TPTP Problem File: SWW637_2.p
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%------------------------------------------------------------------------------
% File : SWW637_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Relabel-T-WP parameter relabel
% 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 : relabel-T-WP_parameter_relabel [Fil14]
% Status : Theorem
% Rating : 0.62 v8.2.0, 0.88 v8.1.0, 0.75 v7.5.0, 0.80 v7.4.0, 0.75 v7.3.0, 0.67 v7.0.0, 0.71 v6.4.0, 1.00 v6.3.0, 0.86 v6.2.0, 1.00 v6.1.0
% Syntax : Number of formulae : 122 ( 43 unt; 50 typ; 0 def)
% Number of atoms : 152 ( 52 equ)
% Maximal formula atoms : 18 ( 1 avg)
% Number of connectives : 87 ( 7 ~; 9 |; 33 &)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 33 ( 13 atm; 4 fun; 5 num; 11 var)
% Number of types : 10 ( 8 usr; 1 ari)
% Number of type conns : 67 ( 33 >; 34 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 0 prp; 2-4 aty)
% Number of functors : 42 ( 38 usr; 11 con; 0-5 aty)
% Number of variables : 205 ( 194 !; 11 ?; 205 :)
% 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(list,type,
list: ty > ty ).
tff(nil,type,
nil: ty > uni ).
tff(nil_sort,axiom,
! [A: ty] : sort(list(A),nil(A)) ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(cons_sort,axiom,
! [A: ty,X: uni,X1: uni] : sort(list(A),cons(A,X,X1)) ).
tff(match_list,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_list_sort,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort(A1,match_list(A1,A,X,X1,X2)) ).
tff(match_list_Nil,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort(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] :
( sort(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_sort,axiom,
! [A: ty,X: uni] : sort(A,cons_proj_1(A,X)) ).
tff(cons_proj_1_def,axiom,
! [A: ty,U: uni,U1: uni] :
( sort(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_sort,axiom,
! [A: ty,X: uni] : sort(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(mem,type,
mem: ( ty * uni * uni ) > $o ).
tff(mem_def,axiom,
! [A: ty,X: uni] :
( sort(A,X)
=> ( ~ mem(A,X,nil(A))
& ! [X1: uni,X2: uni] :
( sort(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_sort,axiom,
! [A: ty,X: uni,X1: uni] : sort(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,
length: ( ty * uni ) > $int ).
tff(length_def,axiom,
! [A: ty] :
( ( length(A,nil(A)) = 0 )
& ! [X: uni,X1: uni] : length(A,cons(A,X,X1)) = $sum(1,length(A,X1)) ) ).
tff(length_nonnegative,axiom,
! [A: ty,L: uni] : $lesseq(0,length(A,L)) ).
tff(length_nil,axiom,
! [A: ty,L: uni] :
( ( length(A,L) = 0 )
<=> ( L = nil(A) ) ) ).
tff(append_length,axiom,
! [A: ty,L1: uni,L2: uni] : length(A,infix_plpl(A,L1,L2)) = $sum(length(A,L1),length(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] :
( sort(list(A),L1)
& sort(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] :
( sort(A,X)
& ( Z = cons(A,X,nil(A)) ) )
| ? [X: uni,L: uni] :
( sort(A,X)
& sort(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] :
( sort(A,X)
=> ( mem(A,X,L1)
=> ~ mem(A,X,L2) ) )
=> distinct(A,infix_plpl(A,L1,L2)) ) ) ) ).
tff(tree,type,
tree: ty > ty ).
tff(leaf,type,
leaf: ( ty * uni ) > uni ).
tff(leaf_sort,axiom,
! [A: ty,X: uni] : sort(tree(A),leaf(A,X)) ).
tff(node,type,
node: ( ty * uni * uni ) > uni ).
tff(node_sort,axiom,
! [A: ty,X: uni,X1: uni] : sort(tree(A),node(A,X,X1)) ).
tff(match_tree,type,
match_tree: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_tree_sort,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort(A1,match_tree(A1,A,X,X1,X2)) ).
tff(match_tree_Leaf,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni] :
( sort(A1,Z)
=> ( match_tree(A1,A,leaf(A,U),Z,Z1) = Z ) ) ).
tff(match_tree_Node,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni,U1: uni] :
( sort(A1,Z1)
=> ( match_tree(A1,A,node(A,U,U1),Z,Z1) = Z1 ) ) ).
tff(leaf_Node,axiom,
! [A: ty,U: uni,V: uni,V1: uni] : leaf(A,U) != node(A,V,V1) ).
tff(leaf_proj_1,type,
leaf_proj_1: ( ty * uni ) > uni ).
tff(leaf_proj_1_sort,axiom,
! [A: ty,X: uni] : sort(A,leaf_proj_1(A,X)) ).
tff(leaf_proj_1_def,axiom,
! [A: ty,U: uni] :
( sort(A,U)
=> ( leaf_proj_1(A,leaf(A,U)) = U ) ) ).
tff(node_proj_1,type,
node_proj_1: ( ty * uni ) > uni ).
tff(node_proj_1_sort,axiom,
! [A: ty,X: uni] : sort(tree(A),node_proj_1(A,X)) ).
tff(node_proj_1_def,axiom,
! [A: ty,U: uni,U1: uni] : node_proj_1(A,node(A,U,U1)) = U ).
tff(node_proj_2,type,
node_proj_2: ( ty * uni ) > uni ).
tff(node_proj_2_sort,axiom,
! [A: ty,X: uni] : sort(tree(A),node_proj_2(A,X)) ).
tff(node_proj_2_def,axiom,
! [A: ty,U: uni,U1: uni] : node_proj_2(A,node(A,U,U1)) = U1 ).
tff(tree_inversion,axiom,
! [A: ty,U: uni] :
( ( U = leaf(A,leaf_proj_1(A,U)) )
| ( U = node(A,node_proj_1(A,U),node_proj_2(A,U)) ) ) ).
tff(labels,type,
labels: ( ty * uni ) > uni ).
tff(labels_sort,axiom,
! [A: ty,X: uni] : sort(list(A),labels(A,X)) ).
tff(labels_def,axiom,
! [A: ty] :
( ! [X: uni] : labels(A,leaf(A,X)) = cons(A,X,nil(A))
& ! [X: uni,X1: uni] : labels(A,node(A,X,X1)) = infix_plpl(A,labels(A,X),labels(A,X1)) ) ).
tff(labels_Leaf,axiom,
! [A: ty,X: uni,Y: uni] :
( sort(A,X)
=> ( sort(A,Y)
=> ( mem(A,X,labels(A,leaf(A,Y)))
<=> ( X = Y ) ) ) ) ).
tff(labels_Node,axiom,
! [A: ty,X: uni,L: uni,R: uni] :
( mem(A,X,labels(A,node(A,L,R)))
<=> ( mem(A,X,labels(A,L))
| mem(A,X,labels(A,R)) ) ) ).
tff(same_shape,type,
same_shape: ( ty * ty * uni * uni ) > $o ).
tff(same_shape_Leaf,axiom,
! [A: ty,B: ty,X1: uni,X2: uni] : same_shape(B,A,leaf(A,X1),leaf(B,X2)) ).
tff(same_shape_Node,axiom,
! [A: ty,B: ty,L1: uni,R1: uni,L2: uni,R2: uni] :
( same_shape(B,A,L1,L2)
=> ( same_shape(B,A,R1,R2)
=> same_shape(B,A,node(A,L1,R1),node(B,L2,R2)) ) ) ).
tff(same_shape_inversion,axiom,
! [A: ty,B: ty,Z: uni,Z1: uni] :
( same_shape(B,A,Z,Z1)
=> ( ? [X1: uni,X2: uni] :
( sort(A,X1)
& sort(B,X2)
& ( Z = leaf(A,X1) )
& ( Z1 = leaf(B,X2) ) )
| ? [L1: uni,R1: uni,L2: uni,R2: uni] :
( sort(tree(A),L1)
& sort(tree(A),R1)
& sort(tree(B),L2)
& sort(tree(B),R2)
& same_shape(B,A,L1,L2)
& same_shape(B,A,R1,R2)
& ( Z = node(A,L1,R1) )
& ( Z1 = node(B,L2,R2) ) ) ) ) ).
tff(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(mk_ref_sort,axiom,
! [A: ty,X: uni] : sort(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort,axiom,
! [A: ty,X: uni] : sort(A,contents(A,X)) ).
tff(contents_def,axiom,
! [A: ty,U: uni] :
( sort(A,U)
=> ( contents(A,mk_ref(A,U)) = U ) ) ).
tff(ref_inversion,axiom,
! [A: ty,U: uni] :
( sort(ref(A),U)
=> ( U = mk_ref(A,contents(A,U)) ) ) ).
tff(a,type,
a: $tType ).
tff(a1,type,
a1: ty ).
tff(tree_int,type,
tree_int: $tType ).
tff(t2tb,type,
t2tb: tree_int > uni ).
tff(t2tb_sort,axiom,
! [X: tree_int] : sort(tree(int),t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > tree_int ).
tff(bridgeL,axiom,
! [I: tree_int] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] : t2tb(tb2t(J)) = J ).
tff(list_int,type,
list_int: $tType ).
tff(t2tb1,type,
t2tb1: list_int > uni ).
tff(t2tb_sort1,axiom,
! [X: list_int] : sort(list(int),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > list_int ).
tff(bridgeL1,axiom,
! [I: list_int] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(tree_a1,type,
tree_a1: $tType ).
tff(t2tb2,type,
t2tb2: tree_a1 > uni ).
tff(t2tb_sort2,axiom,
! [X: tree_a1] : sort(tree(a1),t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > tree_a1 ).
tff(bridgeL2,axiom,
! [I: tree_a1] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(t2tb3,type,
t2tb3: $int > uni ).
tff(t2tb_sort3,axiom,
! [X: $int] : sort(int,t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > $int ).
tff(bridgeL3,axiom,
! [I: $int] : tb2t3(t2tb3(I)) = I ).
tff(bridgeR3,axiom,
! [J: uni] : t2tb3(tb2t3(J)) = J ).
tff(wP_parameter_relabel,conjecture,
! [R: $int,X: tree_a1,X1: tree_a1,R1: $int,O: tree_int] :
( ( same_shape(int,a1,t2tb2(X1),t2tb(O))
& distinct(int,labels(int,t2tb(O)))
& $lesseq(R,R1)
& ! [X2: $int] :
( mem(int,t2tb3(X2),labels(int,t2tb(O)))
=> ( $less(R,X2)
& $lesseq(X2,R1) ) ) )
=> ! [R2: $int,O1: tree_int] :
( ( same_shape(int,a1,t2tb2(X),t2tb(O1))
& distinct(int,labels(int,t2tb(O1)))
& $lesseq(R1,R2)
& ! [X2: $int] :
( mem(int,t2tb3(X2),labels(int,t2tb(O1)))
=> ( $less(R1,X2)
& $lesseq(X2,R2) ) ) )
=> ( same_shape(int,a1,node(a1,t2tb2(X),t2tb2(X1)),node(int,t2tb(O1),t2tb(O)))
& distinct(int,labels(int,node(int,t2tb(O1),t2tb(O))))
& $lesseq(R,R2)
& ! [X2: $int] :
( mem(int,t2tb3(X2),labels(int,node(int,t2tb(O1),t2tb(O))))
=> ( $less(R,X2)
& $lesseq(X2,R2) ) ) ) ) ) ).
%------------------------------------------------------------------------------