TPTP Problem File: SWW591=2.p
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%------------------------------------------------------------------------------
% File : SWW591=2 : TPTP v7.4.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Fib memo-T-WP parameter memo fibo
% 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 : fib_memo-T-WP_parameter_memo_fibo [Fil14]
% Status : Theorem
% Rating : 0.40 v7.4.0, 0.25 v7.3.0, 0.17 v7.0.0, 0.14 v6.4.0, 0.00 v6.3.0, 0.29 v6.2.0, 0.38 v6.1.0
% Syntax : Number of formulae : 78 ( 25 unit; 37 type)
% Number of atoms : 70 ( 33 equality)
% Maximal formula depth : 11 ( 4 average)
% Number of connectives : 32 ( 3 ~; 2 |; 3 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% ( 0 ~|; 0 ~&)
% Number of type conns : 45 ( 23 >; 22 *; 0 +; 0 <<)
% Number of predicates : 44 ( 40 propositional; 0-2 arity)
% Number of functors : 31 ( 7 constant; 0-5 arity)
% Number of variables : 94 ( 0 sgn; 94 !; 0 ?)
% ( 94 :; 0 !>; 0 ?*)
% Maximal term depth : 6 ( 2 average)
% Arithmetic symbols : 16 ( 1 prd; 3 fun; 3 num; 9 var)
% 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(option,type,(
option: ty > ty )).
tff(none,type,(
none: ty > uni )).
tff(none_sort,axiom,(
! [A: ty] : sort(option(A),none(A)) )).
tff(some,type,(
some: ( ty * uni ) > uni )).
tff(some_sort,axiom,(
! [A: ty,X: uni] : sort(option(A),some(A,X)) )).
tff(match_option,type,(
match_option: ( ty * ty * uni * uni * uni ) > uni )).
tff(match_option_sort,axiom,(
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort(A1,match_option(A1,A,X,X1,X2)) )).
tff(match_option_None,axiom,(
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort(A1,Z)
=> match_option(A1,A,none(A),Z,Z1) = Z ) )).
tff(match_option_Some,axiom,(
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni] :
( sort(A1,Z1)
=> match_option(A1,A,some(A,U),Z,Z1) = Z1 ) )).
tff(none_Some,axiom,(
! [A: ty,V: uni] : none(A) != some(A,V) )).
tff(some_proj_1,type,(
some_proj_1: ( ty * uni ) > uni )).
tff(some_proj_1_sort,axiom,(
! [A: ty,X: uni] : sort(A,some_proj_1(A,X)) )).
tff(some_proj_1_def,axiom,(
! [A: ty,U: uni] :
( sort(A,U)
=> some_proj_1(A,some(A,U)) = U ) )).
tff(option_inversion,axiom,(
! [A: ty,U: uni] :
( sort(option(A),U)
=> ( U = none(A)
| U = some(A,some_proj_1(A,U)) ) ) )).
tff(compatOrderMult,axiom,(
! [X: $int,Y: $int,Z: $int] :
( $lesseq(X,Y)
=> ( $lesseq(0,Z)
=> $lesseq($product(X,Z),$product(Y,Z)) ) ) )).
tff(fib,type,(
fib: $int > $int )).
tff(fib0,axiom,(
fib(0) = 0 )).
tff(fib1,axiom,(
fib(1) = 1 )).
tff(fibn,axiom,(
! [N: $int] :
( $lesseq(2,N)
=> fib(N) = $sum(fib($difference(N,1)),fib($difference(N,2))) ) )).
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(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(map_int_lpoption_intrp,type,(
map_int_lpoption_intrp: $tType )).
tff(inv,type,(
inv: map_int_lpoption_intrp > $o )).
tff(t2tb,type,(
t2tb: map_int_lpoption_intrp > uni )).
tff(t2tb_sort,axiom,(
! [X: map_int_lpoption_intrp] : sort(map(int,option(int)),t2tb(X)) )).
tff(tb2t,type,(
tb2t: uni > map_int_lpoption_intrp )).
tff(bridgeL,axiom,(
! [I: map_int_lpoption_intrp] : tb2t(t2tb(I)) = I )).
tff(bridgeR,axiom,(
! [J: uni] : t2tb(tb2t(J)) = J )).
tff(option_int,type,(
option_int: $tType )).
tff(t2tb1,type,(
t2tb1: option_int > uni )).
tff(t2tb_sort1,axiom,(
! [X: option_int] : sort(option(int),t2tb1(X)) )).
tff(tb2t1,type,(
tb2t1: uni > option_int )).
tff(bridgeL1,axiom,(
! [I: option_int] : tb2t1(t2tb1(I)) = I )).
tff(bridgeR1,axiom,(
! [J: uni] : t2tb1(tb2t1(J)) = J )).
tff(t2tb2,type,(
t2tb2: $int > uni )).
tff(t2tb_sort2,axiom,(
! [X: $int] : sort(int,t2tb2(X)) )).
tff(tb2t2,type,(
tb2t2: uni > $int )).
tff(bridgeL2,axiom,(
! [I: $int] : tb2t2(t2tb2(I)) = I )).
tff(bridgeR2,axiom,(
! [J: uni] : t2tb2(tb2t2(J)) = J )).
tff(inv_def,axiom,(
! [T: map_int_lpoption_intrp] :
( inv(T)
<=> ! [X: $int,Y: $int] :
( tb2t1(get(option(int),int,t2tb(T),t2tb2(X))) = tb2t1(some(int,t2tb2(Y)))
=> Y = fib(X) ) ) )).
tff(wP_parameter_memo_fibo,conjecture,(
! [N: $int,Table: map_int_lpoption_intrp] :
( ( $lesseq(0,N)
& inv(Table) )
=> ( tb2t1(get(option(int),int,t2tb(Table),t2tb2(N))) = tb2t1(none(int))
=> ( ( $lesseq(0,N)
& inv(Table) )
=> ! [Table1: map_int_lpoption_intrp] :
( inv(Table1)
=> ! [Table2: map_int_lpoption_intrp] :
( Table2 = tb2t(set(option(int),int,t2tb(Table1),t2tb2(N),some(int,t2tb2(fib(N)))))
=> ( fib(N) = fib(N)
& inv(Table2) ) ) ) ) ) ) )).
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