TPTP Problem File: SWW671_2.p
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%------------------------------------------------------------------------------
% File : SWW671_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Vstte10 search list-T-WP parameter search
% 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 : vstte10_search_list-T-WP_parameter_search [Fil14]
% Status : Theorem
% Rating : 0.75 v8.2.0, 0.62 v8.1.0, 0.88 v7.5.0, 0.70 v7.4.0, 0.75 v7.3.0, 0.83 v7.0.0, 0.86 v6.4.0, 0.33 v6.3.0, 0.86 v6.2.0, 1.00 v6.1.0
% Syntax : Number of formulae : 83 ( 27 unt; 38 typ; 0 def)
% Number of atoms : 96 ( 46 equ)
% Maximal formula atoms : 25 ( 1 avg)
% Number of connectives : 59 ( 8 ~; 7 |; 22 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 69 ( 16 atm; 20 fun; 19 num; 14 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 46 ( 24 >; 22 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 34 ( 29 usr; 10 con; 0-5 aty)
% Number of variables : 109 ( 109 !; 0 ?; 109 :)
% 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(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(option,type,
option: ty > ty ).
tff(none,type,
none: ty > uni ).
tff(none_sort1,axiom,
! [A: ty] : sort1(option(A),none(A)) ).
tff(some,type,
some: ( ty * uni ) > uni ).
tff(some_sort1,axiom,
! [A: ty,X: uni] : sort1(option(A),some(A,X)) ).
tff(match_option,type,
match_option1: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_option_sort1,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort1(A1,match_option1(A1,A,X,X1,X2)) ).
tff(match_option_None1,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort1(A1,Z)
=> ( match_option1(A1,A,none(A),Z,Z1) = Z ) ) ).
tff(match_option_Some1,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni] :
( sort1(A1,Z1)
=> ( match_option1(A1,A,some(A,U),Z,Z1) = Z1 ) ) ).
tff(none_Some1,axiom,
! [A: ty,V: uni] : none(A) != some(A,V) ).
tff(some_proj_1,type,
some_proj_11: ( ty * uni ) > uni ).
tff(some_proj_1_sort1,axiom,
! [A: ty,X: uni] : sort1(A,some_proj_11(A,X)) ).
tff(some_proj_1_def1,axiom,
! [A: ty,U: uni] :
( sort1(A,U)
=> ( some_proj_11(A,some(A,U)) = U ) ) ).
tff(option_inversion1,axiom,
! [A: ty,U: uni] :
( sort1(option(A),U)
=> ( ( U = none(A) )
| ( U = some(A,some_proj_11(A,U)) ) ) ) ).
tff(nth,type,
nth1: ( ty * $int * uni ) > uni ).
tff(nth_sort1,axiom,
! [A: ty,X: $int,X1: uni] : sort1(option(A),nth1(A,X,X1)) ).
tff(nth_def,axiom,
! [A: ty,N: $int] :
( ( nth1(A,N,nil(A)) = none(A) )
& ! [X: uni,X1: uni] :
( ( ( N = 0 )
=> ( nth1(A,N,cons(A,X,X1)) = some(A,X) ) )
& ( ( N != 0 )
=> ( nth1(A,N,cons(A,X,X1)) = nth1(A,$difference(N,1),X1) ) ) ) ) ).
tff(list_int,type,
list_int: $tType ).
tff(zero_at,type,
zero_at1: ( list_int * $int ) > $o ).
tff(option_int,type,
option_int: $tType ).
tff(t2tb,type,
t2tb: option_int > uni ).
tff(t2tb_sort,axiom,
! [X: option_int] : sort1(option(int),t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > option_int ).
tff(bridgeL,axiom,
! [I: option_int] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] : t2tb(tb2t(J)) = J ).
tff(t2tb1,type,
t2tb1: list_int > uni ).
tff(t2tb_sort1,axiom,
! [X: list_int] : sort1(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(t2tb2,type,
t2tb2: $int > uni ).
tff(t2tb_sort2,axiom,
! [X: $int] : sort1(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(zero_at_def,axiom,
! [L: list_int,I: $int] :
( zero_at1(L,I)
<=> ( ( tb2t(nth1(int,I,t2tb1(L))) = tb2t(some(int,t2tb2(0))) )
& ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,I) )
=> ( tb2t(nth1(int,J,t2tb1(L))) != tb2t(some(int,t2tb2(0))) ) ) ) ) ).
tff(no_zero,type,
no_zero1: list_int > $o ).
tff(no_zero_def,axiom,
! [L: list_int] :
( no_zero1(L)
<=> ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,length1(int,t2tb1(L))) )
=> ( tb2t(nth1(int,J,t2tb1(L))) != tb2t(some(int,t2tb2(0))) ) ) ) ).
tff(wP_parameter_search,conjecture,
! [I: $int] :
( ( ( $lesseq(I,I)
& $less(I,$sum(I,length1(int,nil(int))))
& zero_at1(tb2t1(nil(int)),$difference(I,I)) )
| ( ( I = $sum(I,length1(int,nil(int))) )
& no_zero1(tb2t1(nil(int))) ) )
& ! [X: $int,X1: list_int] :
( ( ( X = 0 )
=> ( ( $lesseq(I,I)
& $less(I,$sum(I,length1(int,cons(int,t2tb2(X),t2tb1(X1)))))
& zero_at1(tb2t1(cons(int,t2tb2(X),t2tb1(X1))),$difference(I,I)) )
| ( ( I = $sum(I,length1(int,cons(int,t2tb2(X),t2tb1(X1)))) )
& no_zero1(tb2t1(cons(int,t2tb2(X),t2tb1(X1)))) ) ) )
& ( ( X != 0 )
=> ( ( tb2t1(cons(int,t2tb2(X),t2tb1(X1))) != tb2t1(nil(int)) )
& ! [X2: $int,X3: list_int] :
( ( tb2t1(cons(int,t2tb2(X),t2tb1(X1))) = tb2t1(cons(int,t2tb2(X2),t2tb1(X3))) )
=> ( X3 = X1 ) )
& ! [Result: $int] :
( ( ( $lesseq($sum(I,1),Result)
& $less(Result,$sum($sum(I,1),length1(int,t2tb1(X1))))
& zero_at1(X1,$difference(Result,$sum(I,1))) )
| ( ( Result = $sum($sum(I,1),length1(int,t2tb1(X1))) )
& no_zero1(X1) ) )
=> ( ( $lesseq(I,Result)
& $less(Result,$sum(I,length1(int,cons(int,t2tb2(X),t2tb1(X1)))))
& zero_at1(tb2t1(cons(int,t2tb2(X),t2tb1(X1))),$difference(Result,I)) )
| ( ( Result = $sum(I,length1(int,cons(int,t2tb2(X),t2tb1(X1)))) )
& no_zero1(tb2t1(cons(int,t2tb2(X),t2tb1(X1)))) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------