TPTP Problem File: SWW582_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW582_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Conjugate-T-WP parameter conjugate
% 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 : conjugate-T-WP_parameter_conjugate [Fil14]
% Status : Theorem
% Rating : 0.75 v8.2.0, 0.88 v8.1.0, 0.75 v7.5.0, 0.80 v7.4.0, 0.75 v7.3.0, 0.67 v7.0.0, 0.86 v6.4.0, 0.33 v6.3.0, 0.86 v6.2.0, 0.75 v6.1.0
% Syntax : Number of formulae : 82 ( 28 unt; 40 typ; 0 def)
% Number of atoms : 179 ( 45 equ)
% Maximal formula atoms : 94 ( 2 avg)
% Number of connectives : 143 ( 6 ~; 1 |; 83 &)
% ( 1 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 50 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 255 ( 98 atm; 35 fun; 79 num; 43 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 56 ( 26 >; 30 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 0 prp; 1-3 aty)
% Number of functors : 35 ( 30 usr; 10 con; 0-5 aty)
% Number of variables : 131 ( 131 !; 0 ?; 131 :)
% 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(array_int,type,
array_int: $tType ).
tff(is_partition,type,
is_partition: array_int > $o ).
tff(t2tb1,type,
t2tb1: array_int > uni ).
tff(t2tb_sort1,axiom,
! [X: array_int] : sort(array(int),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > array_int ).
tff(bridgeL1,axiom,
! [I: array_int] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(is_partition_def,axiom,
! [A: array_int] :
( ( is_partition(A)
=> ( $less(0,length(int,t2tb1(A)))
& ! [I: $int,J: $int] :
( ( $lesseq(0,I)
& $lesseq(I,J)
& $less(J,length(int,t2tb1(A))) )
=> $lesseq(tb2t(get1(int,t2tb1(A),J)),tb2t(get1(int,t2tb1(A),I))) )
& ( tb2t(get1(int,t2tb1(A),$difference(length(int,t2tb1(A)),1))) = 0 ) ) )
& ( ( $less(0,length(int,t2tb1(A)))
& ! [I: $int,J: $int] :
( ( $lesseq(0,I)
& $lesseq(I,J)
& $less(J,length(int,t2tb1(A))) )
=> $lesseq(tb2t(get1(int,t2tb1(A),J)),tb2t(get1(int,t2tb1(A),I))) )
& ( tb2t(get1(int,t2tb1(A),$difference(length(int,t2tb1(A)),1))) = 0 ) )
=> is_partition(A) ) ) ).
tff(numofgt,type,
numofgt: ( array_int * $int * $int ) > $o ).
tff(numofgt_def,axiom,
! [A: array_int,N: $int,V: $int] :
( ( numofgt(A,N,V)
=> ( $lesseq(0,N)
& $less(N,length(int,t2tb1(A)))
& ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,N) )
=> $less(V,tb2t(get1(int,t2tb1(A),J))) )
& $lesseq(tb2t(get1(int,t2tb1(A),N)),V) ) )
& ( ( $lesseq(0,N)
& $less(N,length(int,t2tb1(A)))
& ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,N) )
=> $less(V,tb2t(get1(int,t2tb1(A),J))) )
& $lesseq(tb2t(get1(int,t2tb1(A),N)),V) )
=> numofgt(A,N,V) ) ) ).
tff(is_conjugate,type,
is_conjugate: ( array_int * array_int ) > $o ).
tff(is_conjugate_def,axiom,
! [A: array_int,B: array_int] :
( is_conjugate(A,B)
<=> ( $less(tb2t(get1(int,t2tb1(A),0)),length(int,t2tb1(B)))
& ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,length(int,t2tb1(B))) )
=> numofgt(A,tb2t(get1(int,t2tb1(B),J)),J) ) ) ) ).
tff(map_int_int,type,
map_int_int: $tType ).
tff(t2tb2,type,
t2tb2: map_int_int > uni ).
tff(t2tb_sort2,axiom,
! [X: map_int_int] : sort(map(int,int),t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > map_int_int ).
tff(bridgeL2,axiom,
! [I: map_int_int] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(wP_parameter_conjugate,conjecture,
! [A: $int,A1: map_int_int] :
( ( $lesseq(0,A)
& is_partition(tb2t1(mk_array(int,A,t2tb2(A1)))) )
=> ( $lesseq(0,0)
& $less(0,A)
& $lesseq(0,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1))
& ( $lesseq(0,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1))
=> ( $lesseq(0,0)
& $less(0,A)
& ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(0))),J)
& $less(J,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1)) )
=> numofgt(tb2t1(mk_array(int,A,t2tb2(A1))),tb2t(get(int,int,const(int,int,t2tb(0)),t2tb(J))),J) )
& ! [Partc: $int,B: map_int_int] :
( ( $lesseq(0,Partc)
& $less(Partc,A)
& ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),J)
& $less(J,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1)) )
=> numofgt(tb2t1(mk_array(int,A,t2tb2(A1))),tb2t(get(int,int,t2tb2(B),t2tb(J))),J) ) )
=> ( $lesseq(0,Partc)
& $less(Partc,A)
& ( ( tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) != 0 )
=> ( $lesseq(0,Partc)
& $less(Partc,A)
& ! [Partc1: $int] :
( ( Partc1 = $sum(Partc,1) )
=> ( $lesseq(Partc,Partc1)
& $less(Partc1,A)
& ! [J: $int] :
( ( $lesseq(Partc,J)
& $less(J,Partc1) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(J))) = tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) ) )
& ! [Partc2: $int] :
( ( $lesseq(Partc,Partc2)
& $less(Partc2,A)
& ! [J: $int] :
( ( $lesseq(Partc,J)
& $less(J,Partc2) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(J))) = tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) ) ) )
=> ( $lesseq(0,Partc2)
& $less(Partc2,A)
& ( ( tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))) = tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) )
=> ! [Partc3: $int] :
( ( Partc3 = $sum(Partc2,1) )
=> ( $lesseq(Partc,Partc3)
& $less(Partc3,A)
& ! [J: $int] :
( ( $lesseq(Partc,J)
& $less(J,Partc3) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(J))) = tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) ) )
& $lesseq(0,$difference(A,Partc2))
& $less($difference(A,Partc3),$difference(A,Partc2)) ) ) )
& ( ( tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))) != tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) )
=> ( $lesseq(0,Partc2)
& $less(Partc2,A)
& ( $less($difference(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),1),tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))))
=> ( $lesseq(0,Partc2)
& $less(Partc2,A)
& ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),J)
& $less(J,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1)) )
=> numofgt(tb2t1(mk_array(int,A,t2tb2(A1))),tb2t(get(int,int,t2tb2(B),t2tb(J))),J) )
& $lesseq(0,$difference(A,Partc))
& $less($difference(A,Partc2),$difference(A,Partc)) ) )
& ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),$difference(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),1))
=> ( ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),J)
& $less(J,tb2t(get(int,int,t2tb2(A1),t2tb(Partc2)))) )
=> ( tb2t(get(int,int,t2tb2(B),t2tb(J))) = Partc2 ) )
& ! [B1: map_int_int] :
( ! [I: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),I)
& $lesseq(I,$difference(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),1)) )
=> ( ( ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),J)
& $less(J,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1)) )
=> ( tb2t(get(int,int,t2tb2(B1),t2tb(J))) = tb2t(get(int,int,t2tb2(B),t2tb(J))) ) )
& ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),J)
& $less(J,I) )
=> ( tb2t(get(int,int,t2tb2(B1),t2tb(J))) = Partc2 ) ) )
=> ( $lesseq(0,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1))
& $lesseq(0,I)
& $less(I,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1))
& ! [B2: map_int_int] :
( ( $lesseq(0,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1))
& ( B2 = tb2t2(set(int,int,t2tb2(B1),t2tb(I),t2tb(Partc2))) ) )
=> ( ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),J)
& $less(J,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1)) )
=> ( tb2t(get(int,int,t2tb2(B2),t2tb(J))) = tb2t(get(int,int,t2tb2(B),t2tb(J))) ) )
& ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),J)
& $less(J,$sum(I,1)) )
=> ( tb2t(get(int,int,t2tb2(B2),t2tb(J))) = Partc2 ) ) ) ) ) ) )
& ( ( ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),J)
& $less(J,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1)) )
=> ( tb2t(get(int,int,t2tb2(B1),t2tb(J))) = tb2t(get(int,int,t2tb2(B),t2tb(J))) ) )
& ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),J)
& $less(J,$sum($difference(tb2t(get(int,int,t2tb2(A1),t2tb(Partc))),1),1)) )
=> ( tb2t(get(int,int,t2tb2(B1),t2tb(J))) = Partc2 ) ) )
=> ( $lesseq(0,Partc2)
& $less(Partc2,A)
& ! [J: $int] :
( ( $lesseq(tb2t(get(int,int,t2tb2(A1),t2tb(Partc2))),J)
& $less(J,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1)) )
=> numofgt(tb2t1(mk_array(int,A,t2tb2(A1))),tb2t(get(int,int,t2tb2(B1),t2tb(J))),J) )
& $lesseq(0,$difference(A,Partc))
& $less($difference(A,Partc2),$difference(A,Partc)) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ~ ( ( tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) != 0 ) )
=> ( ( tb2t(get(int,int,t2tb2(A1),t2tb(Partc))) = 0 )
& $lesseq(0,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1))
& is_conjugate(tb2t1(mk_array(int,A,t2tb2(A1))),tb2t1(mk_array(int,$sum(tb2t(get(int,int,t2tb2(A1),t2tb(0))),1),t2tb2(B)))) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------