TPTP Problem File: SWW666_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW666_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Vstte10 inverting-T-WP parameter test
% 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_inverting-T-WP_parameter_test [Fil14]
% Status : Theorem
% Rating : 0.25 v8.1.0, 0.38 v7.5.0, 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, 0.50 v6.1.0
% Syntax : Number of formulae : 93 ( 26 unt; 41 typ; 0 def)
% Number of atoms : 161 ( 57 equ)
% Maximal formula atoms : 54 ( 1 avg)
% Number of connectives : 115 ( 6 ~; 1 |; 44 &)
% ( 7 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 252 ( 66 atm; 9 fun; 126 num; 51 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 62 ( 27 >; 35 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 0 prp; 2-2 aty)
% Number of functors : 42 ( 28 usr; 19 con; 0-5 aty)
% Number of variables : 168 ( 166 !; 2 ?; 168 :)
% 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(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(length,type,
length1: ( ty * uni ) > $int ).
tff(length_def1,axiom,
! [A: ty,U: $int,U1: uni] : length1(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,length1(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,length1(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(map_int_int,type,
map_int_int: $tType ).
tff(injective,type,
injective2: ( map_int_int * $int ) > $o ).
tff(t2tb1,type,
t2tb1: map_int_int > uni ).
tff(t2tb_sort1,axiom,
! [X: map_int_int] : sort1(map(int,int),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > map_int_int ).
tff(bridgeL1,axiom,
! [I: map_int_int] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(injective_def,axiom,
! [A: map_int_int,N: $int] :
( injective2(A,N)
<=> ! [I: $int,J: $int] :
( ( $lesseq(0,I)
& $less(I,N) )
=> ( ( $lesseq(0,J)
& $less(J,N) )
=> ( ( I != J )
=> ( tb2t(get(int,int,t2tb1(A),t2tb(I))) != tb2t(get(int,int,t2tb1(A),t2tb(J))) ) ) ) ) ) ).
tff(surjective,type,
surjective2: ( map_int_int * $int ) > $o ).
tff(surjective_def,axiom,
! [A: map_int_int,N: $int] :
( surjective2(A,N)
<=> ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,N) )
=> ? [J: $int] :
( $lesseq(0,J)
& $less(J,N)
& ( tb2t(get(int,int,t2tb1(A),t2tb(J))) = I ) ) ) ) ).
tff(range,type,
range2: ( map_int_int * $int ) > $o ).
tff(range_def,axiom,
! [A: map_int_int,N: $int] :
( range2(A,N)
<=> ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,N) )
=> ( $lesseq(0,tb2t(get(int,int,t2tb1(A),t2tb(I))))
& $less(tb2t(get(int,int,t2tb1(A),t2tb(I))),N) ) ) ) ).
tff(injective_surjective,axiom,
! [A: map_int_int,N: $int] :
( injective2(A,N)
=> ( range2(A,N)
=> surjective2(A,N) ) ) ).
tff(occ,type,
occ1: ( ty * uni * uni * $int * $int ) > $int ).
tff(occ_empty,axiom,
! [A: ty,V: uni,M: uni,L: $int,U: $int] :
( $lesseq(U,L)
=> ( occ1(A,V,M,L,U) = 0 ) ) ).
tff(occ_right_no_add,axiom,
! [A: ty,V: uni,M: uni,L: $int,U: $int] :
( sort1(A,V)
=> ( $less(L,U)
=> ( ( get(A,int,M,t2tb($difference(U,1))) != V )
=> ( occ1(A,V,M,L,U) = occ1(A,V,M,L,$difference(U,1)) ) ) ) ) ).
tff(occ_right_add,axiom,
! [A: ty,V: uni,M: uni,L: $int,U: $int] :
( $less(L,U)
=> ( ( get(A,int,M,t2tb($difference(U,1))) = V )
=> ( occ1(A,V,M,L,U) = $sum(1,occ1(A,V,M,L,$difference(U,1))) ) ) ) ).
tff(occ_bounds,axiom,
! [A: ty,V: uni,M: uni,L: $int,U: $int] :
( $lesseq(L,U)
=> ( $lesseq(0,occ1(A,V,M,L,U))
& $lesseq(occ1(A,V,M,L,U),$difference(U,L)) ) ) ).
tff(occ_append,axiom,
! [A: ty,V: uni,M: uni,L: $int,Mid: $int,U: $int] :
( ( $lesseq(L,Mid)
& $lesseq(Mid,U) )
=> ( occ1(A,V,M,L,U) = $sum(occ1(A,V,M,L,Mid),occ1(A,V,M,Mid,U)) ) ) ).
tff(occ_neq,axiom,
! [A: ty,V: uni,M: uni,L: $int,U: $int] :
( sort1(A,V)
=> ( ! [I: $int] :
( ( $lesseq(L,I)
& $less(I,U) )
=> ( get(A,int,M,t2tb(I)) != V ) )
=> ( occ1(A,V,M,L,U) = 0 ) ) ) ).
tff(occ_exists,axiom,
! [A: ty,V: uni,M: uni,L: $int,U: $int] :
( sort1(A,V)
=> ( $less(0,occ1(A,V,M,L,U))
=> ? [I: $int] :
( $lesseq(L,I)
& $less(I,U)
& ( get(A,int,M,t2tb(I)) = V ) ) ) ) ).
tff(occ_pos,axiom,
! [A: ty,M: uni,L: $int,U: $int,I: $int] :
( ( $lesseq(L,I)
& $less(I,U) )
=> $less(0,occ1(A,get(A,int,M,t2tb(I)),M,L,U)) ) ).
tff(occ_eq,axiom,
! [A: ty,V: uni,M1: uni,M2: uni,L: $int,U: $int] :
( ! [I: $int] :
( ( $lesseq(L,I)
& $less(I,U) )
=> ( get(A,int,M1,t2tb(I)) = get(A,int,M2,t2tb(I)) ) )
=> ( occ1(A,V,M1,L,U) = occ1(A,V,M2,L,U) ) ) ).
tff(injection_occ,axiom,
! [M: map_int_int,N: $int] :
( injective2(M,N)
<=> ! [V: $int] : $lesseq(occ1(int,t2tb(V),t2tb1(M),0,N),1) ) ).
tff(array_int,type,
array_int: $tType ).
tff(injective1,type,
injective3: ( array_int * $int ) > $o ).
tff(t2tb2,type,
t2tb2: array_int > uni ).
tff(t2tb_sort2,axiom,
! [X: array_int] : sort1(array(int),t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > array_int ).
tff(bridgeL2,axiom,
! [I: array_int] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(injective_def1,axiom,
! [A: array_int,N: $int] :
( injective3(A,N)
<=> injective2(tb2t1(elts(int,t2tb2(A))),N) ) ).
tff(surjective1,type,
surjective3: ( array_int * $int ) > $o ).
tff(surjective_def1,axiom,
! [A: array_int,N: $int] :
( surjective3(A,N)
<=> surjective2(tb2t1(elts(int,t2tb2(A))),N) ) ).
tff(range1,type,
range3: ( array_int * $int ) > $o ).
tff(range_def1,axiom,
! [A: array_int,N: $int] :
( range3(A,N)
<=> range2(tb2t1(elts(int,t2tb2(A))),N) ) ).
tff(wP_parameter_test,conjecture,
( $lesseq(0,10)
=> ( $lesseq(0,10)
=> ( ( $lesseq(0,0)
& $less(0,10) )
=> ! [A: map_int_int] :
( ( $lesseq(0,10)
& ( A = tb2t1(set(int,int,const(int,int,t2tb(0)),t2tb(0),t2tb(9))) ) )
=> ( ( $lesseq(0,1)
& $less(1,10) )
=> ! [A1: map_int_int] :
( ( $lesseq(0,10)
& ( A1 = tb2t1(set(int,int,t2tb1(A),t2tb(1),t2tb(3))) ) )
=> ( ( $lesseq(0,2)
& $less(2,10) )
=> ! [A2: map_int_int] :
( ( $lesseq(0,10)
& ( A2 = tb2t1(set(int,int,t2tb1(A1),t2tb(2),t2tb(8))) ) )
=> ( ( $lesseq(0,3)
& $less(3,10) )
=> ! [A3: map_int_int] :
( ( $lesseq(0,10)
& ( A3 = tb2t1(set(int,int,t2tb1(A2),t2tb(3),t2tb(2))) ) )
=> ( ( $lesseq(0,4)
& $less(4,10) )
=> ! [A4: map_int_int] :
( ( $lesseq(0,10)
& ( A4 = tb2t1(set(int,int,t2tb1(A3),t2tb(4),t2tb(7))) ) )
=> ( ( $lesseq(0,5)
& $less(5,10) )
=> ! [A5: map_int_int] :
( ( $lesseq(0,10)
& ( A5 = tb2t1(set(int,int,t2tb1(A4),t2tb(5),t2tb(4))) ) )
=> ( ( $lesseq(0,6)
& $less(6,10) )
=> ! [A6: map_int_int] :
( ( $lesseq(0,10)
& ( A6 = tb2t1(set(int,int,t2tb1(A5),t2tb(6),t2tb(0))) ) )
=> ( ( $lesseq(0,7)
& $less(7,10) )
=> ! [A7: map_int_int] :
( ( $lesseq(0,10)
& ( A7 = tb2t1(set(int,int,t2tb1(A6),t2tb(7),t2tb(1))) ) )
=> ( ( $lesseq(0,8)
& $less(8,10) )
=> ! [A8: map_int_int] :
( ( $lesseq(0,10)
& ( A8 = tb2t1(set(int,int,t2tb1(A7),t2tb(8),t2tb(5))) ) )
=> ( ( $lesseq(0,9)
& $less(9,10) )
=> ! [A9: map_int_int] :
( ( $lesseq(0,10)
& ( A9 = tb2t1(set(int,int,t2tb1(A8),t2tb(9),t2tb(6))) ) )
=> ( ( ( tb2t(get(int,int,t2tb1(A9),t2tb(0))) = 9 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(1))) = 3 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(2))) = 8 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(3))) = 2 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(4))) = 7 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(5))) = 4 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(6))) = 0 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(7))) = 1 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(8))) = 5 )
& ( tb2t(get(int,int,t2tb1(A9),t2tb(9))) = 6 ) )
=> ( injective2(A9,10)
& range2(A9,10) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------