TPTP Problem File: SWW631_2.p
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%------------------------------------------------------------------------------
% File : SWW631_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Optimal replay-T-WP parameter distance
% 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 : optimal_replay-T-WP_parameter_distance [Fil14]
% Status : Theorem
% Rating : 0.25 v8.2.0, 0.50 v7.4.0, 0.25 v7.3.0, 0.17 v7.0.0, 0.29 v6.4.0, 0.00 v6.3.0, 0.57 v6.2.0, 0.62 v6.1.0
% Syntax : Number of formulae : 80 ( 27 unt; 38 typ; 0 def)
% Number of atoms : 119 ( 33 equ)
% Maximal formula atoms : 44 ( 1 avg)
% Number of connectives : 79 ( 2 ~; 2 |; 35 &)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 148 ( 54 atm; 15 fun; 42 num; 37 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 53 ( 24 >; 29 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 0 prp; 2-2 aty)
% Number of functors : 36 ( 30 usr; 11 con; 0-5 aty)
% Number of variables : 117 ( 114 !; 3 ?; 117 :)
% 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(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(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(n,type,
n: $int ).
tff(n_nonneg,axiom,
$less(0,n) ).
tff(f,type,
f: $int > $int ).
tff(f_prop,axiom,
! [K: $int] :
( ( $less(0,K)
& $less(K,n) )
=> ( $lesseq(0,f(K))
& $less(f(K),K) ) ) ).
tff(path,type,
path: ( $int * $int ) > $o ).
tff(path0,axiom,
path(0,0) ).
tff(paths,axiom,
! [I: $int] :
( ( $lesseq(0,I)
& $less(I,n) )
=> ! [D: $int,J: $int] :
( path(D,J)
=> ( ( $lesseq(f(I),J)
& $less(J,I) )
=> path($sum(D,1),I) ) ) ) ).
tff(path_inversion,axiom,
! [Z: $int,Z1: $int] :
( path(Z,Z1)
=> ( ( ( Z = 0 )
& ( Z1 = 0 ) )
| ? [I: $int] :
( $lesseq(0,I)
& $less(I,n)
& ? [D: $int,J: $int] :
( path(D,J)
& $lesseq(f(I),J)
& $less(J,I)
& ( Z = $sum(D,1) )
& ( Z1 = I ) ) ) ) ) ).
tff(distance,type,
distance: ( $int * $int ) > $o ).
tff(distance_def,axiom,
! [D: $int,I: $int] :
( distance(D,I)
<=> ( path(D,I)
& ! [Dqt: $int] :
( path(Dqt,I)
=> $lesseq(D,Dqt) ) ) ) ).
tff(map_int_int,type,
map_int_int: $tType ).
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(wP_parameter_distance,conjecture,
( $lesseq(0,n)
=> ( $lesseq(0,n)
=> ( ( $lesseq(0,0)
& $less(0,n) )
=> ! [G: map_int_int] :
( ( $lesseq(0,n)
& ( G = tb2t1(set(int,int,const(int,int,t2tb(0)),t2tb(0),t2tb($uminus(1)))) ) )
=> ( $lesseq(0,n)
=> ( $lesseq(0,n)
=> ( $lesseq(1,$difference(n,1))
=> ! [Count: $int,D: map_int_int,G1: map_int_int,I: $int] :
( ( $lesseq(1,I)
& $lesseq(I,$difference(n,1)) )
=> ( ( ( tb2t(get(int,int,t2tb1(D),t2tb(0))) = 0 )
& ( tb2t(get(int,int,t2tb1(G1),t2tb(0))) = $uminus(1) )
& $lesseq($sum(Count,tb2t(get(int,int,t2tb1(D),t2tb($difference(I,1))))),$difference(I,1))
& ! [K: $int] :
( ( $less(0,K)
& $less(K,I) )
=> ( $less(tb2t(get(int,int,t2tb1(G1),get(int,int,t2tb1(G1),t2tb(K)))),f(K))
& $lesseq(f(K),tb2t(get(int,int,t2tb1(G1),t2tb(K))))
& $less(tb2t(get(int,int,t2tb1(G1),t2tb(K))),K)
& $less(0,tb2t(get(int,int,t2tb1(D),t2tb(K))))
& ( tb2t(get(int,int,t2tb1(D),t2tb(K))) = $sum(tb2t(get(int,int,t2tb1(D),get(int,int,t2tb1(G1),t2tb(K)))),1) )
& ! [Kqt: $int] :
( ( $less(tb2t(get(int,int,t2tb1(G1),t2tb(K))),Kqt)
& $less(Kqt,K) )
=> $less(tb2t(get(int,int,t2tb1(D),get(int,int,t2tb1(G1),t2tb(K)))),tb2t(get(int,int,t2tb1(D),t2tb(Kqt)))) ) ) )
& ! [K: $int] :
( ( $lesseq(0,K)
& $less(K,I) )
=> path(tb2t(get(int,int,t2tb1(D),t2tb(K))),K) ) )
=> ! [J: $int,Count1: $int] :
( ( $lesseq(f(I),J)
& $less(J,I)
& $lesseq($sum(Count1,tb2t(get(int,int,t2tb1(D),t2tb(J)))),$difference(I,1))
& ! [K: $int] :
( ( $less(J,K)
& $less(K,I) )
=> $less(tb2t(get(int,int,t2tb1(D),t2tb(J))),tb2t(get(int,int,t2tb1(D),t2tb(K)))) ) )
=> ( ( $lesseq(0,n)
& $lesseq(0,J)
& $less(J,n) )
=> ( $lesseq(f(I),tb2t(get(int,int,t2tb1(G1),t2tb(J))))
=> ! [Count2: $int] :
( ( Count2 = $sum(Count1,1) )
=> ( ( $lesseq(0,J)
& $less(J,n) )
=> ! [J1: $int] :
( ( J1 = tb2t(get(int,int,t2tb1(G1),t2tb(J))) )
=> ! [K: $int] :
( ( $less(J1,K)
& $less(K,I) )
=> $less(tb2t(get(int,int,t2tb1(D),t2tb(J1))),tb2t(get(int,int,t2tb1(D),t2tb(K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------