TPTP Problem File: SWW593_2.p
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%------------------------------------------------------------------------------
% File : SWW593_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Fill-T-WP parameter fill
% 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 : fill-T-WP_parameter_fill [Fil14]
% Status : Theorem
% Rating : 0.62 v8.2.0, 0.75 v7.5.0, 0.70 v7.4.0, 0.50 v7.3.0, 0.33 v7.0.0, 0.57 v6.4.0, 0.33 v6.3.0, 0.71 v6.2.0, 0.62 v6.1.0
% Syntax : Number of formulae : 88 ( 29 unt; 44 typ; 0 def)
% Number of atoms : 126 ( 49 equ)
% Maximal formula atoms : 62 ( 1 avg)
% Number of connectives : 91 ( 9 ~; 6 |; 41 &)
% ( 1 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 95 ( 43 atm; 7 fun; 18 num; 27 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 57 ( 26 >; 31 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 0 prp; 2-2 aty)
% Number of functors : 39 ( 35 usr; 13 con; 0-5 aty)
% Number of variables : 143 ( 143 !; 0 ?; 143 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
%------------------------------------------------------------------------------
tff(uni,type,
uni: $tType ).
tff(ty,type,
ty: $tType ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(witness,type,
witness: ty > uni ).
tff(witness_sort,axiom,
! [A: ty] : sort(A,witness(A)) ).
tff(int,type,
int: ty ).
tff(real,type,
real: ty ).
tff(bool,type,
bool: $tType ).
tff(bool1,type,
bool1: ty ).
tff(true,type,
true: bool ).
tff(false,type,
false: bool ).
tff(match_bool,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(match_bool_sort,axiom,
! [A: ty,X: bool,X1: uni,X2: uni] : sort(A,match_bool(A,X,X1,X2)) ).
tff(match_bool_True,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z)
=> ( match_bool(A,true,Z,Z1) = Z ) ) ).
tff(match_bool_False,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z1)
=> ( match_bool(A,false,Z,Z1) = Z1 ) ) ).
tff(true_False,axiom,
true != false ).
tff(bool_inversion,axiom,
! [U: bool] :
( ( U = true )
| ( U = false ) ) ).
tff(tuple0,type,
tuple0: $tType ).
tff(tuple01,type,
tuple01: ty ).
tff(tuple02,type,
tuple02: tuple0 ).
tff(tuple0_inversion,axiom,
! [U: tuple0] : U = tuple02 ).
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(map,type,
map: ( ty * ty ) > ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(get_sort,axiom,
! [A: ty,B: ty,X: uni,X1: uni] : sort(B,get(B,A,X,X1)) ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(set_sort,axiom,
! [A: ty,B: ty,X: uni,X1: uni,X2: uni] : sort(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] :
( sort(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] :
( sort(A,A1)
=> ( sort(A,A2)
=> ! [B1: uni] :
( ( A1 != A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = get(B,A,M,A2) ) ) ) ) ).
tff(const,type,
const: ( ty * ty * uni ) > uni ).
tff(const_sort,axiom,
! [A: ty,B: ty,X: uni] : sort(map(A,B),const(B,A,X)) ).
tff(const1,axiom,
! [A: ty,B: ty,B1: uni,A1: uni] :
( sort(B,B1)
=> ( get(B,A,const(B,A,B1),A1) = B1 ) ) ).
tff(array,type,
array: ty > ty ).
tff(mk_array,type,
mk_array: ( ty * $int * uni ) > uni ).
tff(mk_array_sort,axiom,
! [A: ty,X: $int,X1: uni] : sort(array(A),mk_array(A,X,X1)) ).
tff(length,type,
length: ( ty * uni ) > $int ).
tff(length_def,axiom,
! [A: ty,U: $int,U1: uni] : length(A,mk_array(A,U,U1)) = U ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(elts_sort,axiom,
! [A: ty,X: uni] : sort(map(int,A),elts(A,X)) ).
tff(elts_def,axiom,
! [A: ty,U: $int,U1: uni] :
( sort(map(int,A),U1)
=> ( elts(A,mk_array(A,U,U1)) = U1 ) ) ).
tff(array_inversion,axiom,
! [A: ty,U: uni] : U = mk_array(A,length(A,U),elts(A,U)) ).
tff(get1,type,
get1: ( ty * uni * $int ) > uni ).
tff(get_sort1,axiom,
! [A: ty,X: uni,X1: $int] : sort(A,get1(A,X,X1)) ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(t2tb_sort,axiom,
! [X: $int] : sort(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] : get1(A,A1,I) = get(A,int,elts(A,A1),t2tb(I)) ).
tff(set1,type,
set1: ( ty * uni * $int * uni ) > uni ).
tff(set_sort1,axiom,
! [A: ty,X: uni,X1: $int,X2: uni] : sort(array(A),set1(A,X,X1,X2)) ).
tff(set_def,axiom,
! [A: ty,A1: uni,I: $int,V: uni] : set1(A,A1,I,V) = mk_array(A,length(A,A1),set(A,int,elts(A,A1),t2tb(I),V)) ).
tff(make,type,
make: ( ty * $int * uni ) > uni ).
tff(make_sort,axiom,
! [A: ty,X: $int,X1: uni] : sort(array(A),make(A,X,X1)) ).
tff(make_def,axiom,
! [A: ty,N: $int,V: uni] : make(A,N,V) = mk_array(A,N,const(A,int,V)) ).
tff(elt,type,
elt: $tType ).
tff(elt1,type,
elt1: ty ).
tff(tree,type,
tree: $tType ).
tff(tree1,type,
tree1: ty ).
tff(null,type,
null: tree ).
tff(node,type,
node: ( tree * elt * tree ) > tree ).
tff(match_tree,type,
match_tree: ( ty * tree * uni * uni ) > uni ).
tff(match_tree_sort,axiom,
! [A: ty,X: tree,X1: uni,X2: uni] : sort(A,match_tree(A,X,X1,X2)) ).
tff(match_tree_Null,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z)
=> ( match_tree(A,null,Z,Z1) = Z ) ) ).
tff(match_tree_Node,axiom,
! [A: ty,Z: uni,Z1: uni,U: tree,U1: elt,U2: tree] :
( sort(A,Z1)
=> ( match_tree(A,node(U,U1,U2),Z,Z1) = Z1 ) ) ).
tff(null_Node,axiom,
! [V: tree,V1: elt,V2: tree] : null != node(V,V1,V2) ).
tff(node_proj_1,type,
node_proj_1: tree > tree ).
tff(node_proj_1_def,axiom,
! [U: tree,U1: elt,U2: tree] : node_proj_1(node(U,U1,U2)) = U ).
tff(node_proj_2,type,
node_proj_2: tree > elt ).
tff(node_proj_2_def,axiom,
! [U: tree,U1: elt,U2: tree] : node_proj_2(node(U,U1,U2)) = U1 ).
tff(node_proj_3,type,
node_proj_3: tree > tree ).
tff(node_proj_3_def,axiom,
! [U: tree,U1: elt,U2: tree] : node_proj_3(node(U,U1,U2)) = U2 ).
tff(tree_inversion,axiom,
! [U: tree] :
( ( U = null )
| ( U = node(node_proj_1(U),node_proj_2(U),node_proj_3(U)) ) ) ).
tff(contains,type,
contains: ( tree * elt ) > $o ).
tff(contains_def,axiom,
! [X: elt] :
( ~ contains(null,X)
& ! [X1: tree,X2: elt,X3: tree] :
( contains(node(X1,X2,X3),X)
<=> ( contains(X1,X)
| ( X = X2 )
| contains(X3,X) ) ) ) ).
tff(t2tb1,type,
t2tb1: elt > uni ).
tff(t2tb_sort1,axiom,
! [X: elt] : sort(elt1,t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > elt ).
tff(bridgeL1,axiom,
! [I: elt] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] :
( sort(elt1,J)
=> ( t2tb1(tb2t1(J)) = J ) ) ).
tff(map_int_elt,type,
map_int_elt: $tType ).
tff(t2tb2,type,
t2tb2: map_int_elt > uni ).
tff(t2tb_sort2,axiom,
! [X: map_int_elt] : sort(map(int,elt1),t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > map_int_elt ).
tff(bridgeL2,axiom,
! [I: map_int_elt] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] :
( sort(map(int,elt1),J)
=> ( t2tb2(tb2t2(J)) = J ) ) ).
tff(wP_parameter_fill,conjecture,
! [T: tree,A: $int,A1: map_int_elt,Start: $int] :
( ( $lesseq(0,A)
& $lesseq(0,Start)
& $lesseq(Start,A) )
=> ( ( ( T = null )
=> ( $lesseq(Start,Start)
& $lesseq(Start,A)
& ! [I: $int] :
( ( $lesseq(Start,I)
& $less(I,Start) )
=> contains(T,tb2t1(get(elt1,int,t2tb2(A1),t2tb(I)))) ) ) )
& ! [X: tree,X1: elt,X2: tree] :
( ( T = node(X,X1,X2) )
=> ( ( T != null )
& ! [X3: tree,X4: elt,X5: tree] :
( ( T = node(X3,X4,X5) )
=> ( ( X3 = X )
| ( X5 = X ) ) )
& $lesseq(0,Start)
& $lesseq(Start,A)
& ! [A2: map_int_elt,Res: $int] :
( ( $lesseq(0,A)
& $lesseq(Start,Res)
& $lesseq(Res,A)
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,Start) )
=> ( tb2t1(get(elt1,int,t2tb2(A2),t2tb(I))) = tb2t1(get(elt1,int,t2tb2(A1),t2tb(I))) ) )
& ! [I: $int] :
( ( $lesseq(Start,I)
& $less(I,Res) )
=> contains(X,tb2t1(get(elt1,int,t2tb2(A2),t2tb(I)))) ) )
=> ( ( ( Res != A )
=> ( $lesseq(0,Res)
& $less(Res,A)
& ! [A3: map_int_elt] :
( ( $lesseq(0,A)
& ( A3 = tb2t2(set(elt1,int,t2tb2(A2),t2tb(Res),t2tb1(X1))) ) )
=> ( ( T != null )
& ! [X3: tree,X4: elt,X5: tree] :
( ( T = node(X3,X4,X5) )
=> ( ( X3 = X2 )
| ( X5 = X2 ) ) )
& $lesseq(0,$sum(Res,1))
& $lesseq($sum(Res,1),A)
& ! [A4: map_int_elt,Result: $int] :
( ( $lesseq(0,A)
& $lesseq($sum(Res,1),Result)
& $lesseq(Result,A)
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,$sum(Res,1)) )
=> ( tb2t1(get(elt1,int,t2tb2(A4),t2tb(I))) = tb2t1(get(elt1,int,t2tb2(A3),t2tb(I))) ) )
& ! [I: $int] :
( ( $lesseq($sum(Res,1),I)
& $less(I,Result) )
=> contains(X2,tb2t1(get(elt1,int,t2tb2(A4),t2tb(I)))) ) )
=> ( $lesseq(Start,Result)
& $lesseq(Result,A)
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,Start) )
=> ( tb2t1(get(elt1,int,t2tb2(A4),t2tb(I))) = tb2t1(get(elt1,int,t2tb2(A1),t2tb(I))) ) )
& ! [I: $int] :
( ( $lesseq(Start,I)
& $less(I,Result) )
=> contains(T,tb2t1(get(elt1,int,t2tb2(A4),t2tb(I)))) ) ) ) ) ) ) )
& ( ~ ( ( Res != A ) )
=> ( $lesseq(Start,Res)
& $lesseq(Res,A)
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,Start) )
=> ( tb2t1(get(elt1,int,t2tb2(A2),t2tb(I))) = tb2t1(get(elt1,int,t2tb2(A1),t2tb(I))) ) )
& ! [I: $int] :
( ( $lesseq(Start,I)
& $less(I,Res) )
=> contains(T,tb2t1(get(elt1,int,t2tb2(A2),t2tb(I)))) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------