TPTP Problem File: SWW641_2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW641_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Ropes-T-WP parameter insert
% 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 : ropes-T-WP_parameter_insert [Fil14]
% Status : Theorem
% Rating : 0.50 v8.2.0, 0.62 v7.5.0, 0.70 v7.4.0, 0.50 v7.3.0, 0.33 v7.1.0, 0.50 v7.0.0, 0.71 v6.4.0, 0.33 v6.3.0, 0.71 v6.2.0, 0.50 v6.1.0
% Syntax : Number of formulae : 164 ( 49 unt; 71 typ; 0 def)
% Number of atoms : 224 ( 78 equ)
% Maximal formula atoms : 22 ( 1 avg)
% Number of connectives : 136 ( 5 ~; 6 |; 66 &)
% ( 3 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 273 ( 92 atm; 27 fun; 60 num; 94 var)
% Number of types : 11 ( 9 usr; 1 ari)
% Number of type conns : 91 ( 47 >; 44 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 65 ( 59 usr; 18 con; 0-5 aty)
% Number of variables : 254 ( 254 !; 0 ?; 254 :)
% 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(char,type,
char1: $tType ).
tff(char1,type,
char: ty ).
tff(dummy_char,type,
dummy_char1: char1 ).
tff(string,type,
string2: $tType ).
tff(string1,type,
string: ty ).
tff(length,type,
length3: string2 > $int ).
tff(length_nonnegative,axiom,
! [S: string2] : $lesseq(0,length3(S)) ).
tff(mixfix_lbrb,type,
mixfix_lbrb1: ( string2 * $int ) > char1 ).
tff(empty,type,
empty1: string2 ).
tff(empty_def,axiom,
length3(empty1) = 0 ).
tff(infix_eqeq,type,
infix_eqeq1: ( string2 * string2 ) > $o ).
tff(infix_eqeq_def,axiom,
! [S1: string2,S2: string2] :
( infix_eqeq1(S1,S2)
<=> ( ( length3(S1) = length3(S2) )
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,length3(S1)) )
=> ( mixfix_lbrb1(S1,I) = mixfix_lbrb1(S2,I) ) ) ) ) ).
tff(extensionality,axiom,
! [S1: string2,S2: string2] :
( infix_eqeq1(S1,S2)
=> ( S1 = S2 ) ) ).
tff(app,type,
app2: ( string2 * string2 ) > string2 ).
tff(app_def1,axiom,
! [S1: string2,S2: string2] : length3(app2(S1,S2)) = $sum(length3(S1),length3(S2)) ).
tff(app_def2,axiom,
! [S1: string2,S2: string2,I: $int] :
( ( $lesseq(0,I)
& $less(I,length3(S1)) )
=> ( mixfix_lbrb1(app2(S1,S2),I) = mixfix_lbrb1(S1,I) ) ) ).
tff(app_def3,axiom,
! [S1: string2,S2: string2,I: $int] :
( ( $lesseq(length3(S1),I)
& $less(I,$sum(length3(S1),length3(S2))) )
=> ( mixfix_lbrb1(app2(S1,S2),I) = mixfix_lbrb1(S2,$difference(I,length3(S1))) ) ) ).
tff(app_assoc,axiom,
! [S1: string2,S2: string2,S3: string2] : infix_eqeq1(app2(S1,app2(S2,S3)),app2(app2(S1,S2),S3)) ).
tff(sub,type,
sub1: ( string2 * $int * $int ) > string2 ).
tff(sub_def1,axiom,
! [S: string2,Ofs: $int,Len: $int] :
( $lesseq(0,Len)
=> ( ( $lesseq(0,Ofs)
& $lesseq(Ofs,length3(S)) )
=> ( $lesseq($sum(Ofs,Len),length3(S))
=> ( length3(sub1(S,Ofs,Len)) = Len ) ) ) ) ).
tff(sub_def2,axiom,
! [S: string2,Ofs: $int,Len: $int] :
( $lesseq(0,Len)
=> ( ( $lesseq(0,Ofs)
& $lesseq(Ofs,length3(S)) )
=> ( $lesseq($sum(Ofs,Len),length3(S))
=> ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,Len) )
=> ( mixfix_lbrb1(sub1(S,Ofs,Len),I) = mixfix_lbrb1(S,$sum(Ofs,I)) ) ) ) ) ) ).
tff(rope,type,
rope1: $tType ).
tff(rope1,type,
rope: ty ).
tff(emp,type,
emp1: rope1 ).
tff(str,type,
str1: ( string2 * $int * $int ) > rope1 ).
tff(app1,type,
app3: ( rope1 * rope1 * $int ) > rope1 ).
tff(match_rope,type,
match_rope1: ( ty * rope1 * uni * uni * uni ) > uni ).
tff(match_rope_sort2,axiom,
! [A: ty,X: rope1,X1: uni,X2: uni,X3: uni] : sort1(A,match_rope1(A,X,X1,X2,X3)) ).
tff(match_rope_Emp1,axiom,
! [A: ty,Z: uni,Z1: uni,Z2: uni] :
( sort1(A,Z)
=> ( match_rope1(A,emp1,Z,Z1,Z2) = Z ) ) ).
tff(match_rope_Str1,axiom,
! [A: ty,Z: uni,Z1: uni,Z2: uni,U: string2,U1: $int,U2: $int] :
( sort1(A,Z1)
=> ( match_rope1(A,str1(U,U1,U2),Z,Z1,Z2) = Z1 ) ) ).
tff(match_rope_App1,axiom,
! [A: ty,Z: uni,Z1: uni,Z2: uni,U: rope1,U1: rope1,U2: $int] :
( sort1(A,Z2)
=> ( match_rope1(A,app3(U,U1,U2),Z,Z1,Z2) = Z2 ) ) ).
tff(emp_Str1,axiom,
! [V: string2,V1: $int,V2: $int] : emp1 != str1(V,V1,V2) ).
tff(emp_App1,axiom,
! [V: rope1,V1: rope1,V2: $int] : emp1 != app3(V,V1,V2) ).
tff(str_App1,axiom,
! [U: string2,U1: $int,U2: $int,V: rope1,V1: rope1,V2: $int] : str1(U,U1,U2) != app3(V,V1,V2) ).
tff(str_proj_1,type,
str_proj_11: rope1 > string2 ).
tff(str_proj_1_def1,axiom,
! [U: string2,U1: $int,U2: $int] : str_proj_11(str1(U,U1,U2)) = U ).
tff(str_proj_2,type,
str_proj_21: rope1 > $int ).
tff(str_proj_2_def1,axiom,
! [U: string2,U1: $int,U2: $int] : str_proj_21(str1(U,U1,U2)) = U1 ).
tff(str_proj_3,type,
str_proj_31: rope1 > $int ).
tff(str_proj_3_def1,axiom,
! [U: string2,U1: $int,U2: $int] : str_proj_31(str1(U,U1,U2)) = U2 ).
tff(app_proj_1,type,
app_proj_11: rope1 > rope1 ).
tff(app_proj_1_def1,axiom,
! [U: rope1,U1: rope1,U2: $int] : app_proj_11(app3(U,U1,U2)) = U ).
tff(app_proj_2,type,
app_proj_21: rope1 > rope1 ).
tff(app_proj_2_def1,axiom,
! [U: rope1,U1: rope1,U2: $int] : app_proj_21(app3(U,U1,U2)) = U1 ).
tff(app_proj_3,type,
app_proj_31: rope1 > $int ).
tff(app_proj_3_def1,axiom,
! [U: rope1,U1: rope1,U2: $int] : app_proj_31(app3(U,U1,U2)) = U2 ).
tff(rope_inversion1,axiom,
! [U: rope1] :
( ( U = emp1 )
| ( U = str1(str_proj_11(U),str_proj_21(U),str_proj_31(U)) )
| ( U = app3(app_proj_11(U),app_proj_21(U),app_proj_31(U)) ) ) ).
tff(length1,type,
length4: rope1 > $int ).
tff(length_def,axiom,
( ( length4(emp1) = 0 )
& ! [X: string2,X1: $int,X2: $int] : length4(str1(X,X1,X2)) = X2
& ! [X: rope1,X1: rope1,X2: $int] : length4(app3(X,X1,X2)) = X2 ) ).
tff(inv,type,
inv1: rope1 > $o ).
tff(inv_def,axiom,
( inv1(emp1)
& ! [X: string2,X1: $int,X2: $int] :
( inv1(str1(X,X1,X2))
<=> ( $less(0,X2)
& $lesseq(0,X1)
& $less(X1,length3(X))
& $lesseq($sum(X1,X2),length3(X)) ) )
& ! [X: rope1,X1: rope1,X2: $int] :
( inv1(app3(X,X1,X2))
<=> ( $less(0,length4(X))
& inv1(X)
& $less(0,length4(X1))
& inv1(X1)
& ( X2 = $sum(length4(X),length4(X1)) ) ) ) ) ).
tff(string2,type,
string3: rope1 > string2 ).
tff(string_def,axiom,
( ( string3(emp1) = empty1 )
& ! [X: string2,X1: $int,X2: $int] : string3(str1(X,X1,X2)) = sub1(X,X1,X2)
& ! [X: rope1,X1: rope1,X2: $int] : string3(app3(X,X1,X2)) = app2(string3(X),string3(X1)) ) ).
tff(rope_length_is_string_length,axiom,
! [R: rope1] :
( inv1(R)
=> ( length3(string3(R)) = length4(R) ) ) ).
tff(fib,type,
fib1: $int > $int ).
tff(fib0,axiom,
fib1(0) = 0 ).
tff(fib1,axiom,
fib1(1) = 1 ).
tff(fibn,axiom,
! [N: $int] :
( $lesseq(2,N)
=> ( fib1(N) = $sum(fib1($difference(N,1)),fib1($difference(N,2))) ) ) ).
tff(min,type,
min1: ( $int * $int ) > $int ).
tff(max,type,
max2: ( $int * $int ) > $int ).
tff(max_is_ge,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,max2(X,Y))
& $lesseq(Y,max2(X,Y)) ) ).
tff(max_is_some,axiom,
! [X: $int,Y: $int] :
( ( max2(X,Y) = X )
| ( max2(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)
=> ( max2(X,Y) = X ) ) ).
tff(max_y,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> ( max2(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)
=> ( max2(X,Y) = max2(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(length2,type,
length5: ( ty * uni ) > $int ).
tff(length_def2,axiom,
! [A: ty,U: $int,U1: uni] : length5(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,length5(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,length5(A,A1),set(A,int,elts(A,A1),t2tb(I),V)) ).
tff(make,type,
make1: ( ty * $int * uni ) > uni ).
tff(make_sort1,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(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(mk_ref_sort1,axiom,
! [A: ty,X: uni] : sort1(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort1,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(max1,type,
max3: $int ).
tff(max_at_least_2,axiom,
$lesseq(2,max3) ).
tff(array_rope,type,
array_rope: $tType ).
tff(string_of_array,type,
string_of_array1: ( array_rope * $int * $int ) > string2 ).
tff(t2tb1,type,
t2tb1: array_rope > uni ).
tff(t2tb_sort1,axiom,
! [X: array_rope] : sort1(array(rope),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > array_rope ).
tff(bridgeL1,axiom,
! [I: array_rope] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(string_of_array_empty,axiom,
! [Q: array_rope,L: $int] :
( ( $lesseq(0,L)
& $lesseq(L,length5(rope,t2tb1(Q))) )
=> infix_eqeq1(string_of_array1(Q,L,L),empty1) ) ).
tff(t2tb2,type,
t2tb2: rope1 > uni ).
tff(t2tb_sort2,axiom,
! [X: rope1] : sort1(rope,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > rope1 ).
tff(bridgeL2,axiom,
! [I: rope1] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(string_of_array_concat_left,axiom,
! [Q: array_rope,L: $int,U: $int] :
( ( $lesseq(0,L)
& $less(L,U)
& $lesseq(U,length5(rope,t2tb1(Q))) )
=> infix_eqeq1(string_of_array1(Q,L,U),app2(string_of_array1(Q,$sum(L,1),U),string3(tb2t2(get2(rope,t2tb1(Q),L))))) ) ).
tff(string_of_array_concat,axiom,
! [Q: array_rope,L: $int,Mid: $int,U: $int] :
( ( $lesseq(0,length5(rope,t2tb1(Q)))
& $lesseq(0,L)
& $lesseq(L,Mid)
& $lesseq(Mid,U)
& $lesseq(U,length5(rope,t2tb1(Q))) )
=> infix_eqeq1(string_of_array1(Q,L,U),app2(string_of_array1(Q,Mid,U),string_of_array1(Q,L,Mid))) ) ).
tff(string_of_array_concat_right,axiom,
! [Q: array_rope,L: $int,U: $int] :
( ( $lesseq(0,length5(rope,t2tb1(Q)))
& $lesseq(0,L)
& $less(L,U)
& $lesseq(U,length5(rope,t2tb1(Q))) )
=> infix_eqeq1(string_of_array1(Q,L,U),app2(string3(tb2t2(get2(rope,t2tb1(Q),$difference(U,1)))),string_of_array1(Q,L,$difference(U,1)))) ) ).
tff(string_of_array_length,axiom,
! [Q: array_rope,L: $int,U: $int,I: $int] :
( ( $lesseq(0,length5(rope,t2tb1(Q)))
& $lesseq(0,L)
& $lesseq(L,I)
& $less(I,U)
& $lesseq(U,length5(rope,t2tb1(Q)))
& ! [J: $int] :
( ( $lesseq(L,J)
& $less(J,U) )
=> inv1(tb2t2(get2(rope,t2tb1(Q),J))) ) )
=> $lesseq(length3(string3(tb2t2(get2(rope,t2tb1(Q),I)))),length3(string_of_array1(Q,L,U))) ) ).
tff(string_of_array_eq,axiom,
! [Q1: array_rope,Q2: array_rope,L: $int,U: $int] :
( ( $lesseq(0,length5(rope,t2tb1(Q1)))
& $lesseq(0,length5(rope,t2tb1(Q2)))
& $lesseq(0,L)
& $lesseq(L,U)
& $lesseq(U,length5(rope,t2tb1(Q1)))
& ( length5(rope,t2tb1(Q1)) = length5(rope,t2tb1(Q2)) )
& ! [J: $int] :
( ( $lesseq(L,J)
& $less(J,U) )
=> ( tb2t2(get2(rope,t2tb1(Q1),J)) = tb2t2(get2(rope,t2tb1(Q2),J)) ) ) )
=> infix_eqeq1(string_of_array1(Q1,L,U),string_of_array1(Q2,L,U)) ) ).
tff(string_of_array_frame,axiom,
! [Q: array_rope,L: $int,U: $int] :
( ( $lesseq(0,L)
& $lesseq(L,U)
& $lesseq(U,length5(rope,t2tb1(Q))) )
=> ! [I: $int,R: rope1] :
( ( ( $lesseq(0,I)
& $less(I,L) )
| ( $lesseq(U,I)
& $less(I,length5(rope,t2tb1(Q))) ) )
=> infix_eqeq1(string_of_array1(Q,L,U),string_of_array1(tb2t1(set2(rope,t2tb1(Q),I,t2tb2(R))),L,U)) ) ) ).
tff(string_of_array_concat_empty,axiom,
! [Q: array_rope,L: $int,U: $int] :
( ( $lesseq(0,length5(rope,t2tb1(Q)))
& $lesseq(0,L)
& $lesseq(L,U)
& $lesseq(U,length5(rope,t2tb1(Q)))
& ! [J: $int] :
( ( $lesseq(L,J)
& $less(J,U) )
=> ( tb2t2(get2(rope,t2tb1(Q),J)) = emp1 ) ) )
=> infix_eqeq1(string_of_array1(Q,L,U),empty1) ) ).
tff(string_of_queue,type,
string_of_queue1: array_rope > string2 ).
tff(string_of_queue_def,axiom,
! [Q: array_rope] : string_of_queue1(Q) = string_of_array1(Q,2,length5(rope,t2tb1(Q))) ).
tff(map_int_rope,type,
map_int_rope: $tType ).
tff(t2tb3,type,
t2tb3: map_int_rope > uni ).
tff(t2tb_sort3,axiom,
! [X: map_int_rope] : sort1(map(int,rope),t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > map_int_rope ).
tff(bridgeL3,axiom,
! [I: map_int_rope] : tb2t3(t2tb3(I)) = I ).
tff(bridgeR3,axiom,
! [J: uni] : t2tb3(tb2t3(J)) = J ).
tff(wP_parameter_insert,conjecture,
! [Q: $int,Q1: map_int_rope,I: $int,R: rope1] :
( ( $lesseq(0,Q)
& $lesseq(2,I)
& $less(I,Q)
& ( Q = $sum(max3,1) )
& inv1(R)
& ! [J: $int] :
( ( $lesseq(2,J)
& $lesseq(J,max3) )
=> inv1(tb2t2(get(rope,int,t2tb3(Q1),t2tb(J)))) )
& $less($sum(length3(string_of_array1(tb2t1(mk_array1(rope,Q,t2tb3(Q1))),I,$sum(max3,1))),tb2t(match_rope1(int,R,t2tb(0),t2tb(str_proj_31(R)),t2tb(app_proj_31(R))))),fib1($sum(max3,1))) )
=> ( ( $lesseq(0,I)
& $less(I,Q) )
=> ( ( inv1(tb2t2(get(rope,int,t2tb3(Q1),t2tb(I))))
& inv1(R) )
=> ! [Rqt: rope1] :
( ( inv1(Rqt)
& infix_eqeq1(string3(Rqt),app2(string3(tb2t2(get(rope,int,t2tb3(Q1),t2tb(I)))),string3(R))) )
=> ( $less(tb2t(match_rope1(int,Rqt,t2tb(0),t2tb(str_proj_31(Rqt)),t2tb(app_proj_31(Rqt)))),fib1($sum(I,1)))
=> ( ( $lesseq(0,I)
& $less(I,Q) )
=> ! [Q2: map_int_rope] :
( ( $lesseq(0,Q)
& ( Q2 = tb2t3(set(rope,int,t2tb3(Q1),t2tb(I),t2tb2(Rqt))) ) )
=> ( infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope,Q,t2tb3(Q2))),$sum(I,1),$sum(max3,1)),string_of_array1(tb2t1(mk_array1(rope,Q,t2tb3(Q1))),$sum(I,1),$sum(max3,1)))
=> infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope,Q,t2tb3(Q2))),I,$sum(max3,1)),app2(string_of_array1(tb2t1(mk_array1(rope,Q,t2tb3(Q1))),I,$sum(max3,1)),string3(R))) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------