length,type,
length2: ( ty * uni ) > $int ).
tff(length_def2,axiom,
! [A: ty,U: $int,U1: uni] : length2(A,mk_array1(A,U,U1)) = U ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(elts_sort1,axiom,
! [A: ty,X: uni] : sort1(map(int,A),elts(A,X)) ).
tff(elts_def1,axiom,
! [A: ty,U: $int,U1: uni] :
( sort1(map(int,A),U1)
=> ( elts(A,mk_array1(A,U,U1)) = U1 ) ) ).
tff(array_inversion1,axiom,
! [A: ty,U: uni] : U = mk_array1(A,length2(A,U),elts(A,U)) ).
tff(get1,type,
get2: ( ty * uni * $int ) > uni ).
tff(get_sort3,axiom,
! [A: ty,X: uni,X1: $int] : sort1(A,get2(A,X,X1)) ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(t2tb_sort,axiom,
! [X: $int] : sort1(int,t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > $int ).
tff(bridgeL,axiom,
! [I: $int] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] : t2tb(tb2t(J)) = J ).
tff(get_def,axiom,
! [A: ty,A1: uni,I: $int] : get2(A,A1,I) = get(A,int,elts(A,A1),t2tb(I)) ).
tff(set1,type,
set2: ( ty * uni * $int * uni ) > uni ).
tff(set_sort3,axiom,
! [A: ty,X: uni,X1: $int,X2: uni] : sort1(array(A),set2(A,X,X1,X2)) ).
tff(set_def,axiom,
! [A: ty,A1: uni,I: $int,V: uni] : set2(A,A1,I,V) = mk_array1(A,length2(A,A1),set(A,int,elts(A,A1),t2tb(I),V)) ).
tff(make,type,
make2: ( ty * $int * uni ) > uni ).
tff(make_sort2,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),make2(A,X,X1)) ).
tff(make_def,axiom,
! [A: ty,N: $int,V: uni] : make2(A,N,V) = mk_array1(A,N,const(A,int,V)) ).
tff(rarray,type,
rarray: ty > ty ).
tff(mk_rarray,type,
mk_rarray1: ( ty * uni * $int * uni ) > uni ).
tff(mk_rarray_sort1,axiom,
! [A: ty,X: uni,X1: $int,X2: uni] : sort1(rarray(A),mk_rarray1(A,X,X1,X2)) ).
tff(dummy,type,
dummy: ( ty * uni ) > uni ).
tff(dummy_sort1,axiom,
! [A: ty,X: uni] : sort1(A,dummy(A,X)) ).
tff(dummy_def1,axiom,
! [A: ty,U: uni,U1: $int,U2: uni] :
( sort1(A,U)
=> ( dummy(A,mk_rarray1(A,U,U1,U2)) = U ) ) ).
tff(length1,type,
length3: ( ty * uni ) > $int ).
tff(length_def3,axiom,
! [A: ty,U: uni,U1: $int,U2: uni] : length3(A,mk_rarray1(A,U,U1,U2)) = U1 ).
tff(data,type,
data: ( ty * uni ) > uni ).
tff(data_sort1,axiom,
! [A: ty,X: uni] : sort1(array(A),data(A,X)) ).
tff(data_def1,axiom,
! [A: ty,U: uni,U1: $int,U2: uni] : data(A,mk_rarray1(A,U,U1,U2)) = U2 ).
tff(rarray_inversion1,axiom,
! [A: ty,U: uni] : U = mk_rarray1(A,dummy(A,U),length3(A,U),data(A,U)) ).
tff(mixfix_lbrb,type,
mixfix_lbrb1: ( ty * uni * $int ) > uni ).
tff(mixfix_lbrb_sort1,axiom,
! [A: ty,X: uni,X1: $int] : sort1(A,mixfix_lbrb1(A,X,X1)) ).
tff(mixfix_lbrb_def,axiom,
! [A: ty,R: uni,I: $int] : mixfix_lbrb1(A,R,I) = get2(A,data(A,R),I) ).
tff(mixfix_lblsmnrb,type,
mixfix_lblsmnrb1: ( ty * uni * $int * uni ) > uni ).
tff(mixfix_lblsmnrb_sort1,axiom,
! [A: ty,X: uni,X1: $int,X2: uni] : sort1(rarray(A),mixfix_lblsmnrb1(A,X,X1,X2)) ).
tff(mixfix_lblsmnrb_def,axiom,
! [A: ty,R: uni,I: $int,V: uni] : mixfix_lblsmnrb1(A,R,I,V) = mk_rarray1(A,dummy(A,R),length3(A,R),set2(A,data(A,R),I,V)) ).
tff(make1,type,
make3: ( ty * $int * uni ) > uni ).
tff(make_sort3,axiom,
! [A: ty,X: $int,X1: uni] : sort1(rarray(A),make3(A,X,X1)) ).
tff(make_def1,axiom,
! [A: ty,Len: $int,Dummy: uni] : make3(A,Len,Dummy) = mk_rarray1(A,Dummy,Len,make2(A,Len,Dummy)) ).
tff(map_int_int,type,
map_int_int: $tType ).
tff(t2tb1,type,
t2tb1: map_int_int > uni ).
tff(t2tb_sort1,axiom,
! [X: map_int_int] : sort1(map(int,int),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > map_int_int ).
tff(bridgeL1,axiom,
! [I: map_int_int] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(array_int,type,
array_int: $tType ).
tff(t2tb2,type,
t2tb2: array_int > uni ).
tff(t2tb_sort2,axiom,
! [X: array_int] : sort1(array(int),t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > array_int ).
tff(bridgeL2,axiom,
! [I: array_int] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(rarray_int,type,
rarray_int: $tType ).
tff(t2tb3,type,
t2tb3: rarray_int > uni ).
tff(t2tb_sort3,axiom,
! [X: rarray_int] : sort1(rarray(int),t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > rarray_int ).
tff(bridgeL3,axiom,
! [I: rarray_int] : tb2t3(t2tb3(I)) = I ).
tff(bridgeR3,axiom,
! [J: uni] : t2tb3(tb2t3(J)) = J ).
tff(wP_parameter_test2,conjecture,
( $lesseq(0,10)
& ( ( $lesseq(0,length3(int,make3(int,10,t2tb(0))))
& $lesseq(length3(int,make3(int,10,t2tb(0))),length2(int,data(int,make3(int,10,t2tb(0)))))
& ! [I: $int] :
( ( $lesseq(length3(int,make3(int,10,t2tb(0))),I)
& $less(I,length2(int,data(int,make3(int,10,t2tb(0))))) )
=> ( tb2t(get(int,int,elts(int,data(int,make3(int,10,t2tb(0)))),t2tb(I))) = tb2t(dummy(int,make3(int,10,t2tb(0)))) ) )
& ? [X: $int,X1: $int,X2: array_int] :
( ( tb2t3(make3(int,10,t2tb(0))) = tb2t3(mk_rarray1(int,t2tb(X),X1,t2tb2(X2))) )
& $lesseq(0,length2(int,t2tb2(X2))) ) )
=> ( $lesseq(0,0)
& $less(0,length3(int,make3(int,10,t2tb(0))))
& ! [Rho: map_int_int] :
( ( $lesseq(0,length3(int,make3(int,10,t2tb(0))))
& $lesseq(length3(int,make3(int,10,t2tb(0))),length2(int,data(int,make3(int,10,t2tb(0)))))
& ! [I: $int] :
( ( $lesseq(length3(int,make3(int,10,t2tb(0))),I)
& $less(I,length2(int,data(int,make3(int,10,t2tb(0))))) )
=> ( tb2t(get(int,int,t2tb1(Rho),t2tb(I))) = tb2t(dummy(int,make3(int,10,t2tb(0)))) ) )
& ? [X: $int,X1: $int,X2: array_int] :
( ( tb2t3(make3(int,10,t2tb(0))) = tb2t3(mk_rarray1(int,t2tb(X),X1,t2tb2(X2))) )
& $lesseq(0,length2(int,t2tb2(X2))) )
& ? [X: $int,X1: $int,X2: array_int] :
( ( tb2t3(make3(int,10,t2tb(0))) = tb2t3(mk_rarray1(int,t2tb(X),X1,t2tb2(X2))) )
& ( tb2t(dummy(int,make3(int,10,t2tb(0)))) = X )
& ( length3(int,make3(int,10,t2tb(0))) = X1 )
& ? [X3: $int,X4: map_int_int] :
( ( X2 = tb2t2(mk_array1(int,X3,t2tb1(X4))) )
& ( length2(int,data(int,make3(int,10,t2tb(0)))) = X3 )
& ( tb2t1(set(int,int,elts(int,data(int,make3(int,10,t2tb(0)))),t2tb(0),t2tb(17))) = Rho ) ) ) )
=> ( $lesseq(0,10)
& ( ( $lesseq(0,length3(int,make3(int,10,t2tb(0))))
& $lesseq(length3(int,make3(int,10,t2tb(0))),length2(int,data(int,make3(int,10,t2tb(0)))))
& ! [I: $int] :
( ( $lesseq(length3(int,make3(int,10,t2tb(0))),I)
& $less(I,length2(int,data(int,make3(int,10,t2tb(0))))) )
=> ( tb2t(get(int,int,elts(int,data(int,make3(int,10,t2tb(0)))),t2tb(I))) = tb2t(dummy(int,make3(int,10,t2tb(0)))) ) )
& ? [X: $int,X1: $int,X2: array_int] :
( ( tb2t3(make3(int,10,t2tb(0))) = tb2t3(mk_rarray1(int,t2tb(X),X1,t2tb2(X2))) )
& $lesseq(0,length2(int,t2tb2(X2))) ) )
=> ( $lesseq(0,0)
& $less(0,length3(int,make3(int,10,t2tb(0))))
& ! [Rho1: map_int_int] :
( ( $lesseq(0,length3(int,make3(int,10,t2tb(0))))
& $lesseq(length3(int,make3(int,10,t2tb(0))),length2(int,data(int,make3(int,10,t2tb(0)))))
& ! [I: $int] :
( ( $lesseq(length3(int,make3(int,10,t2tb(0))),I)
& $less(I,length2(int,data(int,make3(int,10,t2tb(0))))) )
=> ( tb2t(get(int,int,t2tb1(Rho1),t2tb(I))) = tb2t(dummy(int,make3(int,10,t2tb(0)))) ) )
& ? [X: $int,X1: $int,X2: array_int] :
( ( tb2t3(make3(int,10,t2tb(0))) = tb2t3(mk_rarray1(int,t2tb(X),X1,t2tb2(X2))) )
& $lesseq(0,length2(int,t2tb2(X2))) )
& ? [X: $int,X1: $int,X2: array_int] :
( ( tb2t3(make3(int,10,t2tb(0))) = tb2t3(mk_rarray1(int,t2tb(X),X1,t2tb2(X2))) )
& ( tb2t(dummy(int,make3(int,10,t2tb(0)))) = X )
& ( length3(int,make3(int,10,t2tb(0))) = X1 )
& ? [X3: $int,X4: map_int_int] :
( ( X2 = tb2t2(mk_array1(int,X3,t2tb1(X4))) )
& ( length2(int,data(int,make3(int,10,t2tb(0)))) = X3 )
& ( tb2t1(set(int,int,elts(int,data(int,make3(int,10,t2tb(0)))),t2tb(0),t2tb(42))) = Rho1 ) ) ) )
=> ! [Rho2: $int,Rho3: map_int_int,Rho4: $int] :
( ( $lesseq(0,Rho4)
& $lesseq(Rho4,Rho2)
& ! [I: $int] :
( ( $lesseq(Rho4,I)
& $less(I,Rho2) )
=> ( tb2t(get(int,int,t2tb1(Rho3),t2tb(I))) = tb2t(dummy(int,make3(int,10,t2tb(0)))) ) )
& ? [X: $int,X1: $int,X2: array_int] :
( ( tb2t3(make3(int,10,t2tb(0))) = tb2t3(mk_rarray1(int,t2tb(X),X1,t2tb2(X2))) )
& $lesseq(0,Rho2) )
& ( Rho4 = $sum(length3(int,make3(int,10,t2tb(0))),length3(int,make3(int,10,t2tb(0)))) )
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,Rho4) )
=> ( ( $less(I,length3(int,make3(int,10,t2tb(0))))
=> ( tb2t(get(int,int,t2tb1(Rho3),t2tb(I))) = tb2t(get(int,int,t2tb1(Rho),t2tb(I))) ) )
& ( $lesseq(length3(int,make3(int,10,t2tb(0))),I)
=> ( tb2t(get(int,int,t2tb1(Rho3),t2tb(I))) = tb2t(get(int,int,t2tb1(Rho1),t2tb($difference(I,length3(int,make3(int,10,t2tb(0))))))) ) ) ) ) )
=> ( ( Rho4 = 20 )
& ( tb2t(get(int,int,t2tb1(Rho3),t2tb(0))) = 17 )
& $lesseq(0,10)
& $less(10,Rho4)
& ( tb2t(get(int,int,t2tb1(Rho3),t2tb(10))) = 42 )
& $lesseq(0,0)
& $less(0,length3(int,make3(int,10,t2tb(0))))
& ( tb2t(get(int,int,t2tb1(Rho1),t2tb(0))) = 42 ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------