TPTP Problem File: SWW661_2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW661_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Verifythis fm2012 treedel-T-inorder zip
% 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 : verifythis_fm2012_treedel-T-inorder_zip [Fil14]
% Status : Theorem
% Rating : 0.62 v8.2.0, 0.75 v7.5.0, 0.80 v7.4.0, 0.62 v7.3.0, 0.50 v7.1.0, 0.67 v7.0.0, 0.71 v6.4.0, 1.00 v6.3.0, 0.86 v6.2.0, 0.88 v6.1.0
% Syntax : Number of formulae : 188 ( 70 unt; 81 typ; 0 def)
% Number of atoms : 177 ( 84 equ)
% Maximal formula atoms : 10 ( 0 avg)
% Number of connectives : 81 ( 11 ~; 9 |; 19 &)
% ( 3 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number arithmetic : 19 ( 4 atm; 4 fun; 5 num; 6 var)
% Number of types : 14 ( 12 usr; 1 ari)
% Number of type conns : 114 ( 57 >; 57 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 0 prp; 2-3 aty)
% Number of functors : 69 ( 65 usr; 14 con; 0-5 aty)
% Number of variables : 297 ( 287 !; 10 ?; 297 :)
% 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(map,type,
map: ( ty * ty ) > ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(get_sort1,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_sort1,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(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_def,axiom,
! [A: ty,U: uni] :
( sort1(A,U)
=> ( contents(A,mk_ref(A,U)) = U ) ) ).
tff(ref_inversion,axiom,
! [A: ty,U: uni] :
( sort1(ref(A),U)
=> ( U = mk_ref(A,contents(A,U)) ) ) ).
tff(loc,type,
loc1: $tType ).
tff(loc1,type,
loc: ty ).
tff(null,type,
null1: loc1 ).
tff(node1,type,
node2: $tType ).
tff(node2,type,
node: ty ).
tff(mk_node,type,
mk_node1: ( loc1 * loc1 * $int ) > node2 ).
tff(left,type,
left2: node2 > loc1 ).
tff(left_def,axiom,
! [U: loc1,U1: loc1,U2: $int] : left2(mk_node1(U,U1,U2)) = U ).
tff(right,type,
right1: node2 > loc1 ).
tff(right_def,axiom,
! [U: loc1,U1: loc1,U2: $int] : right1(mk_node1(U,U1,U2)) = U1 ).
tff(data,type,
data1: node2 > $int ).
tff(data_def,axiom,
! [U: loc1,U1: loc1,U2: $int] : data1(mk_node1(U,U1,U2)) = U2 ).
tff(node_inversion,axiom,
! [U: node2] : U = mk_node1(left2(U),right1(U),data1(U)) ).
tff(tree,type,
tree: ty > ty ).
tff(empty,type,
empty: ty > uni ).
tff(empty_sort1,axiom,
! [A: ty] : sort1(tree(A),empty(A)) ).
tff(node3,type,
node1: ( ty * uni * uni * uni ) > uni ).
tff(node_sort1,axiom,
! [A: ty,X: uni,X1: uni,X2: uni] : sort1(tree(A),node1(A,X,X1,X2)) ).
tff(match_tree,type,
match_tree: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_tree_sort1,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort1(A1,match_tree(A1,A,X,X1,X2)) ).
tff(match_tree_Empty,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort1(A1,Z)
=> ( match_tree(A1,A,empty(A),Z,Z1) = Z ) ) ).
tff(match_tree_Node,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni,U1: uni,U2: uni] :
( sort1(A1,Z1)
=> ( match_tree(A1,A,node1(A,U,U1,U2),Z,Z1) = Z1 ) ) ).
tff(empty_Node,axiom,
! [A: ty,V: uni,V1: uni,V2: uni] : empty(A) != node1(A,V,V1,V2) ).
tff(node_proj_1,type,
node_proj_1: ( ty * uni ) > uni ).
tff(node_proj_1_sort1,axiom,
! [A: ty,X: uni] : sort1(tree(A),node_proj_1(A,X)) ).
tff(node_proj_1_def,axiom,
! [A: ty,U: uni,U1: uni,U2: uni] : node_proj_1(A,node1(A,U,U1,U2)) = U ).
tff(node_proj_2,type,
node_proj_2: ( ty * uni ) > uni ).
tff(node_proj_2_sort1,axiom,
! [A: ty,X: uni] : sort1(A,node_proj_2(A,X)) ).
tff(node_proj_2_def,axiom,
! [A: ty,U: uni,U1: uni,U2: uni] :
( sort1(A,U1)
=> ( node_proj_2(A,node1(A,U,U1,U2)) = U1 ) ) ).
tff(node_proj_3,type,
node_proj_3: ( ty * uni ) > uni ).
tff(node_proj_3_sort1,axiom,
! [A: ty,X: uni] : sort1(tree(A),node_proj_3(A,X)) ).
tff(node_proj_3_def,axiom,
! [A: ty,U: uni,U1: uni,U2: uni] : node_proj_3(A,node1(A,U,U1,U2)) = U2 ).
tff(tree_inversion,axiom,
! [A: ty,U: uni] :
( ( U = empty(A) )
| ( U = node1(A,node_proj_1(A,U),node_proj_2(A,U),node_proj_3(A,U)) ) ) ).
tff(list,type,
list: ty > ty ).
tff(nil,type,
nil: ty > uni ).
tff(nil_sort1,axiom,
! [A: ty] : sort1(list(A),nil(A)) ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(cons_sort1,axiom,
! [A: ty,X: uni,X1: uni] : sort1(list(A),cons(A,X,X1)) ).
tff(match_list,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_list_sort1,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort1(A1,match_list(A1,A,X,X1,X2)) ).
tff(match_list_Nil,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort1(A1,Z)
=> ( match_list(A1,A,nil(A),Z,Z1) = Z ) ) ).
tff(match_list_Cons,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni,U1: uni] :
( sort1(A1,Z1)
=> ( match_list(A1,A,cons(A,U,U1),Z,Z1) = Z1 ) ) ).
tff(nil_Cons,axiom,
! [A: ty,V: uni,V1: uni] : nil(A) != cons(A,V,V1) ).
tff(cons_proj_1,type,
cons_proj_1: ( ty * uni ) > uni ).
tff(cons_proj_1_sort1,axiom,
! [A: ty,X: uni] : sort1(A,cons_proj_1(A,X)) ).
tff(cons_proj_1_def,axiom,
! [A: ty,U: uni,U1: uni] :
( sort1(A,U)
=> ( cons_proj_1(A,cons(A,U,U1)) = U ) ) ).
tff(cons_proj_2,type,
cons_proj_2: ( ty * uni ) > uni ).
tff(cons_proj_2_sort1,axiom,
! [A: ty,X: uni] : sort1(list(A),cons_proj_2(A,X)) ).
tff(cons_proj_2_def,axiom,
! [A: ty,U: uni,U1: uni] : cons_proj_2(A,cons(A,U,U1)) = U1 ).
tff(list_inversion,axiom,
! [A: ty,U: uni] :
( ( U = nil(A) )
| ( U = cons(A,cons_proj_1(A,U),cons_proj_2(A,U)) ) ) ).
tff(infix_plpl,type,
infix_plpl: ( ty * uni * uni ) > uni ).
tff(infix_plpl_sort1,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(compatOrderMult,axiom,
! [X: $int,Y: $int,Z: $int] :
( $lesseq(X,Y)
=> ( $lesseq(0,Z)
=> $lesseq($product(X,Z),$product(Y,Z)) ) ) ).
tff(length,type,
length1: ( ty * uni ) > $int ).
tff(length_def,axiom,
! [A: ty] :
( ( length1(A,nil(A)) = 0 )
& ! [X: uni,X1: uni] : length1(A,cons(A,X,X1)) = $sum(1,length1(A,X1)) ) ).
tff(length_nonnegative,axiom,
! [A: ty,L: uni] : $lesseq(0,length1(A,L)) ).
tff(length_nil,axiom,
! [A: ty,L: uni] :
( ( length1(A,L) = 0 )
<=> ( L = nil(A) ) ) ).
tff(append_length,axiom,
! [A: ty,L1: uni,L2: uni] : length1(A,infix_plpl(A,L1,L2)) = $sum(length1(A,L1),length1(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(inorder,type,
inorder: ( ty * uni ) > uni ).
tff(inorder_sort1,axiom,
! [A: ty,X: uni] : sort1(list(A),inorder(A,X)) ).
tff(inorder_def,axiom,
! [A: ty] :
( ( inorder(A,empty(A)) = nil(A) )
& ! [X: uni,X1: uni,X2: uni] : inorder(A,node1(A,X,X1,X2)) = infix_plpl(A,inorder(A,X),cons(A,X1,inorder(A,X2))) ) ).
tff(distinct,type,
distinct: ( ty * uni ) > $o ).
tff(distinct_zero,axiom,
! [A: ty] : distinct(A,nil(A)) ).
tff(distinct_one,axiom,
! [A: ty,X: uni] : distinct(A,cons(A,X,nil(A))) ).
tff(distinct_many,axiom,
! [A: ty,X: uni,L: uni] :
( ~ mem(A,X,L)
=> ( distinct(A,L)
=> distinct(A,cons(A,X,L)) ) ) ).
tff(distinct_inversion,axiom,
! [A: ty,Z: uni] :
( distinct(A,Z)
=> ( ( Z = nil(A) )
| ? [X: uni] :
( sort1(A,X)
& ( Z = cons(A,X,nil(A)) ) )
| ? [X: uni,L: uni] :
( sort1(A,X)
& sort1(list(A),L)
& ~ mem(A,X,L)
& distinct(A,L)
& ( Z = cons(A,X,L) ) ) ) ) ).
tff(distinct_append,axiom,
! [A: ty,L1: uni,L2: uni] :
( distinct(A,L1)
=> ( distinct(A,L2)
=> ( ! [X: uni] :
( sort1(A,X)
=> ( mem(A,X,L1)
=> ~ mem(A,X,L2) ) )
=> distinct(A,infix_plpl(A,L1,L2)) ) ) ) ).
tff(tree_loc,type,
tree_loc: $tType ).
tff(map_loc_node,type,
map_loc_node: $tType ).
tff(istree,type,
istree1: ( map_loc_node * loc1 * tree_loc ) > $o ).
tff(t2tb,type,
t2tb: tree_loc > uni ).
tff(t2tb_sort,axiom,
! [X: tree_loc] : sort1(tree(loc),t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > tree_loc ).
tff(bridgeL,axiom,
! [I: tree_loc] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] : t2tb(tb2t(J)) = J ).
tff(leaf,axiom,
! [M: map_loc_node] : istree1(M,null1,tb2t(empty(loc))) ).
tff(t2tb1,type,
t2tb1: map_loc_node > uni ).
tff(t2tb_sort1,axiom,
! [X: map_loc_node] : sort1(map(loc,node),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > map_loc_node ).
tff(bridgeL1,axiom,
! [I: map_loc_node] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(t2tb2,type,
t2tb2: node2 > uni ).
tff(t2tb_sort2,axiom,
! [X: node2] : sort1(node,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > node2 ).
tff(bridgeL2,axiom,
! [I: node2] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(t2tb3,type,
t2tb3: loc1 > uni ).
tff(t2tb_sort3,axiom,
! [X: loc1] : sort1(loc,t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > loc1 ).
tff(bridgeL3,axiom,
! [I: loc1] : tb2t3(t2tb3(I)) = I ).
tff(bridgeR3,axiom,
! [J: uni] :
( sort1(loc,J)
=> ( t2tb3(tb2t3(J)) = J ) ) ).
tff(node,axiom,
! [M: map_loc_node,P: loc1,L: tree_loc,R: tree_loc] :
( ( P != null1 )
=> ( istree1(M,left2(tb2t2(get(node,loc,t2tb1(M),t2tb3(P)))),L)
=> ( istree1(M,right1(tb2t2(get(node,loc,t2tb1(M),t2tb3(P)))),R)
=> istree1(M,P,tb2t(node1(loc,t2tb(L),t2tb3(P),t2tb(R)))) ) ) ) ).
tff(istree_inversion,axiom,
! [Z: map_loc_node,Z1: loc1,Z2: tree_loc] :
( istree1(Z,Z1,Z2)
=> ( ? [M: map_loc_node] :
( ( Z = M )
& ( Z1 = null1 )
& ( Z2 = tb2t(empty(loc)) ) )
| ? [M: map_loc_node,P: loc1,L: tree_loc,R: tree_loc] :
( ( P != null1 )
& istree1(M,left2(tb2t2(get(node,loc,t2tb1(M),t2tb3(P)))),L)
& istree1(M,right1(tb2t2(get(node,loc,t2tb1(M),t2tb3(P)))),R)
& ( Z = M )
& ( Z1 = P )
& ( Z2 = tb2t(node1(loc,t2tb(L),t2tb3(P),t2tb(R))) ) ) ) ) ).
tff(zipper,type,
zipper: ty > ty ).
tff(top,type,
top: ty > uni ).
tff(top_sort1,axiom,
! [A: ty] : sort1(zipper(A),top(A)) ).
tff(left1,type,
left1: ( ty * uni * uni * uni ) > uni ).
tff(left_sort2,axiom,
! [A: ty,X: uni,X1: uni,X2: uni] : sort1(zipper(A),left1(A,X,X1,X2)) ).
tff(match_zipper,type,
match_zipper1: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_zipper_sort1,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort1(A1,match_zipper1(A1,A,X,X1,X2)) ).
tff(match_zipper_Top1,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort1(A1,Z)
=> ( match_zipper1(A1,A,top(A),Z,Z1) = Z ) ) ).
tff(match_zipper_Left1,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni,U1: uni,U2: uni] :
( sort1(A1,Z1)
=> ( match_zipper1(A1,A,left1(A,U,U1,U2),Z,Z1) = Z1 ) ) ).
tff(top_Left1,axiom,
! [A: ty,V: uni,V1: uni,V2: uni] : top(A) != left1(A,V,V1,V2) ).
tff(left_proj_1,type,
left_proj_11: ( ty * uni ) > uni ).
tff(left_proj_1_sort1,axiom,
! [A: ty,X: uni] : sort1(zipper(A),left_proj_11(A,X)) ).
tff(left_proj_1_def1,axiom,
! [A: ty,U: uni,U1: uni,U2: uni] : left_proj_11(A,left1(A,U,U1,U2)) = U ).
tff(left_proj_2,type,
left_proj_21: ( ty * uni ) > uni ).
tff(left_proj_2_sort1,axiom,
! [A: ty,X: uni] : sort1(A,left_proj_21(A,X)) ).
tff(left_proj_2_def1,axiom,
! [A: ty,U: uni,U1: uni,U2: uni] :
( sort1(A,U1)
=> ( left_proj_21(A,left1(A,U,U1,U2)) = U1 ) ) ).
tff(left_proj_3,type,
left_proj_31: ( ty * uni ) > uni ).
tff(left_proj_3_sort1,axiom,
! [A: ty,X: uni] : sort1(tree(A),left_proj_31(A,X)) ).
tff(left_proj_3_def1,axiom,
! [A: ty,U: uni,U1: uni,U2: uni] : left_proj_31(A,left1(A,U,U1,U2)) = U2 ).
tff(zipper_inversion1,axiom,
! [A: ty,U: uni] :
( ( U = top(A) )
| ( U = left1(A,left_proj_11(A,U),left_proj_21(A,U),left_proj_31(A,U)) ) ) ).
tff(zip,type,
zip: ( ty * uni * uni ) > uni ).
tff(zip_sort1,axiom,
! [A: ty,X: uni,X1: uni] : sort1(tree(A),zip(A,X,X1)) ).
tff(zip_def,axiom,
! [A: ty,T: uni] :
( ( zip(A,T,top(A)) = T )
& ! [X: uni,X1: uni,X2: uni] : zip(A,T,left1(A,X,X1,X2)) = zip(A,node1(A,T,X1,X2),X) ) ).
tff(a,type,
a1: $tType ).
tff(a1,type,
a: ty ).
tff(zipper_a,type,
zipper_a: $tType ).
tff(t2tb4,type,
t2tb4: zipper_a > uni ).
tff(t2tb_sort4,axiom,
! [X: zipper_a] : sort1(zipper(a),t2tb4(X)) ).
tff(tb2t4,type,
tb2t4: uni > zipper_a ).
tff(bridgeL4,axiom,
! [I: zipper_a] : tb2t4(t2tb4(I)) = I ).
tff(bridgeR4,axiom,
! [J: uni] : t2tb4(tb2t4(J)) = J ).
tff(t2tb5,type,
t2tb5: a1 > uni ).
tff(t2tb_sort5,axiom,
! [X: a1] : sort1(a,t2tb5(X)) ).
tff(tb2t5,type,
tb2t5: uni > a1 ).
tff(bridgeL5,axiom,
! [I: a1] : tb2t5(t2tb5(I)) = I ).
tff(bridgeR5,axiom,
! [J: uni] :
( sort1(a,J)
=> ( t2tb5(tb2t5(J)) = J ) ) ).
tff(list_a,type,
list_a: $tType ).
tff(t2tb6,type,
t2tb6: list_a > uni ).
tff(t2tb_sort6,axiom,
! [X: list_a] : sort1(list(a),t2tb6(X)) ).
tff(tb2t6,type,
tb2t6: uni > list_a ).
tff(bridgeL6,axiom,
! [I: list_a] : tb2t6(t2tb6(I)) = I ).
tff(bridgeR6,axiom,
! [J: uni] : t2tb6(tb2t6(J)) = J ).
tff(tree_a,type,
tree_a: $tType ).
tff(t2tb7,type,
t2tb7: tree_a > uni ).
tff(t2tb_sort7,axiom,
! [X: tree_a] : sort1(tree(a),t2tb7(X)) ).
tff(tb2t7,type,
tb2t7: uni > tree_a ).
tff(bridgeL7,axiom,
! [I: tree_a] : tb2t7(t2tb7(I)) = I ).
tff(bridgeR7,axiom,
! [J: uni] : t2tb7(tb2t7(J)) = J ).
tff(inorder_zip,conjecture,
! [X: zipper_a,X1: a1,X2: tree_a] :
( ! [X3: a1,L: tree_a,R: tree_a] : tb2t6(inorder(a,zip(a,node1(a,t2tb7(L),t2tb5(X3),t2tb7(R)),t2tb4(X)))) = tb2t6(infix_plpl(a,inorder(a,t2tb7(L)),cons(a,t2tb5(X3),inorder(a,zip(a,t2tb7(R),t2tb4(X))))))
=> ! [X3: a1,L: tree_a,R: tree_a] : tb2t6(inorder(a,zip(a,node1(a,t2tb7(L),t2tb5(X3),t2tb7(R)),left1(a,t2tb4(X),t2tb5(X1),t2tb7(X2))))) = tb2t6(infix_plpl(a,inorder(a,t2tb7(L)),cons(a,t2tb5(X3),inorder(a,zip(a,t2tb7(R),left1(a,t2tb4(X),t2tb5(X1),t2tb7(X2))))))) ) ).
%------------------------------------------------------------------------------