TPTP Problem File: SWW589_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW589_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Edit distance-T-WP parameter distance
% 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 : edit_distance-T-WP_parameter_distance [Fil14]
% Status : Theorem
% Rating : 0.38 v8.2.0, 0.50 v7.5.0, 0.40 v7.4.0, 0.25 v7.3.0, 0.17 v7.1.0, 0.33 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.57 v6.2.0, 0.88 v6.1.0
% Syntax : Number of formulae : 161 ( 49 unt; 61 typ; 0 def)
% Number of atoms : 205 ( 86 equ)
% Maximal formula atoms : 20 ( 1 avg)
% Number of connectives : 110 ( 5 ~; 9 |; 35 &)
% ( 5 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 162 ( 36 atm; 27 fun; 35 num; 64 var)
% Number of types : 10 ( 8 usr; 1 ari)
% Number of type conns : 97 ( 44 >; 53 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 0 prp; 2-5 aty)
% Number of functors : 53 ( 48 usr; 11 con; 0-5 aty)
% Number of variables : 292 ( 270 !; 22 ?; 292 :)
% 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_sort2,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(list,type,
list: ty > ty ).
tff(nil,type,
nil: ty > uni ).
tff(nil_sort2,axiom,
! [A: ty] : sort1(list(A),nil(A)) ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(cons_sort2,axiom,
! [A: ty,X: uni,X1: uni] : sort1(list(A),cons(A,X,X1)) ).
tff(match_list,type,
match_list1: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_list_sort2,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort1(A1,match_list1(A1,A,X,X1,X2)) ).
tff(match_list_Nil1,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort1(A1,Z)
=> ( match_list1(A1,A,nil(A),Z,Z1) = Z ) ) ).
tff(match_list_Cons1,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni,U1: uni] :
( sort1(A1,Z1)
=> ( match_list1(A1,A,cons(A,U,U1),Z,Z1) = Z1 ) ) ).
tff(nil_Cons1,axiom,
! [A: ty,V: uni,V1: uni] : nil(A) != cons(A,V,V1) ).
tff(cons_proj_1,type,
cons_proj_11: ( ty * uni ) > uni ).
tff(cons_proj_1_sort2,axiom,
! [A: ty,X: uni] : sort1(A,cons_proj_11(A,X)) ).
tff(cons_proj_1_def1,axiom,
! [A: ty,U: uni,U1: uni] :
( sort1(A,U)
=> ( cons_proj_11(A,cons(A,U,U1)) = U ) ) ).
tff(cons_proj_2,type,
cons_proj_21: ( ty * uni ) > uni ).
tff(cons_proj_2_sort2,axiom,
! [A: ty,X: uni] : sort1(list(A),cons_proj_21(A,X)) ).
tff(cons_proj_2_def1,axiom,
! [A: ty,U: uni,U1: uni] : cons_proj_21(A,cons(A,U,U1)) = U1 ).
tff(list_inversion1,axiom,
! [A: ty,U: uni] :
( ( U = nil(A) )
| ( U = cons(A,cons_proj_11(A,U),cons_proj_21(A,U)) ) ) ).
tff(length,type,
length2: ( ty * uni ) > $int ).
tff(length_def,axiom,
! [A: ty] :
( ( length2(A,nil(A)) = 0 )
& ! [X: uni,X1: uni] : length2(A,cons(A,X,X1)) = $sum(1,length2(A,X1)) ) ).
tff(length_nonnegative,axiom,
! [A: ty,L: uni] : $lesseq(0,length2(A,L)) ).
tff(length_nil,axiom,
! [A: ty,L: uni] :
( ( length2(A,L) = 0 )
<=> ( L = nil(A) ) ) ).
tff(char,type,
char1: $tType ).
tff(char1,type,
char: ty ).
tff(list_char,type,
list_char: $tType ).
tff(dist,type,
dist1: ( list_char * list_char * $int ) > $o ).
tff(t2tb,type,
t2tb: list_char > uni ).
tff(t2tb_sort6,axiom,
! [X: list_char] : sort1(list(char),t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > list_char ).
tff(bridgeL,axiom,
! [I: list_char] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] : t2tb(tb2t(J)) = J ).
tff(dist_eps,axiom,
dist1(tb2t(nil(char)),tb2t(nil(char)),0) ).
tff(t2tb1,type,
t2tb1: char1 > uni ).
tff(t2tb_sort7,axiom,
! [X: char1] : sort1(char,t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > char1 ).
tff(bridgeL1,axiom,
! [I: char1] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] :
( sort1(char,J)
=> ( t2tb1(tb2t1(J)) = J ) ) ).
tff(dist_add_left,axiom,
! [W1: list_char,W2: list_char,N: $int] :
( dist1(W1,W2,N)
=> ! [A: char1] : dist1(tb2t(cons(char,t2tb1(A),t2tb(W1))),W2,$sum(N,1)) ) ).
tff(dist_add_right,axiom,
! [W1: list_char,W2: list_char,N: $int] :
( dist1(W1,W2,N)
=> ! [A: char1] : dist1(W1,tb2t(cons(char,t2tb1(A),t2tb(W2))),$sum(N,1)) ) ).
tff(dist_context,axiom,
! [W1: list_char,W2: list_char,N: $int] :
( dist1(W1,W2,N)
=> ! [A: char1] : dist1(tb2t(cons(char,t2tb1(A),t2tb(W1))),tb2t(cons(char,t2tb1(A),t2tb(W2))),N) ) ).
tff(dist_inversion,axiom,
! [Z: list_char,Z1: list_char,Z2: $int] :
( dist1(Z,Z1,Z2)
=> ( ( ( Z = tb2t(nil(char)) )
& ( Z1 = tb2t(nil(char)) )
& ( Z2 = 0 ) )
| ? [W1: list_char,W2: list_char,N: $int] :
( dist1(W1,W2,N)
& ? [A: char1] :
( ( Z = tb2t(cons(char,t2tb1(A),t2tb(W1))) )
& ( Z1 = W2 )
& ( Z2 = $sum(N,1) ) ) )
| ? [W1: list_char,W2: list_char,N: $int] :
( dist1(W1,W2,N)
& ? [A: char1] :
( ( Z = W1 )
& ( Z1 = tb2t(cons(char,t2tb1(A),t2tb(W2))) )
& ( Z2 = $sum(N,1) ) ) )
| ? [W1: list_char,W2: list_char,N: $int] :
( dist1(W1,W2,N)
& ? [A: char1] :
( ( Z = tb2t(cons(char,t2tb1(A),t2tb(W1))) )
& ( Z1 = tb2t(cons(char,t2tb1(A),t2tb(W2))) )
& ( Z2 = N ) ) ) ) ) ).
tff(min_dist,type,
min_dist1: ( list_char * list_char * $int ) > $o ).
tff(min_dist_def,axiom,
! [W1: list_char,W2: list_char,N: $int] :
( min_dist1(W1,W2,N)
<=> ( dist1(W1,W2,N)
& ! [M: $int] :
( dist1(W1,W2,M)
=> $lesseq(N,M) ) ) ) ).
tff(infix_plpl,type,
infix_plpl: ( ty * uni * uni ) > uni ).
tff(infix_plpl_sort2,axiom,
! [A: ty,X: uni,X1: uni] : sort1(list(A),infix_plpl(A,X,X1)) ).
tff(infix_plpl_def,axiom,
! [A: ty,L2: uni] :
( ( infix_plpl(A,nil(A),L2) = L2 )
& ! [X: uni,X1: uni] : infix_plpl(A,cons(A,X,X1),L2) = cons(A,X,infix_plpl(A,X1,L2)) ) ).
tff(append_assoc,axiom,
! [A: ty,L1: uni,L2: uni,L3: uni] : infix_plpl(A,L1,infix_plpl(A,L2,L3)) = infix_plpl(A,infix_plpl(A,L1,L2),L3) ).
tff(append_l_nil,axiom,
! [A: ty,L: uni] : infix_plpl(A,L,nil(A)) = L ).
tff(append_length,axiom,
! [A: ty,L1: uni,L2: uni] : length2(A,infix_plpl(A,L1,L2)) = $sum(length2(A,L1),length2(A,L2)) ).
tff(mem,type,
mem: ( ty * uni * uni ) > $o ).
tff(mem_def,axiom,
! [A: ty,X: uni] :
( sort1(A,X)
=> ( ~ mem(A,X,nil(A))
& ! [X1: uni,X2: uni] :
( sort1(A,X1)
=> ( mem(A,X,cons(A,X1,X2))
<=> ( ( X = X1 )
| mem(A,X,X2) ) ) ) ) ) ).
tff(mem_append,axiom,
! [A: ty,X: uni,L1: uni,L2: uni] :
( mem(A,X,infix_plpl(A,L1,L2))
<=> ( mem(A,X,L1)
| mem(A,X,L2) ) ) ).
tff(mem_decomp,axiom,
! [A: ty,X: uni,L: uni] :
( mem(A,X,L)
=> ? [L1: uni,L2: uni] :
( sort1(list(A),L1)
& sort1(list(A),L2)
& ( L = infix_plpl(A,L1,cons(A,X,L2)) ) ) ) ).
tff(last_char,type,
last_char1: ( char1 * list_char ) > char1 ).
tff(last_char_def,axiom,
! [A: char1] :
( ( last_char1(A,tb2t(nil(char))) = A )
& ! [X: char1,X1: list_char] : last_char1(A,tb2t(cons(char,t2tb1(X),t2tb(X1)))) = last_char1(X,X1) ) ).
tff(but_last,type,
but_last1: ( char1 * list_char ) > list_char ).
tff(but_last_def,axiom,
! [A: char1] :
( ( but_last1(A,tb2t(nil(char))) = tb2t(nil(char)) )
& ! [X: char1,X1: list_char] : but_last1(A,tb2t(cons(char,t2tb1(X),t2tb(X1)))) = tb2t(cons(char,t2tb1(A),t2tb(but_last1(X,X1)))) ) ).
tff(first_last_explicit,axiom,
! [U: list_char,A: char1] : tb2t(infix_plpl(char,t2tb(but_last1(A,U)),cons(char,t2tb1(last_char1(A,U)),nil(char)))) = tb2t(cons(char,t2tb1(A),t2tb(U))) ).
tff(first_last,axiom,
! [A: char1,U: list_char] :
? [V: list_char,B: char1] :
( ( tb2t(infix_plpl(char,t2tb(V),cons(char,t2tb1(B),nil(char)))) = tb2t(cons(char,t2tb1(A),t2tb(U))) )
& ( length2(char,t2tb(V)) = length2(char,t2tb(U)) ) ) ).
tff(key_lemma_right,axiom,
! [W1: list_char,Wqt2: list_char,M: $int,A: char1] :
( dist1(W1,Wqt2,M)
=> ! [W2: list_char] :
( ( Wqt2 = tb2t(cons(char,t2tb1(A),t2tb(W2))) )
=> ? [U1: list_char,V1: list_char,K: $int] :
( ( W1 = tb2t(infix_plpl(char,t2tb(U1),t2tb(V1))) )
& dist1(V1,W2,K)
& $lesseq($sum(K,length2(char,t2tb(U1))),$sum(M,1)) ) ) ) ).
tff(dist_symetry,axiom,
! [W1: list_char,W2: list_char,N: $int] :
( dist1(W1,W2,N)
=> dist1(W2,W1,N) ) ).
tff(key_lemma_left,axiom,
! [W1: list_char,W2: list_char,M: $int,A: char1] :
( dist1(tb2t(cons(char,t2tb1(A),t2tb(W1))),W2,M)
=> ? [U2: list_char,V2: list_char,K: $int] :
( ( W2 = tb2t(infix_plpl(char,t2tb(U2),t2tb(V2))) )
& dist1(W1,V2,K)
& $lesseq($sum(K,length2(char,t2tb(U2))),$sum(M,1)) ) ) ).
tff(dist_concat_left,axiom,
! [U: list_char,V: list_char,W: list_char,N: $int] :
( dist1(V,W,N)
=> dist1(tb2t(infix_plpl(char,t2tb(U),t2tb(V))),W,$sum(length2(char,t2tb(U)),N)) ) ).
tff(dist_concat_right,axiom,
! [U: list_char,V: list_char,W: list_char,N: $int] :
( dist1(V,W,N)
=> dist1(V,tb2t(infix_plpl(char,t2tb(U),t2tb(W))),$sum(length2(char,t2tb(U)),N)) ) ).
tff(min_dist_equal,axiom,
! [W1: list_char,W2: list_char,A: char1,N: $int] :
( min_dist1(W1,W2,N)
=> min_dist1(tb2t(cons(char,t2tb1(A),t2tb(W1))),tb2t(cons(char,t2tb1(A),t2tb(W2))),N) ) ).
tff(min_dist_diff,axiom,
! [W1: list_char,W2: list_char,A: char1,B: char1,M: $int,P: $int] :
( ( A != B )
=> ( min_dist1(tb2t(cons(char,t2tb1(A),t2tb(W1))),W2,P)
=> ( min_dist1(W1,tb2t(cons(char,t2tb1(B),t2tb(W2))),M)
=> min_dist1(tb2t(cons(char,t2tb1(A),t2tb(W1))),tb2t(cons(char,t2tb1(B),t2tb(W2))),$sum(min1(M,P),1)) ) ) ) ).
tff(min_dist_eps,axiom,
! [W: list_char,A: char1,N: $int] :
( min_dist1(W,tb2t(nil(char)),N)
=> min_dist1(tb2t(cons(char,t2tb1(A),t2tb(W))),tb2t(nil(char)),$sum(N,1)) ) ).
tff(min_dist_eps_length,axiom,
! [W: list_char] : min_dist1(tb2t(nil(char)),W,length2(char,t2tb(W))) ).
tff(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(mk_ref_sort2,axiom,
! [A: ty,X: uni] : sort1(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort2,axiom,
! [A: ty,X: uni] : sort1(A,contents(A,X)) ).
tff(contents_def1,axiom,
! [A: ty,U: uni] :
( sort1(A,U)
=> ( contents(A,mk_ref(A,U)) = U ) ) ).
tff(ref_inversion1,axiom,
! [A: ty,U: uni] :
( sort1(ref(A),U)
=> ( U = mk_ref(A,contents(A,U)) ) ) ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(get_sort4,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_sort4,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_sort2,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_sort2,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),mk_array1(A,X,X1)) ).
tff(length1,type,
length3: ( ty * uni ) > $int ).
tff(length_def2,axiom,
! [A: ty,U: $int,U1: uni] : length3(A,mk_array1(A,U,U1)) = U ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(elts_sort2,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,length3(A,U),elts(A,U)) ).
tff(get1,type,
get2: ( ty * uni * $int ) > uni ).
tff(get_sort5,axiom,
! [A: ty,X: uni,X1: $int] : sort1(A,get2(A,X,X1)) ).
tff(t2tb2,type,
t2tb2: $int > uni ).
tff(t2tb_sort8,axiom,
! [X: $int] : sort1(int,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > $int ).
tff(bridgeL2,axiom,
! [I: $int] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(get_def,axiom,
! [A: ty,A1: uni,I: $int] : get2(A,A1,I) = get(A,int,elts(A,A1),t2tb2(I)) ).
tff(set1,type,
set2: ( ty * uni * $int * uni ) > uni ).
tff(set_sort5,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,length3(A,A1),set(A,int,elts(A,A1),t2tb2(I),V)) ).
tff(make,type,
make1: ( ty * $int * uni ) > uni ).
tff(make_sort2,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),make1(A,X,X1)) ).
tff(make_def,axiom,
! [A: ty,N: $int,V: uni] : make1(A,N,V) = mk_array1(A,N,const(A,int,V)) ).
tff(array_char,type,
array_char: $tType ).
tff(suffix,type,
suffix1: ( array_char * $int ) > list_char ).
tff(t2tb3,type,
t2tb3: array_char > uni ).
tff(t2tb_sort9,axiom,
! [X: array_char] : sort1(array(char),t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > array_char ).
tff(bridgeL3,axiom,
! [I: array_char] : tb2t3(t2tb3(I)) = I ).
tff(bridgeR3,axiom,
! [J: uni] : t2tb3(tb2t3(J)) = J ).
tff(suffix_nil,axiom,
! [A: array_char] : suffix1(A,length3(char,t2tb3(A))) = tb2t(nil(char)) ).
tff(suffix_cons,axiom,
! [A: array_char,I: $int] :
( ( $lesseq(0,I)
& $less(I,length3(char,t2tb3(A))) )
=> ( suffix1(A,I) = tb2t(cons(char,get2(char,t2tb3(A),I),t2tb(suffix1(A,$sum(I,1))))) ) ) ).
tff(suffix_length,axiom,
! [A: array_char,I: $int] :
( ( $lesseq(0,I)
& $lesseq(I,length3(char,t2tb3(A))) )
=> ( length2(char,t2tb(suffix1(A,I))) = $difference(length3(char,t2tb3(A)),I) ) ) ).
tff(min_suffix,type,
min_suffix1: ( array_char * array_char * $int * $int * $int ) > $o ).
tff(min_suffix_def,axiom,
! [A1: array_char,A2: array_char,I: $int,J: $int,N: $int] :
( min_suffix1(A1,A2,I,J,N)
<=> min_dist1(suffix1(A1,I),suffix1(A2,J),N) ) ).
tff(map_int_int,type,
map_int_int: $tType ).
tff(t2tb5,type,
t2tb5: map_int_int > uni ).
tff(t2tb_sort10,axiom,
! [X: map_int_int] : sort1(map(int,int),t2tb5(X)) ).
tff(tb2t5,type,
tb2t5: uni > map_int_int ).
tff(bridgeL5,axiom,
! [I: map_int_int] : tb2t5(t2tb5(I)) = I ).
tff(bridgeR5,axiom,
! [J: uni] : t2tb5(tb2t5(J)) = J ).
tff(wP_parameter_distance,conjecture,
! [W1: $int,W11: uni,W2: $int,W21: uni] :
( sort1(map(int,char),W11)
=> ( sort1(map(int,char),W21)
=> ( ( $lesseq(0,W1)
& $lesseq(0,W2) )
=> ( $lesseq(0,$sum(W2,1))
=> ( $lesseq(0,$sum(W2,1))
=> ( $lesseq(0,W2)
=> ! [T: map_int_int,I: $int] :
( ( $lesseq(0,I)
& $lesseq(I,W2) )
=> ( ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,I) )
=> ( tb2t2(get(int,int,t2tb5(T),t2tb2(J))) = $difference(W2,J) ) )
=> ( ( $lesseq(0,$sum(W2,1))
& $lesseq(0,I)
& $less(I,$sum(W2,1)) )
=> ! [T1: map_int_int] :
( ( $lesseq(0,$sum(W2,1))
& ( T1 = tb2t5(set(int,int,t2tb5(T),t2tb2(I),t2tb2($difference(W2,I)))) ) )
=> ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,$sum(I,1)) )
=> ( tb2t2(get(int,int,t2tb5(T1),t2tb2(J))) = $difference(W2,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------