TPTP Problem File: SWW603_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW603_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Generate all trees-T-WP parameter combine
% 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 : generate_all_trees-T-WP_parameter_combine [Fil14]
% Status : Theorem
% Rating : 0.75 v8.2.0, 0.88 v7.5.0, 0.90 v7.4.0, 0.88 v7.3.0, 0.83 v7.0.0, 0.86 v6.4.0, 1.00 v6.3.0, 0.86 v6.2.0, 1.00 v6.1.0
% Syntax : Number of formulae : 127 ( 46 unt; 52 typ; 0 def)
% Number of atoms : 146 ( 60 equ)
% Maximal formula atoms : 18 ( 1 avg)
% Number of connectives : 81 ( 10 ~; 7 |; 21 &)
% ( 7 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 44 ( 9 atm; 6 fun; 12 num; 17 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 80 ( 36 >; 44 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 0 prp; 2-3 aty)
% Number of functors : 46 ( 42 usr; 12 con; 0-5 aty)
% Number of variables : 217 ( 207 !; 10 ?; 217 :)
% 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(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_list1: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_list_sort1,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_sort1,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_sort1,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(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(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(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(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_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(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(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(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_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,length3(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,length3(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(tree,type,
tree1: $tType ).
tff(tree1,type,
tree: ty ).
tff(empty,type,
empty1: tree1 ).
tff(node,type,
node1: ( tree1 * tree1 ) > tree1 ).
tff(match_tree,type,
match_tree1: ( ty * tree1 * uni * uni ) > uni ).
tff(match_tree_sort1,axiom,
! [A: ty,X: tree1,X1: uni,X2: uni] : sort1(A,match_tree1(A,X,X1,X2)) ).
tff(match_tree_Empty1,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z)
=> ( match_tree1(A,empty1,Z,Z1) = Z ) ) ).
tff(match_tree_Node1,axiom,
! [A: ty,Z: uni,Z1: uni,U: tree1,U1: tree1] :
( sort1(A,Z1)
=> ( match_tree1(A,node1(U,U1),Z,Z1) = Z1 ) ) ).
tff(empty_Node1,axiom,
! [V: tree1,V1: tree1] : empty1 != node1(V,V1) ).
tff(node_proj_1,type,
node_proj_11: tree1 > tree1 ).
tff(node_proj_1_def1,axiom,
! [U: tree1,U1: tree1] : node_proj_11(node1(U,U1)) = U ).
tff(node_proj_2,type,
node_proj_21: tree1 > tree1 ).
tff(node_proj_2_def1,axiom,
! [U: tree1,U1: tree1] : node_proj_21(node1(U,U1)) = U1 ).
tff(tree_inversion1,axiom,
! [U: tree1] :
( ( U = empty1 )
| ( U = node1(node_proj_11(U),node_proj_21(U)) ) ) ).
tff(size,type,
size1: tree1 > $int ).
tff(size_def,axiom,
( ( size1(empty1) = 0 )
& ! [X: tree1,X1: tree1] : size1(node1(X,X1)) = $sum($sum(1,size1(X)),size1(X1)) ) ).
tff(size_nonneg,axiom,
! [T: tree1] : $lesseq(0,size1(T)) ).
tff(size_left,axiom,
! [T: tree1] :
( $less(0,size1(T))
=> ? [L: tree1,R: tree1] :
( ( T = node1(L,R) )
& $less(size1(L),size1(T)) ) ) ).
tff(list_tree,type,
list_tree: $tType ).
tff(all_trees,type,
all_trees1: ( $int * list_tree ) > $o ).
tff(t2tb1,type,
t2tb1: list_tree > uni ).
tff(t2tb_sort1,axiom,
! [X: list_tree] : sort1(list(tree),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > list_tree ).
tff(bridgeL1,axiom,
! [I: list_tree] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(t2tb2,type,
t2tb2: tree1 > uni ).
tff(t2tb_sort2,axiom,
! [X: tree1] : sort1(tree,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > tree1 ).
tff(bridgeL2,axiom,
! [I: tree1] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(all_trees_def,axiom,
! [N: $int,L: list_tree] :
( all_trees1(N,L)
<=> ( distinct(tree,t2tb1(L))
& ! [T: tree1] :
( ( size1(T) = N )
<=> mem(tree,t2tb2(T),t2tb1(L)) ) ) ) ).
tff(all_trees_0,axiom,
all_trees1(0,tb2t1(cons(tree,t2tb2(empty1),nil(tree)))) ).
tff(tree_diff,axiom,
! [L1: tree1,L2: tree1] :
( ( size1(L1) != size1(L2) )
=> ! [R1: tree1,R2: tree1] : node1(L1,R1) != node1(L2,R2) ) ).
tff(wP_parameter_combine,conjecture,
! [I1: $int,L1: list_tree,I2: $int,L2: list_tree] :
( ( $lesseq(0,I1)
& all_trees1(I1,L1)
& $lesseq(0,I2)
& all_trees1(I2,L2) )
=> ! [L11: list_tree] :
( distinct(tree,t2tb1(L11))
=> ! [X: tree1,X1: list_tree] :
( ( L11 = tb2t1(cons(tree,t2tb2(X),t2tb1(X1))) )
=> ( distinct(tree,t2tb1(X1))
=> ! [O: list_tree] :
( ( distinct(tree,t2tb1(O))
& ! [T: tree1] :
( mem(tree,t2tb2(T),t2tb1(O))
<=> ? [L: tree1,R: tree1] :
( ( T = node1(L,R) )
& mem(tree,t2tb2(L),t2tb1(X1))
& mem(tree,t2tb2(R),t2tb1(L2)) ) ) )
=> ( distinct(tree,t2tb1(L2))
=> ! [O1: list_tree] :
( ( distinct(tree,t2tb1(O1))
& ! [T: tree1] :
( mem(tree,t2tb2(T),t2tb1(O1))
<=> ? [R: tree1] :
( ( T = node1(X,R) )
& mem(tree,t2tb2(R),t2tb1(L2)) ) ) )
=> distinct(tree,infix_plpl(tree,t2tb1(O1),t2tb1(O))) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------