TPTP Problem File: SWW596_2.p
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%------------------------------------------------------------------------------
% File : SWW596_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Flag2-T-WP parameter swap
% 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 : flag2-T-WP_parameter_swap [Fil14]
% Status : Theorem
% Rating : 0.75 v8.2.0, 0.88 v8.1.0, 0.75 v7.5.0, 0.80 v7.4.0, 0.62 v7.3.0, 0.67 v7.0.0, 0.86 v6.4.0, 1.00 v6.3.0, 0.86 v6.2.0, 0.88 v6.1.0
% Syntax : Number of formulae : 85 ( 20 unt; 37 typ; 0 def)
% Number of atoms : 105 ( 52 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 67 ( 10 ~; 3 |; 14 &)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 89 ( 28 atm; 10 fun; 9 num; 42 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 45 ( 19 >; 26 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 0 prp; 2-4 aty)
% Number of functors : 34 ( 29 usr; 14 con; 0-5 aty)
% Number of variables : 147 ( 147 !; 0 ?; 147 :)
% 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(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(color,type,
color: $tType ).
tff(color1,type,
color1: ty ).
tff(blue,type,
blue: color ).
tff(white,type,
white: color ).
tff(red,type,
red: color ).
tff(match_color,type,
match_color: ( ty * color * uni * uni * uni ) > uni ).
tff(match_color_sort,axiom,
! [A: ty,X: color,X1: uni,X2: uni,X3: uni] : sort(A,match_color(A,X,X1,X2,X3)) ).
tff(match_color_Blue,axiom,
! [A: ty,Z: uni,Z1: uni,Z2: uni] :
( sort(A,Z)
=> ( match_color(A,blue,Z,Z1,Z2) = Z ) ) ).
tff(match_color_White,axiom,
! [A: ty,Z: uni,Z1: uni,Z2: uni] :
( sort(A,Z1)
=> ( match_color(A,white,Z,Z1,Z2) = Z1 ) ) ).
tff(match_color_Red,axiom,
! [A: ty,Z: uni,Z1: uni,Z2: uni] :
( sort(A,Z2)
=> ( match_color(A,red,Z,Z1,Z2) = Z2 ) ) ).
tff(blue_White,axiom,
blue != white ).
tff(blue_Red,axiom,
blue != red ).
tff(white_Red,axiom,
white != red ).
tff(color_inversion,axiom,
! [U: color] :
( ( U = blue )
| ( U = white )
| ( U = red ) ) ).
tff(map_int_color,type,
map_int_color: $tType ).
tff(monochrome,type,
monochrome: ( map_int_color * $int * $int * color ) > $o ).
tff(t2tb,type,
t2tb: map_int_color > uni ).
tff(t2tb_sort,axiom,
! [X: map_int_color] : sort(map(int,color1),t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > map_int_color ).
tff(bridgeL,axiom,
! [I: map_int_color] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] :
( sort(map(int,color1),J)
=> ( t2tb(tb2t(J)) = J ) ) ).
tff(t2tb1,type,
t2tb1: color > uni ).
tff(t2tb_sort1,axiom,
! [X: color] : sort(color1,t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > color ).
tff(bridgeL1,axiom,
! [I: color] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] :
( sort(color1,J)
=> ( t2tb1(tb2t1(J)) = J ) ) ).
tff(t2tb2,type,
t2tb2: $int > uni ).
tff(t2tb_sort2,axiom,
! [X: $int] : sort(int,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > $int ).
tff(bridgeL2,axiom,
! [I: $int] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(monochrome_def,axiom,
! [A: map_int_color,I: $int,J: $int,C: color] :
( monochrome(A,I,J,C)
<=> ! [K: $int] :
( ( $lesseq(I,K)
& $less(K,J) )
=> ( tb2t1(get(color1,int,t2tb(A),t2tb2(K))) = C ) ) ) ).
tff(nb_occ,type,
nb_occ: ( map_int_color * $int * $int * color ) > $int ).
tff(nb_occ_null,axiom,
! [A: map_int_color,I: $int,J: $int,C: color] :
( $lesseq(J,I)
=> ( nb_occ(A,I,J,C) = 0 ) ) ).
tff(nb_occ_add_eq,axiom,
! [A: map_int_color,I: $int,J: $int,C: color] :
( ( $less(I,J)
& ( tb2t1(get(color1,int,t2tb(A),t2tb2($difference(J,1)))) = C ) )
=> ( nb_occ(A,I,J,C) = $sum(nb_occ(A,I,$difference(J,1),C),1) ) ) ).
tff(nb_occ_add_neq,axiom,
! [A: map_int_color,I: $int,J: $int,C: color] :
( ( $less(I,J)
& ( tb2t1(get(color1,int,t2tb(A),t2tb2($difference(J,1)))) != C ) )
=> ( nb_occ(A,I,J,C) = nb_occ(A,I,$difference(J,1),C) ) ) ).
tff(nb_occ_split,axiom,
! [A: map_int_color,I: $int,J: $int,K: $int,C: color] :
( ( $lesseq(I,J)
& $lesseq(J,K) )
=> ( nb_occ(A,I,K,C) = $sum(nb_occ(A,I,J,C),nb_occ(A,J,K,C)) ) ) ).
tff(nb_occ_ext,axiom,
! [A1: map_int_color,A2: map_int_color,I: $int,J: $int,C: color] :
( ! [K: $int] :
( ( $lesseq(I,K)
& $less(K,J) )
=> ( tb2t1(get(color1,int,t2tb(A1),t2tb2(K))) = tb2t1(get(color1,int,t2tb(A2),t2tb2(K))) ) )
=> ( nb_occ(A1,I,J,C) = nb_occ(A2,I,J,C) ) ) ).
tff(nb_occ_store_outside_up,axiom,
! [A: map_int_color,I: $int,J: $int,K: $int,C: color] :
( ( $lesseq(I,J)
& $lesseq(J,K) )
=> ( nb_occ(tb2t(set(color1,int,t2tb(A),t2tb2(K),t2tb1(C))),I,J,C) = nb_occ(A,I,J,C) ) ) ).
tff(nb_occ_store_outside_down,axiom,
! [A: map_int_color,I: $int,J: $int,K: $int,C: color] :
( ( $less(K,I)
& $lesseq(I,J) )
=> ( nb_occ(tb2t(set(color1,int,t2tb(A),t2tb2(K),t2tb1(C))),I,J,C) = nb_occ(A,I,J,C) ) ) ).
tff(nb_occ_store_eq_eq,axiom,
! [A: map_int_color,I: $int,J: $int,K: $int,C: color] :
( ( $lesseq(I,K)
& $less(K,J) )
=> ( ( tb2t1(get(color1,int,t2tb(A),t2tb2(K))) = C )
=> ( nb_occ(tb2t(set(color1,int,t2tb(A),t2tb2(K),t2tb1(C))),I,J,C) = nb_occ(A,I,J,C) ) ) ) ).
tff(nb_occ_store_eq_neq,axiom,
! [A: map_int_color,I: $int,J: $int,K: $int,C: color] :
( ( $lesseq(I,K)
& $less(K,J) )
=> ( ( tb2t1(get(color1,int,t2tb(A),t2tb2(K))) != C )
=> ( nb_occ(tb2t(set(color1,int,t2tb(A),t2tb2(K),t2tb1(C))),I,J,C) = $sum(nb_occ(A,I,J,C),1) ) ) ) ).
tff(nb_occ_store_neq_eq,axiom,
! [A: map_int_color,I: $int,J: $int,K: $int,C: color,Cqt: color] :
( ( $lesseq(I,K)
& $less(K,J) )
=> ( ( C != Cqt )
=> ( ( tb2t1(get(color1,int,t2tb(A),t2tb2(K))) = C )
=> ( nb_occ(tb2t(set(color1,int,t2tb(A),t2tb2(K),t2tb1(Cqt))),I,J,C) = $difference(nb_occ(A,I,J,C),1) ) ) ) ) ).
tff(nb_occ_store_neq_neq,axiom,
! [A: map_int_color,I: $int,J: $int,K: $int,C: color,Cqt: color] :
( ( $lesseq(I,K)
& $less(K,J) )
=> ( ( C != Cqt )
=> ( ( tb2t1(get(color1,int,t2tb(A),t2tb2(K))) != C )
=> ( nb_occ(tb2t(set(color1,int,t2tb(A),t2tb2(K),t2tb1(Cqt))),I,J,C) = nb_occ(A,I,J,C) ) ) ) ) ).
tff(wP_parameter_swap,conjecture,
! [A: map_int_color,I: $int,J: $int,A1: map_int_color] :
( ( A1 = tb2t(set(color1,int,t2tb(A),t2tb2(I),get(color1,int,t2tb(A),t2tb2(J)))) )
=> ! [A2: map_int_color] :
( ( A2 = tb2t(set(color1,int,t2tb(A1),t2tb2(J),get(color1,int,t2tb(A),t2tb2(I)))) )
=> ! [K1: $int,K2: $int,C: color] :
( ( $lesseq(K1,I)
& $less(I,K2)
& $lesseq(K1,J)
& $less(J,K2) )
=> ( nb_occ(A2,K1,K2,C) = nb_occ(A,K1,K2,C) ) ) ) ) ).
%------------------------------------------------------------------------------