TPTP Problem File: SWW669=2.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SWW669=2 : TPTP v7.4.0. Released v6.1.0.
% Domain   : Software Verification
% Problem  : Vstte10 queens-T-WP parameter bt queens
% 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    : vstte10_queens-T-WP_parameter_bt_queens [Fil14]

% Status   : Theorem
% Rating   : 0.90 v7.4.0, 0.88 v7.3.0, 0.83 v7.0.0, 1.00 v6.2.0, 0.88 v6.1.0
% Syntax   : Number of formulae    :   85 (  26 unit;  39 type)
%            Number of atoms       :  171 (  45 equality)
%            Maximal formula depth :   45 (   5 average)
%            Number of connectives :  140 (  15   ~;   1   |;  48   &)
%                                         (   6 <=>;  70  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   57 (  25   >;  32   *;   0   +;   0  <<)
%            Number of predicates  :   51 (  42 propositional; 0-3 arity)
%            Number of functors    :   28 (   6 constant; 0-5 arity)
%            Number of variables   :  149 (   0 sgn; 149   !;   0   ?)
%                                         ( 149   :;   0  !>;   0  ?*)
%            Maximal term depth    :    5 (   2 average)
%            Arithmetic symbols    :   52 (   2 prd;   3 fun;   2 num;  45 var)
% 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(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(eq_board,type,(
    eq_board1: ( array_int * array_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(eq_board_def,axiom,(
    ! [B1: array_int,B2: array_int,Pos: $int] :
      ( eq_board1(B1,B2,Pos)
    <=> ! [Q: $int] :
          ( ( $lesseq(0,Q)
            & $less(Q,Pos) )
         => tb2t(get2(int,t2tb1(B1),Q)) = tb2t(get2(int,t2tb1(B2),Q)) ) ) )).

tff(eq_board_set,axiom,(
    ! [B: array_int,Pos: $int,Q: $int,I: $int] :
      ( $lesseq(Pos,Q)
     => eq_board1(B,tb2t1(set2(int,t2tb1(B),Q,t2tb(I))),Pos) ) )).

tff(eq_board_sym,axiom,(
    ! [B1: array_int,B2: array_int,Pos: $int] :
      ( eq_board1(B1,B2,Pos)
     => eq_board1(B2,B1,Pos) ) )).

tff(eq_board_trans,axiom,(
    ! [B1: array_int,B2: array_int,B3: array_int,Pos: $int] :
      ( eq_board1(B1,B2,Pos)
     => ( eq_board1(B2,B3,Pos)
       => eq_board1(B1,B3,Pos) ) ) )).

tff(eq_board_extension,axiom,(
    ! [B1: array_int,B2: array_int,Pos: $int] :
      ( eq_board1(B1,B2,Pos)
     => ( tb2t(get2(int,t2tb1(B1),Pos)) = tb2t(get2(int,t2tb1(B2),Pos))
       => eq_board1(B1,B2,$sum(Pos,1)) ) ) )).

tff(consistent_row,type,(
    consistent_row1: ( array_int * $int * $int ) > $o )).

tff(consistent_row_def,axiom,(
    ! [Board: array_int,Pos: $int,Q: $int] :
      ( consistent_row1(Board,Pos,Q)
    <=> ( tb2t(get2(int,t2tb1(Board),Q)) != tb2t(get2(int,t2tb1(Board),Pos))
        & $difference(tb2t(get2(int,t2tb1(Board),Q)),tb2t(get2(int,t2tb1(Board),Pos))) != $difference(Pos,Q)
        & $difference(tb2t(get2(int,t2tb1(Board),Pos)),tb2t(get2(int,t2tb1(Board),Q))) != $difference(Pos,Q) ) ) )).

tff(consistent_row_eq,axiom,(
    ! [B1: array_int,B2: array_int,Pos: $int] :
      ( eq_board1(B1,B2,$sum(Pos,1))
     => ! [Q: $int] :
          ( ( $lesseq(0,Q)
            & $less(Q,Pos) )
         => ( consistent_row1(B1,Pos,Q)
           => consistent_row1(B2,Pos,Q) ) ) ) )).

tff(is_consistent,type,(
    is_consistent1: ( array_int * $int ) > $o )).

tff(is_consistent_def,axiom,(
    ! [Board: array_int,Pos: $int] :
      ( is_consistent1(Board,Pos)
    <=> ! [Q: $int] :
          ( ( $lesseq(0,Q)
            & $less(Q,Pos) )
         => consistent_row1(Board,Pos,Q) ) ) )).

tff(is_board,type,(
    is_board1: ( array_int * $int ) > $o )).

tff(is_board_def,axiom,(
    ! [Board: array_int,Pos: $int] :
      ( is_board1(Board,Pos)
    <=> ! [Q: $int] :
          ( ( $lesseq(0,Q)
            & $less(Q,Pos) )
         => ( $lesseq(0,tb2t(get2(int,t2tb1(Board),Q)))
            & $less(tb2t(get2(int,t2tb1(Board),Q)),length1(int,t2tb1(Board))) ) ) ) )).

tff(solution,type,(
    solution1: ( array_int * $int ) > $o )).

tff(solution_def,axiom,(
    ! [Board: array_int,Pos: $int] :
      ( solution1(Board,Pos)
    <=> ( is_board1(Board,Pos)
        & ! [Q: $int] :
            ( ( $lesseq(0,Q)
              & $less(Q,Pos) )
           => is_consistent1(Board,Q) ) ) ) )).

tff(solution_eq_board,axiom,(
    ! [B1: array_int,B2: array_int,Pos: $int] :
      ( length1(int,t2tb1(B1)) = length1(int,t2tb1(B2))
     => ( eq_board1(B1,B2,Pos)
       => ( solution1(B1,Pos)
         => solution1(B2,Pos) ) ) ) )).

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(wP_parameter_bt_queens,conjecture,(
    ! [Board: $int,Board1: map_int_int,N: $int,Pos: $int] :
      ( ( $lesseq(0,Board)
        & Board = N
        & $lesseq(0,Pos)
        & $lesseq(Pos,N)
        & solution1(tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos) )
     => ( ( Pos = N
         => solution1(tb2t1(mk_array1(int,Board,t2tb2(Board1))),N) )
        & ( Pos != N
         => ( ( $less($difference(N,1),0)
             => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board1))),tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos)
                & ! [B: $int,B1: map_int_int] :
                    ( B = N
                   => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                     => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board1))),tb2t1(mk_array1(int,B,t2tb2(B1))),Pos)
                       => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) ) )
            & ( $lesseq(0,$difference(N,1))
             => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board1))),tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos)
                & ! [B: $int,B1: map_int_int] :
                    ( B = N
                   => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                     => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board1))),tb2t1(mk_array1(int,B,t2tb2(B1))),Pos)
                       => ( ( $lesseq(0,tb2t(get(int,int,t2tb2(B1),t2tb(Pos))))
                            & $less(tb2t(get(int,int,t2tb2(B1),t2tb(Pos))),0) )
                         => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) )
                & ! [Board2: map_int_int] :
                    ( ! [I: $int] :
                        ( ( $lesseq(0,I)
                          & $lesseq(I,$difference(N,1)) )
                       => ( ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board2))),tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos)
                            & ! [B: $int,B1: map_int_int] :
                                ( B = N
                               => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                                 => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board2))),tb2t1(mk_array1(int,B,t2tb2(B1))),Pos)
                                   => ( ( $lesseq(0,tb2t(get(int,int,t2tb2(B1),t2tb(Pos))))
                                        & $less(tb2t(get(int,int,t2tb2(B1),t2tb(Pos))),I) )
                                     => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) ) )
                         => ( $lesseq(0,Board)
                            & $lesseq(0,Pos)
                            & $less(Pos,Board)
                            & ! [Board3: map_int_int] :
                                ( ( $lesseq(0,Board)
                                  & Board3 = tb2t2(set(int,int,t2tb2(Board2),t2tb(Pos),t2tb(I))) )
                               => ( $lesseq(0,Pos)
                                  & $less(Pos,Board)
                                  & ! [Result: bool1] :
                                      ( ( Result = true1
                                      <=> is_consistent1(tb2t1(mk_array1(int,Board,t2tb2(Board3))),Pos) )
                                     => ( ( Result = true1
                                         => ( $lesseq(0,$difference(N,Pos))
                                            & $less($difference(N,$sum(Pos,1)),$difference(N,Pos))
                                            & Board = N
                                            & $lesseq(0,$sum(Pos,1))
                                            & $lesseq($sum(Pos,1),N)
                                            & solution1(tb2t1(mk_array1(int,Board,t2tb2(Board3))),$sum(Pos,1))
                                            & ! [Board4: map_int_int] :
                                                ( ( $lesseq(0,Board)
                                                  & eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board4))),tb2t1(mk_array1(int,Board,t2tb2(Board3))),$sum(Pos,1))
                                                  & ! [B: $int,B1: map_int_int] :
                                                      ( B = N
                                                     => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                                                       => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board4))),tb2t1(mk_array1(int,B,t2tb2(B1))),$sum(Pos,1))
                                                         => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) )
                                               => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board4))),tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos)
                                                  & ! [B: $int,B1: map_int_int] :
                                                      ( B = N
                                                     => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                                                       => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board4))),tb2t1(mk_array1(int,B,t2tb2(B1))),Pos)
                                                         => ( ( $lesseq(0,tb2t(get(int,int,t2tb2(B1),t2tb(Pos))))
                                                              & $less(tb2t(get(int,int,t2tb2(B1),t2tb(Pos))),$sum(I,1)) )
                                                           => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) ) ) )
                                            & ! [Board4: map_int_int] :
                                                ( ( $lesseq(0,Board)
                                                  & solution1(tb2t1(mk_array1(int,Board,t2tb2(Board4))),N) )
                                               => solution1(tb2t1(mk_array1(int,Board,t2tb2(Board4))),N) ) ) )
                                        & ( Result != true1
                                         => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board3))),tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos)
                                            & ! [B: $int,B1: map_int_int] :
                                                ( B = N
                                               => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                                                 => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board3))),tb2t1(mk_array1(int,B,t2tb2(B1))),Pos)
                                                   => ( ( $lesseq(0,tb2t(get(int,int,t2tb2(B1),t2tb(Pos))))
                                                        & $less(tb2t(get(int,int,t2tb2(B1),t2tb(Pos))),$sum(I,1)) )
                                                     => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) ) ) ) ) ) ) ) ) ) )
                    & ( ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board2))),tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos)
                        & ! [B: $int,B1: map_int_int] :
                            ( B = N
                           => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                             => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board2))),tb2t1(mk_array1(int,B,t2tb2(B1))),Pos)
                               => ( ( $lesseq(0,tb2t(get(int,int,t2tb2(B1),t2tb(Pos))))
                                    & $less(tb2t(get(int,int,t2tb2(B1),t2tb(Pos))),$sum($difference(N,1),1)) )
                                 => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) ) )
                     => ( $lesseq(0,Board)
                        & eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board2))),tb2t1(mk_array1(int,Board,t2tb2(Board1))),Pos)
                        & ! [B: $int,B1: map_int_int] :
                            ( B = N
                           => ( is_board1(tb2t1(mk_array1(int,B,t2tb2(B1))),N)
                             => ( eq_board1(tb2t1(mk_array1(int,Board,t2tb2(Board2))),tb2t1(mk_array1(int,B,t2tb2(B1))),Pos)
                               => ~ solution1(tb2t1(mk_array1(int,B,t2tb2(B1))),N) ) ) ) ) ) ) ) ) ) ) ) ) )).

%------------------------------------------------------------------------------