TPTP Problem File: SWW592_2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW592_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Fibonacci-T-WP parameter logfib
% 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 : fibonacci-T-WP_parameter_logfib [Fil14]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.12 v7.5.0, 0.20 v7.4.0, 0.12 v7.3.0, 0.00 v7.0.0, 0.14 v6.4.0, 0.00 v6.3.0, 0.14 v6.2.0, 0.38 v6.1.0
% Syntax : Number of formulae : 60 ( 19 unt; 26 typ; 0 def)
% Number of atoms : 56 ( 32 equ)
% Maximal formula atoms : 4 ( 0 avg)
% Number of connectives : 24 ( 2 ~; 1 |; 2 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 138 ( 20 atm; 33 fun; 47 num; 38 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 29 ( 20 usr; 12 con; 0-4 aty)
% Number of variables : 69 ( 69 !; 0 ?; 69 :)
% 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(fib,type,
fib1: $int > $int ).
tff(fib0,axiom,
fib1(0) = 0 ).
tff(fib1,axiom,
fib1(1) = 1 ).
tff(fibn,axiom,
! [N: $int] :
( $lesseq(2,N)
=> ( fib1(N) = $sum(fib1($difference(N,1)),fib1($difference(N,2))) ) ) ).
tff(abs,type,
abs1: $int > $int ).
tff(abs_def,axiom,
! [X: $int] :
( ( $lesseq(0,X)
=> ( abs1(X) = X ) )
& ( ~ $lesseq(0,X)
=> ( abs1(X) = $uminus(X) ) ) ) ).
tff(abs_le,axiom,
! [X: $int,Y: $int] :
( $lesseq(abs1(X),Y)
<=> ( $lesseq($uminus(Y),X)
& $lesseq(X,Y) ) ) ).
tff(abs_pos,axiom,
! [X: $int] : $lesseq(0,abs1(X)) ).
tff(div_mult,axiom,
! [X: $int,Y: $int,Z: $int] :
( $less(0,X)
=> ( $quotient_e($sum($product(X,Y),Z),X) = $sum(Y,$quotient_e(Z,X)) ) ) ).
tff(mod_mult,axiom,
! [X: $int,Y: $int,Z: $int] :
( $less(0,X)
=> ( $remainder_e($sum($product(X,Y),Z),X) = $remainder_e(Z,X) ) ) ).
tff(t,type,
t1: $tType ).
tff(t1,type,
t: ty ).
tff(mk_t,type,
mk_t1: ( $int * $int * $int * $int ) > t1 ).
tff(a11,type,
a111: t1 > $int ).
tff(a11_def1,axiom,
! [U: $int,U1: $int,U2: $int,U3: $int] : a111(mk_t1(U,U1,U2,U3)) = U ).
tff(a12,type,
a121: t1 > $int ).
tff(a12_def1,axiom,
! [U: $int,U1: $int,U2: $int,U3: $int] : a121(mk_t1(U,U1,U2,U3)) = U1 ).
tff(a21,type,
a211: t1 > $int ).
tff(a21_def1,axiom,
! [U: $int,U1: $int,U2: $int,U3: $int] : a211(mk_t1(U,U1,U2,U3)) = U2 ).
tff(a22,type,
a221: t1 > $int ).
tff(a22_def1,axiom,
! [U: $int,U1: $int,U2: $int,U3: $int] : a221(mk_t1(U,U1,U2,U3)) = U3 ).
tff(t_inversion1,axiom,
! [U: t1] : U = mk_t1(a111(U),a121(U),a211(U),a221(U)) ).
tff(mult,type,
mult1: ( t1 * t1 ) > t1 ).
tff(mult_def,axiom,
! [X: t1,Y: t1] : mult1(X,Y) = mk_t1($sum($product(a111(X),a111(Y)),$product(a121(X),a211(Y))),$sum($product(a111(X),a121(Y)),$product(a121(X),a221(Y))),$sum($product(a211(X),a111(Y)),$product(a221(X),a211(Y))),$sum($product(a211(X),a121(Y)),$product(a221(X),a221(Y)))) ).
tff(assoc2,axiom,
! [X: t1,Y: t1,Z: t1] : mult1(mult1(X,Y),Z) = mult1(X,mult1(Y,Z)) ).
tff(unit_def_l1,axiom,
! [X: t1] : mult1(mk_t1(1,0,0,1),X) = X ).
tff(unit_def_r1,axiom,
! [X: t1] : mult1(X,mk_t1(1,0,0,1)) = X ).
tff(comm2,axiom,
! [X: t1,Y: t1] : mult1(X,Y) = mult1(Y,X) ).
tff(power,type,
power1: ( t1 * $int ) > t1 ).
tff(power_0,axiom,
! [X: t1] : power1(X,0) = mk_t1(1,0,0,1) ).
tff(power_s,axiom,
! [X: t1,N: $int] :
( $lesseq(0,N)
=> ( power1(X,$sum(N,1)) = mult1(X,power1(X,N)) ) ) ).
tff(power_s_alt,axiom,
! [X: t1,N: $int] :
( $less(0,N)
=> ( power1(X,N) = mult1(X,power1(X,$difference(N,1))) ) ) ).
tff(power_1,axiom,
! [X: t1] : power1(X,1) = X ).
tff(power_sum,axiom,
! [X: t1,N: $int,M: $int] :
( $lesseq(0,N)
=> ( $lesseq(0,M)
=> ( power1(X,$sum(N,M)) = mult1(power1(X,N),power1(X,M)) ) ) ) ).
tff(power_mult,axiom,
! [X: t1,N: $int,M: $int] :
( $lesseq(0,N)
=> ( $lesseq(0,M)
=> ( power1(X,$product(N,M)) = power1(power1(X,N),M) ) ) ) ).
tff(power_mult2,axiom,
! [X: t1,Y: t1,N: $int] :
( $lesseq(0,N)
=> ( power1(mult1(X,Y),N) = mult1(power1(X,N),power1(Y,N)) ) ) ).
tff(wP_parameter_logfib,conjecture,
! [N: $int] :
( $lesseq(0,N)
=> ( ( N = 0 )
=> ( power1(mk_t1(1,1,1,0),N) = mk_t1($sum(1,0),0,0,1) ) ) ) ).
%------------------------------------------------------------------------------