TPTP Problem File: SWW669_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW669_2 : TPTP v8.2.0. 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 : 0.88 v7.5.0, 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 unt; 39 typ; 0 def)
% Number of atoms : 171 ( 45 equ)
% Maximal formula atoms : 84 ( 2 avg)
% Number of connectives : 140 ( 15 ~; 1 |; 48 &)
% ( 6 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 157 ( 46 atm; 24 fun; 42 num; 45 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 57 ( 25 >; 32 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 0 prp; 2-3 aty)
% Number of functors : 32 ( 27 usr; 10 con; 0-5 aty)
% Number of variables : 149 ( 149 !; 0 ?; 149 :)
% 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) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------