TPTP Problem File: SWW608_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW608_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Inverse in place-T-WP parameter test1
% 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 : inverse_in_place-T-WP_parameter_test1 [Fil14]
% Status : Theorem
% Rating : 0.62 v8.2.0, 0.50 v8.1.0, 0.62 v7.5.0, 0.60 v7.4.0, 0.25 v7.3.0, 0.17 v7.1.0, 0.33 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.71 v6.2.0, 0.75 v6.1.0
% Syntax : Number of formulae : 100 ( 29 unt; 42 typ; 0 def)
% Number of atoms : 169 ( 44 equ)
% Maximal formula atoms : 24 ( 1 avg)
% Number of connectives : 119 ( 8 ~; 1 |; 41 &)
% ( 3 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number arithmetic : 226 ( 82 atm; 16 fun; 60 num; 68 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 62 ( 28 >; 34 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 0 prp; 1-5 aty)
% Number of functors : 40 ( 32 usr; 12 con; 0-5 aty)
% Number of variables : 173 ( 173 !; 0 ?; 173 :)
% 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(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_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(array,type,
array: ty > ty ).
tff(mk_array,type,
mk_array: ( ty * $int * uni ) > uni ).
tff(mk_array_sort,axiom,
! [A: ty,X: $int,X1: uni] : sort(array(A),mk_array(A,X,X1)) ).
tff(length,type,
length: ( ty * uni ) > $int ).
tff(length_def,axiom,
! [A: ty,U: $int,U1: uni] : length(A,mk_array(A,U,U1)) = U ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(elts_sort,axiom,
! [A: ty,X: uni] : sort(map(int,A),elts(A,X)) ).
tff(elts_def,axiom,
! [A: ty,U: $int,U1: uni] :
( sort(map(int,A),U1)
=> ( elts(A,mk_array(A,U,U1)) = U1 ) ) ).
tff(array_inversion,axiom,
! [A: ty,U: uni] : U = mk_array(A,length(A,U),elts(A,U)) ).
tff(get1,type,
get1: ( ty * uni * $int ) > uni ).
tff(get_sort1,axiom,
! [A: ty,X: uni,X1: $int] : sort(A,get1(A,X,X1)) ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(t2tb_sort,axiom,
! [X: $int] : sort(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] : get1(A,A1,I) = get(A,int,elts(A,A1),t2tb(I)) ).
tff(set1,type,
set1: ( ty * uni * $int * uni ) > uni ).
tff(set_sort1,axiom,
! [A: ty,X: uni,X1: $int,X2: uni] : sort(array(A),set1(A,X,X1,X2)) ).
tff(set_def,axiom,
! [A: ty,A1: uni,I: $int,V: uni] : set1(A,A1,I,V) = mk_array(A,length(A,A1),set(A,int,elts(A,A1),t2tb(I),V)) ).
tff(make,type,
make: ( ty * $int * uni ) > uni ).
tff(make_sort,axiom,
! [A: ty,X: $int,X1: uni] : sort(array(A),make(A,X,X1)) ).
tff(make_def,axiom,
! [A: ty,N: $int,V: uni] : make(A,N,V) = mk_array(A,N,const(A,int,V)) ).
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(prefix_tl,type,
prefix_tl: $int > $int ).
tff(prefix_tl_def,axiom,
! [X: $int] : prefix_tl(X) = $difference($uminus(X),1) ).
tff(map_int_int,type,
map_int_int: $tType ).
tff(pr,type,
pr: ( map_int_int * $int ) > $o ).
tff(t2tb1,type,
t2tb1: map_int_int > uni ).
tff(t2tb_sort1,axiom,
! [X: map_int_int] : sort(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(pr_def,axiom,
! [A: map_int_int,N: $int] :
( pr(A,N)
<=> $lesseq(0,tb2t(get(int,int,t2tb1(A),t2tb(N)))) ) ).
tff(num_of,type,
num_of: ( map_int_int * $int * $int ) > $int ).
tff(num_of_empty,axiom,
! [P: map_int_int,A: $int,B: $int] :
( $lesseq(B,A)
=> ( num_of(P,A,B) = 0 ) ) ).
tff(num_of_right_no_add,axiom,
! [P: map_int_int,A: $int,B: $int] :
( $less(A,B)
=> ( ~ pr(P,$difference(B,1))
=> ( num_of(P,A,B) = num_of(P,A,$difference(B,1)) ) ) ) ).
tff(num_of_right_add,axiom,
! [P: map_int_int,A: $int,B: $int] :
( $less(A,B)
=> ( pr(P,$difference(B,1))
=> ( num_of(P,A,B) = $sum(1,num_of(P,A,$difference(B,1))) ) ) ) ).
tff(num_of_bounds,axiom,
! [P: map_int_int,A: $int,B: $int] :
( $less(A,B)
=> ( $lesseq(0,num_of(P,A,B))
& $lesseq(num_of(P,A,B),$difference(B,A)) ) ) ).
tff(num_of_append,axiom,
! [P: map_int_int,A: $int,B: $int,C: $int] :
( ( $lesseq(A,B)
& $lesseq(B,C) )
=> ( num_of(P,A,C) = $sum(num_of(P,A,B),num_of(P,B,C)) ) ) ).
tff(num_of_left_no_add,axiom,
! [P: map_int_int,A: $int,B: $int] :
( $less(A,B)
=> ( ~ pr(P,A)
=> ( num_of(P,A,B) = num_of(P,$sum(A,1),B) ) ) ) ).
tff(num_of_left_add,axiom,
! [P: map_int_int,A: $int,B: $int] :
( $less(A,B)
=> ( pr(P,A)
=> ( num_of(P,A,B) = $sum(1,num_of(P,$sum(A,1),B)) ) ) ) ).
tff(empty,axiom,
! [P: map_int_int,A: $int,B: $int] :
( ! [N: $int] :
( ( $lesseq(A,N)
& $less(N,B) )
=> ~ pr(P,N) )
=> ( num_of(P,A,B) = 0 ) ) ).
tff(full,axiom,
! [P: map_int_int,A: $int,B: $int] :
( $lesseq(A,B)
=> ( ! [N: $int] :
( ( $lesseq(A,N)
& $less(N,B) )
=> pr(P,N) )
=> ( num_of(P,A,B) = $difference(B,A) ) ) ) ).
tff(num_of_increasing,axiom,
! [P: map_int_int,I: $int,J: $int,K: $int] :
( ( $lesseq(I,J)
& $lesseq(J,K) )
=> $lesseq(num_of(P,I,J),num_of(P,I,K)) ) ).
tff(num_of_strictly_increasing,axiom,
! [P: map_int_int,I: $int,J: $int,K: $int,L: $int] :
( ( $lesseq(I,J)
& $lesseq(J,K)
& $less(K,L) )
=> ( pr(P,K)
=> $less(num_of(P,I,J),num_of(P,I,L)) ) ) ).
tff(num_of_change_any,axiom,
! [P1: map_int_int,P2: map_int_int,A: $int,B: $int] :
( ! [J: $int] :
( ( $lesseq(A,J)
& $less(J,B) )
=> ( pr(P1,J)
=> pr(P2,J) ) )
=> $lesseq(num_of(P1,A,B),num_of(P2,A,B)) ) ).
tff(num_of_change_some,axiom,
! [P1: map_int_int,P2: map_int_int,A: $int,B: $int,I: $int] :
( ( $lesseq(A,I)
& $less(I,B) )
=> ( ! [J: $int] :
( ( $lesseq(A,J)
& $less(J,B) )
=> ( pr(P1,J)
=> pr(P2,J) ) )
=> ( ~ pr(P1,I)
=> ( pr(P2,I)
=> $less(num_of(P1,A,B),num_of(P2,A,B)) ) ) ) ) ).
tff(num_of_decrease,axiom,
! [M: map_int_int,L: $int,R: $int,I: $int,V: $int] :
( ( $lesseq(L,I)
& $less(I,R) )
=> ( $lesseq(0,tb2t(get(int,int,t2tb1(M),t2tb(I))))
=> ( $less(V,0)
=> $less(num_of(tb2t1(set(int,int,t2tb1(M),t2tb(I),t2tb(V))),L,R),num_of(M,L,R)) ) ) ) ).
tff(array_int,type,
array_int: $tType ).
tff(is_permutation,type,
is_permutation: array_int > $o ).
tff(t2tb2,type,
t2tb2: array_int > uni ).
tff(t2tb_sort2,axiom,
! [X: array_int] : sort(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(is_permutation_def,axiom,
! [A: array_int] :
( is_permutation(A)
<=> ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,length(int,t2tb2(A))) )
=> ( $lesseq(0,tb2t(get1(int,t2tb2(A),I)))
& $less(tb2t(get1(int,t2tb2(A),I)),length(int,t2tb2(A)))
& ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,length(int,t2tb2(A))) )
=> ( ( I != J )
=> ( tb2t(get1(int,t2tb2(A),I)) != tb2t(get1(int,t2tb2(A),J)) ) ) ) ) ) ) ).
tff(is_permutation_inverse,axiom,
! [A: array_int,B: array_int] :
( ( length(int,t2tb2(A)) = length(int,t2tb2(B)) )
=> ( is_permutation(A)
=> ( ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,length(int,t2tb2(B))) )
=> ( $lesseq(0,tb2t(get1(int,t2tb2(B),I)))
& $less(tb2t(get1(int,t2tb2(B),I)),length(int,t2tb2(B))) ) )
=> ( ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,length(int,t2tb2(B))) )
=> ( tb2t(get1(int,t2tb2(A),tb2t(get1(int,t2tb2(B),I)))) = I ) )
=> is_permutation(B) ) ) ) ) ).
tff(loopinvariant,type,
loopinvariant: ( array_int * array_int * $int * $int * $int ) > $o ).
tff(loopinvariant_def,axiom,
! [Old: array_int,A: array_int,M: $int,Mqt: $int,N: $int] :
( loopinvariant(Old,A,M,Mqt,N)
<=> ( ! [E: $int] :
( ( $lesseq(0,E)
& $less(E,N) )
=> ( $lesseq($uminus(N),tb2t(get1(int,t2tb2(A),E)))
& $less(tb2t(get1(int,t2tb2(A),E)),N) ) )
& ! [E: $int] :
( ( $less(M,E)
& $less(E,N) )
=> $lesseq(0,tb2t(get1(int,t2tb2(A),E))) )
& ! [E: $int] :
( ( $less(M,E)
& $less(E,N) )
=> ( tb2t(get1(int,t2tb2(Old),tb2t(get1(int,t2tb2(A),E)))) = E ) )
& ! [E: $int] :
( ( $lesseq(0,E)
& $lesseq(E,Mqt) )
=> ( $lesseq(0,tb2t(get1(int,t2tb2(A),E)))
=> ( tb2t(get1(int,t2tb2(Old),E)) = tb2t(get1(int,t2tb2(A),E)) ) ) )
& ! [E: $int] :
( ( $lesseq(0,E)
& $lesseq(E,M) )
=> $lesseq(tb2t(get1(int,t2tb2(A),E)),M) )
& ! [E: $int] :
( ( $lesseq(0,E)
& $lesseq(E,Mqt) )
=> ( $less(tb2t(get1(int,t2tb2(A),E)),0)
=> ( ( tb2t(get1(int,t2tb2(Old),prefix_tl(tb2t(get1(int,t2tb2(A),E))))) = E )
& ( $lesseq(prefix_tl(tb2t(get1(int,t2tb2(A),E))),M)
=> $less(tb2t(get1(int,t2tb2(A),prefix_tl(tb2t(get1(int,t2tb2(A),E))))),0) ) ) ) ) ) ) ).
tff(wP_parameter_test1,conjecture,
( $lesseq(0,3)
& ( $lesseq(0,3)
=> ( $lesseq(0,0)
& $less(0,3)
& ! [A: map_int_int] :
( ( $lesseq(0,3)
& ( A = tb2t1(set(int,int,const(int,int,t2tb(0)),t2tb(0),t2tb(2))) ) )
=> ( $lesseq(0,2)
& $less(2,3)
& ! [A1: map_int_int] :
( ( $lesseq(0,3)
& ( A1 = tb2t1(set(int,int,t2tb1(A),t2tb(2),t2tb(0))) ) )
=> ( $lesseq(0,1)
& $less(1,3)
& ! [A2: map_int_int] :
( ( $lesseq(0,3)
& ( A2 = tb2t1(set(int,int,t2tb1(A1),t2tb(1),t2tb(1))) ) )
=> is_permutation(tb2t2(mk_array(int,3,t2tb1(A2)))) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------