TPTP Problem File: SWW611_2.p
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%------------------------------------------------------------------------------
% File : SWW611_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Kmp-T-WP parameter initnext
% 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 : kmp-T-WP_parameter_initnext [Fil14]
% Status : Theorem
% Rating : 0.88 v8.2.0, 1.00 v8.1.0, 0.88 v7.5.0, 0.90 v7.4.0, 0.88 v7.3.0, 0.83 v7.0.0, 1.00 v6.2.0, 0.88 v6.1.0
% Syntax : Number of formulae : 104 ( 32 unt; 46 typ; 0 def)
% Number of atoms : 190 ( 54 equ)
% Maximal formula atoms : 68 ( 1 avg)
% Number of connectives : 143 ( 11 ~; 15 |; 48 &)
% ( 2 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 279 ( 80 atm; 51 fun; 81 num; 67 var)
% Number of types : 10 ( 8 usr; 1 ari)
% Number of type conns : 62 ( 29 >; 33 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 0 prp; 2-5 aty)
% Number of functors : 40 ( 35 usr; 11 con; 0-5 aty)
% Number of variables : 182 ( 182 !; 0 ?; 182 :)
% 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_sort2,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(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(mk_ref_sort2,axiom,
! [A: ty,X: uni] : sort1(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort2,axiom,
! [A: ty,X: uni] : sort1(A,contents(A,X)) ).
tff(contents_def1,axiom,
! [A: ty,U: uni] :
( sort1(A,U)
=> ( contents(A,mk_ref(A,U)) = U ) ) ).
tff(ref_inversion1,axiom,
! [A: ty,U: uni] :
( sort1(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_sort6,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_sort5,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_sort3,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_sort3,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),mk_array1(A,X,X1)) ).
tff(length,type,
length1: ( ty * uni ) > $int ).
tff(length_def2,axiom,
! [A: ty,U: $int,U1: uni] : length1(A,mk_array1(A,U,U1)) = U ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(elts_sort3,axiom,
! [A: ty,X: uni] : sort1(map(int,A),elts(A,X)) ).
tff(elts_def2,axiom,
! [A: ty,U: $int,U1: uni] :
( sort1(map(int,A),U1)
=> ( elts(A,mk_array1(A,U,U1)) = U1 ) ) ).
tff(array_inversion2,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_sort7,axiom,
! [A: ty,X: uni,X1: $int] : sort1(A,get2(A,X,X1)) ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(t2tb_sort3,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_sort6,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_sort2,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(char,type,
char1: $tType ).
tff(char1,type,
char: ty ).
tff(array_char,type,
array_char: $tType ).
tff(matches,type,
matches1: ( array_char * $int * array_char * $int * $int ) > $o ).
tff(t2tb1,type,
t2tb1: array_char > uni ).
tff(t2tb_sort4,axiom,
! [X: array_char] : sort1(array(char),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > array_char ).
tff(bridgeL1,axiom,
! [I: array_char] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(t2tb2,type,
t2tb2: char1 > uni ).
tff(t2tb_sort5,axiom,
! [X: char1] : sort1(char,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > char1 ).
tff(bridgeL2,axiom,
! [I: char1] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] :
( sort1(char,J)
=> ( t2tb2(tb2t2(J)) = J ) ) ).
tff(matches_def,axiom,
! [A1: array_char,I1: $int,A2: array_char,I2: $int,N: $int] :
( matches1(A1,I1,A2,I2,N)
<=> ( $lesseq(0,I1)
& $lesseq(I1,$difference(length1(char,t2tb1(A1)),N))
& $lesseq(0,I2)
& $lesseq(I2,$difference(length1(char,t2tb1(A2)),N))
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,N) )
=> ( tb2t2(get2(char,t2tb1(A1),$sum(I1,I))) = tb2t2(get2(char,t2tb1(A2),$sum(I2,I))) ) ) ) ) ).
tff(matches_empty,axiom,
! [A1: array_char,A2: array_char,I1: $int,I2: $int] :
( ( $lesseq(0,I1)
& $lesseq(I1,length1(char,t2tb1(A1))) )
=> ( ( $lesseq(0,I2)
& $lesseq(I2,length1(char,t2tb1(A2))) )
=> matches1(A1,I1,A2,I2,0) ) ) ).
tff(matches_right_extension,axiom,
! [A1: array_char,A2: array_char,I1: $int,I2: $int,N: $int] :
( matches1(A1,I1,A2,I2,N)
=> ( $lesseq(I1,$difference($difference(length1(char,t2tb1(A1)),N),1))
=> ( $lesseq(I2,$difference($difference(length1(char,t2tb1(A2)),N),1))
=> ( ( tb2t2(get2(char,t2tb1(A1),$sum(I1,N))) = tb2t2(get2(char,t2tb1(A2),$sum(I2,N))) )
=> matches1(A1,I1,A2,I2,$sum(N,1)) ) ) ) ) ).
tff(matches_contradiction_at_first,axiom,
! [A1: array_char,A2: array_char,I1: $int,I2: $int,N: $int] :
( $less(0,N)
=> ( ( tb2t2(get2(char,t2tb1(A1),I1)) != tb2t2(get2(char,t2tb1(A2),I2)) )
=> ~ matches1(A1,I1,A2,I2,N) ) ) ).
tff(matches_contradiction_at_i,axiom,
! [A1: array_char,A2: array_char,I1: $int,I2: $int,I: $int,N: $int] :
( $less(0,N)
=> ( ( $lesseq(0,I)
& $less(I,N) )
=> ( ( tb2t2(get2(char,t2tb1(A1),$sum(I1,I))) != tb2t2(get2(char,t2tb1(A2),$sum(I2,I))) )
=> ~ matches1(A1,I1,A2,I2,N) ) ) ) ).
tff(matches_right_weakening,axiom,
! [A1: array_char,A2: array_char,I1: $int,I2: $int,N: $int,Nqt: $int] :
( matches1(A1,I1,A2,I2,N)
=> ( $less(Nqt,N)
=> matches1(A1,I1,A2,I2,Nqt) ) ) ).
tff(matches_left_weakening,axiom,
! [A1: array_char,A2: array_char,I1: $int,I2: $int,N: $int,Nqt: $int] :
( matches1(A1,$difference(I1,$difference(N,Nqt)),A2,$difference(I2,$difference(N,Nqt)),N)
=> ( $less(Nqt,N)
=> matches1(A1,I1,A2,I2,Nqt) ) ) ).
tff(matches_sym,axiom,
! [A1: array_char,A2: array_char,I1: $int,I2: $int,N: $int] :
( matches1(A1,I1,A2,I2,N)
=> matches1(A2,I2,A1,I1,N) ) ).
tff(matches_trans,axiom,
! [A1: array_char,A2: array_char,A3: array_char,I1: $int,I2: $int,I3: $int,N: $int] :
( matches1(A1,I1,A2,I2,N)
=> ( matches1(A2,I2,A3,I3,N)
=> matches1(A1,I1,A3,I3,N) ) ) ).
tff(is_next,type,
is_next1: ( array_char * $int * $int ) > $o ).
tff(is_next_def,axiom,
! [P: array_char,J: $int,N: $int] :
( is_next1(P,J,N)
<=> ( $lesseq(0,N)
& $less(N,J)
& matches1(P,$difference(J,N),P,0,N)
& ! [Z: $int] :
( ( $less(N,Z)
& $less(Z,J) )
=> ~ matches1(P,$difference(J,Z),P,0,Z) ) ) ) ).
tff(next_iteration,axiom,
! [P: array_char,A: array_char,I: $int,J: $int,N: $int] :
( ( $less(0,J)
& $less(J,length1(char,t2tb1(P))) )
=> ( ( $lesseq(J,I)
& $lesseq(I,length1(char,t2tb1(A))) )
=> ( matches1(A,$difference(I,J),P,0,J)
=> ( is_next1(P,J,N)
=> matches1(A,$difference(I,N),P,0,N) ) ) ) ) ).
tff(next_is_maximal,axiom,
! [P: array_char,A: array_char,I: $int,J: $int,N: $int,K: $int] :
( ( $less(0,J)
& $less(J,length1(char,t2tb1(P))) )
=> ( ( $lesseq(J,I)
& $lesseq(I,length1(char,t2tb1(A))) )
=> ( ( $less($difference(I,J),K)
& $less(K,$difference(I,N)) )
=> ( matches1(A,$difference(I,J),P,0,J)
=> ( is_next1(P,J,N)
=> ~ matches1(A,K,P,0,length1(char,t2tb1(P))) ) ) ) ) ) ).
tff(next_1_0,axiom,
! [P: array_char] :
( $lesseq(1,length1(char,t2tb1(P)))
=> is_next1(P,1,0) ) ).
tff(map_int_int,type,
map_int_int: $tType ).
tff(t2tb3,type,
t2tb3: map_int_int > uni ).
tff(t2tb_sort6,axiom,
! [X: map_int_int] : sort1(map(int,int),t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > map_int_int ).
tff(bridgeL3,axiom,
! [I: map_int_int] : tb2t3(t2tb3(I)) = I ).
tff(bridgeR3,axiom,
! [J: uni] : t2tb3(tb2t3(J)) = J ).
tff(map_int_char,type,
map_int_char: $tType ).
tff(t2tb4,type,
t2tb4: map_int_char > uni ).
tff(t2tb_sort7,axiom,
! [X: map_int_char] : sort1(map(int,char),t2tb4(X)) ).
tff(tb2t4,type,
tb2t4: uni > map_int_char ).
tff(bridgeL4,axiom,
! [I: map_int_char] : tb2t4(t2tb4(I)) = I ).
tff(bridgeR4,axiom,
! [J: uni] :
( sort1(map(int,char),J)
=> ( t2tb4(tb2t4(J)) = J ) ) ).
tff(wP_parameter_initnext,conjecture,
! [P: $int,P1: map_int_char] :
( ( ( $less(0,P)
| ( 0 = P ) )
& ( $less(1,P)
| ( 1 = P ) ) )
=> ( $lesseq(0,P)
=> ( ( $less(0,P)
| ( 0 = P ) )
=> ( $less(1,P)
=> ( ( ( $less(0,1)
| ( 0 = 1 ) )
& $less(1,P) )
=> ! [Next: map_int_int] :
( ( ( $less(0,P)
| ( 0 = P ) )
& ( Next = tb2t3(set(int,int,const(int,int,t2tb(0)),t2tb(1),t2tb(0))) ) )
=> ! [J: $int,I: $int,Next1: map_int_int] :
( ( ( $less(0,J)
| ( 0 = J ) )
& $less(J,I)
& ( $less(I,P)
| ( I = P ) )
& $lesseq(0,$difference(I,J))
& $lesseq($difference(I,J),$difference(length1(char,mk_array1(char,P,t2tb4(P1))),J))
& $lesseq(0,0)
& $lesseq(0,$difference(length1(char,mk_array1(char,P,t2tb4(P1))),J))
& ! [I1: $int] :
( ( $lesseq(0,I1)
& $less(I1,J) )
=> ( tb2t2(get2(char,mk_array1(char,P,t2tb4(P1)),$sum($difference(I,J),I1))) = tb2t2(get2(char,mk_array1(char,P,t2tb4(P1)),$sum(0,I1))) ) )
& ! [Z: $int] :
( ( $less($sum(J,1),Z)
& $less(Z,$sum(I,1)) )
=> ~ ( $lesseq(0,$difference($sum(I,1),Z))
& $lesseq($difference($sum(I,1),Z),$difference(length1(char,mk_array1(char,P,t2tb4(P1))),Z))
& $lesseq(0,0)
& $lesseq(0,$difference(length1(char,mk_array1(char,P,t2tb4(P1))),Z))
& ! [I1: $int] :
( ( $lesseq(0,I1)
& $less(I1,Z) )
=> ( tb2t2(get2(char,mk_array1(char,P,t2tb4(P1)),$sum($difference($sum(I,1),Z),I1))) = tb2t2(get2(char,mk_array1(char,P,t2tb4(P1)),$sum(0,I1))) ) ) ) )
& ! [K: $int] :
( ( $less(0,K)
& ( $less(K,I)
| ( K = I ) ) )
=> ( $lesseq(0,tb2t(get(int,int,t2tb3(Next1),t2tb(K))))
& $less(tb2t(get(int,int,t2tb3(Next1),t2tb(K))),K)
& matches1(tb2t1(mk_array1(char,P,t2tb4(P1))),$difference(K,tb2t(get(int,int,t2tb3(Next1),t2tb(K)))),tb2t1(mk_array1(char,P,t2tb4(P1))),0,tb2t(get(int,int,t2tb3(Next1),t2tb(K))))
& ! [Z: $int] :
( ( $less(tb2t(get(int,int,t2tb3(Next1),t2tb(K))),Z)
& $less(Z,K) )
=> ~ matches1(tb2t1(mk_array1(char,P,t2tb4(P1))),$difference(K,Z),tb2t1(mk_array1(char,P,t2tb4(P1))),0,Z) ) ) ) )
=> ( $less(I,$difference(P,1))
=> ( ( ( $less(0,J)
| ( 0 = J ) )
& $less(J,P) )
=> ( ( ( $less(0,I)
| ( 0 = I ) )
& $less(I,P) )
=> ( ( tb2t2(get(char,int,t2tb4(P1),t2tb(I))) = tb2t2(get(char,int,t2tb4(P1),t2tb(J))) )
=> ! [I1: $int] :
( ( I1 = $sum(I,1) )
=> ! [J1: $int] :
( ( J1 = $sum(J,1) )
=> ( ( ( $less(0,P)
| ( 0 = P ) )
& ( $less(0,I1)
| ( 0 = I1 ) )
& $less(I1,P) )
=> ! [Next2: map_int_int] :
( ( ( $less(0,P)
| ( 0 = P ) )
& ( Next2 = tb2t3(set(int,int,t2tb3(Next1),t2tb(I1),t2tb(J1))) ) )
=> ! [K: $int] :
( ( $less(0,K)
& ( $less(K,I1)
| ( K = I1 ) ) )
=> ! [Z: $int] :
( ( $less(tb2t(get(int,int,t2tb3(Next2),t2tb(K))),Z)
& $less(Z,K) )
=> ~ matches1(tb2t1(mk_array1(char,P,t2tb4(P1))),$difference(K,Z),tb2t1(mk_array1(char,P,t2tb4(P1))),0,Z) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------