TPTP Problem File: SWW599_2.p
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%------------------------------------------------------------------------------
% File : SWW599_2 : TPTP v9.0.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Foveoos11 challenge3-T-WP parameter two equal elements
% 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 : foveoos11_challenge3-T-WP_parameter_two_equal_elements [Fil14]
% Status : Theorem
% Rating : 0.25 v8.2.0, 0.38 v7.5.0, 0.40 v7.4.0, 0.38 v7.3.0, 0.33 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.57 v6.2.0, 0.75 v6.1.0
% Syntax : Number of formulae : 89 ( 32 unt; 43 typ; 0 def)
% Number of atoms : 108 ( 46 equ)
% Maximal formula atoms : 40 ( 1 avg)
% Number of connectives : 74 ( 12 ~; 2 |; 28 &)
% ( 1 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 119 ( 26 atm; 25 fun; 38 num; 30 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 57 ( 28 >; 29 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 40 ( 34 usr; 11 con; 0-5 aty)
% Number of variables : 119 ( 114 !; 5 ?; 119 :)
% 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_sort1,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_sort1,axiom,
! [A: ty,X: uni] : sort1(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort1,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_sort2,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_sort2,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_sort1,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_sort1,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),mk_array1(A,X,X1)) ).
tff(length,type,
length1: ( ty * uni ) > $int ).
tff(length_def1,axiom,
! [A: ty,U: $int,U1: uni] : ( length1(A,mk_array1(A,U,U1)) = U ) ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(elts_sort1,axiom,
! [A: ty,X: uni] : sort1(map(int,A),elts(A,X)) ).
tff(elts_def1,axiom,
! [A: ty,U: $int,U1: uni] :
( sort1(map(int,A),U1)
=> ( elts(A,mk_array1(A,U,U1)) = U1 ) ) ).
tff(array_inversion1,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_sort3,axiom,
! [A: ty,X: uni,X1: $int] : sort1(A,get2(A,X,X1)) ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(t2tb_sort,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_sort3,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_sort1,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(array_int,type,
array_int: $tType ).
tff(appear_twice,type,
appear_twice1: ( array_int * $int * $int ) > $o ).
tff(t2tb1,type,
t2tb1: array_int > uni ).
tff(t2tb_sort1,axiom,
! [X: array_int] : sort1(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(appear_twice_def,axiom,
! [A: array_int,V: $int,U: $int] :
( appear_twice1(A,V,U)
<=> ? [I: $int] :
( $lesseq(0,I)
& $less(I,U)
& ( tb2t(get2(int,t2tb1(A),I)) = V )
& ? [J: $int] :
( $lesseq(0,J)
& $less(J,U)
& ( J != I )
& ( tb2t(get2(int,t2tb1(A),J)) = V ) ) ) ) ).
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] : sort1(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(t2tb3,type,
t2tb3: bool1 > uni ).
tff(t2tb_sort3,axiom,
! [X: bool1] : sort1(bool,t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > bool1 ).
tff(bridgeL3,axiom,
! [I: bool1] : ( tb2t3(t2tb3(I)) = I ) ).
tff(bridgeR3,axiom,
! [J: uni] :
( sort1(bool,J)
=> ( t2tb3(tb2t3(J)) = J ) ) ).
tff(map_int_bool,type,
map_int_bool: $tType ).
tff(t2tb4,type,
t2tb4: map_int_bool > uni ).
tff(t2tb_sort4,axiom,
! [X: map_int_bool] : sort1(map(int,bool),t2tb4(X)) ).
tff(tb2t4,type,
tb2t4: uni > map_int_bool ).
tff(bridgeL4,axiom,
! [I: map_int_bool] : ( tb2t4(t2tb4(I)) = I ) ).
tff(bridgeR4,axiom,
! [J: uni] :
( sort1(map(int,bool),J)
=> ( t2tb4(tb2t4(J)) = J ) ) ).
tff(wP_parameter_two_equal_elements,conjecture,
! [A: $int,A1: map_int_int,N: $int] :
( ( $lesseq(0,A)
& ( A = $sum(N,2) )
& $lesseq(2,N)
& ! [I: $int] :
( ( $lesseq(0,I)
& $less(I,A) )
=> ( $lesseq(0,tb2t(get(int,int,t2tb2(A1),t2tb(I))))
& $less(tb2t(get(int,int,t2tb2(A1),t2tb(I))),N) ) )
& ? [V1: $int] :
( appear_twice1(tb2t1(mk_array1(int,A,t2tb2(A1))),V1,$sum(N,2))
& ? [V2: $int] :
( appear_twice1(tb2t1(mk_array1(int,A,t2tb2(A1))),V2,$sum(N,2))
& ( V2 != V1 ) ) ) )
=> ( $lesseq(0,N)
=> ( $lesseq(0,N)
=> ( $lesseq(0,$sum(N,1))
=> ! [V2: $int,V1: $int,Deja_vu: map_int_bool] :
( ( ( ( V1 = $uminus(1) )
=> ( V2 = $uminus(1) ) )
& ( ( V1 != $uminus(1) )
=> appear_twice1(tb2t1(mk_array1(int,A,t2tb2(A1))),V1,$sum($sum(N,1),1)) )
& ( ( V2 != $uminus(1) )
=> ( appear_twice1(tb2t1(mk_array1(int,A,t2tb2(A1))),V2,$sum($sum(N,1),1))
& ( V2 != V1 ) ) )
& ! [V: $int] :
( ( $lesseq(0,V)
& $less(V,N) )
=> ( ( ( tb2t3(get(bool,int,t2tb4(Deja_vu),t2tb(V))) = true1 )
& ? [J: $int] :
( $lesseq(0,J)
& $less(J,$sum($sum(N,1),1))
& ( tb2t(get(int,int,t2tb2(A1),t2tb(J))) = V ) ) )
| ( ( tb2t3(get(bool,int,t2tb4(Deja_vu),t2tb(V))) != true1 )
& ! [J: $int] :
( ( $lesseq(0,J)
& $less(J,$sum($sum(N,1),1)) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(J))) != V ) ) ) ) )
& ( ( V1 = $uminus(1) )
=> ! [V: $int] :
( ( $lesseq(0,V)
& $less(V,N) )
=> ~ appear_twice1(tb2t1(mk_array1(int,A,t2tb2(A1))),V,$sum($sum(N,1),1)) ) )
& ( ( V2 = $uminus(1) )
=> ! [V: $int] :
( ( $lesseq(0,V)
& $less(V,N) )
=> ( ( V != V1 )
=> ~ appear_twice1(tb2t1(mk_array1(int,A,t2tb2(A1))),V,$sum($sum(N,1),1)) ) ) ) )
=> appear_twice1(tb2t1(mk_array1(int,A,t2tb2(A1))),V1,$sum(N,2)) ) ) ) ) ) ).
%------------------------------------------------------------------------------