TPTP Problem File: SWW632_2.p
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%------------------------------------------------------------------------------
% File : SWW632_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Power-T-WP parameter fast exp imperative
% 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 : power-T-WP_parameter_fast_exp_imperative [Fil14]
% Status : Theorem
% Rating : 0.25 v7.5.0, 0.40 v7.4.0, 0.38 v7.3.0, 0.33 v7.0.0, 0.29 v6.4.0, 0.67 v6.3.0, 0.57 v6.2.0, 0.75 v6.1.0
% Syntax : Number of formulae : 59 ( 11 unt; 22 typ; 0 def)
% Number of atoms : 85 ( 31 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 8 ~; 1 |; 16 &)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 173 ( 46 atm; 23 fun; 49 num; 55 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 23 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 76 ( 76 !; 0 ?; 76 :)
% 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_sort1,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(power,type,
power: ( $int * $int ) > $int ).
tff(power_0,axiom,
! [X: $int] : power(X,0) = 1 ).
tff(power_s,axiom,
! [X: $int,N: $int] :
( $lesseq(0,N)
=> ( power(X,$sum(N,1)) = $product(X,power(X,N)) ) ) ).
tff(power_s_alt,axiom,
! [X: $int,N: $int] :
( $less(0,N)
=> ( power(X,N) = $product(X,power(X,$difference(N,1))) ) ) ).
tff(power_1,axiom,
! [X: $int] : power(X,1) = X ).
tff(power_sum,axiom,
! [X: $int,N: $int,M: $int] :
( $lesseq(0,N)
=> ( $lesseq(0,M)
=> ( power(X,$sum(N,M)) = $product(power(X,N),power(X,M)) ) ) ) ).
tff(power_mult,axiom,
! [X: $int,N: $int,M: $int] :
( $lesseq(0,N)
=> ( $lesseq(0,M)
=> ( power(X,$product(N,M)) = power(power(X,N),M) ) ) ) ).
tff(power_mult2,axiom,
! [X: $int,Y: $int,N: $int] :
( $lesseq(0,N)
=> ( power($product(X,Y),N) = $product(power(X,N),power(Y,N)) ) ) ).
tff(abs,type,
abs: $int > $int ).
tff(abs_def,axiom,
! [X: $int] :
( ( $lesseq(0,X)
=> ( abs(X) = X ) )
& ( ~ $lesseq(0,X)
=> ( abs(X) = $uminus(X) ) ) ) ).
tff(abs_le,axiom,
! [X: $int,Y: $int] :
( $lesseq(abs(X),Y)
<=> ( $lesseq($uminus(Y),X)
& $lesseq(X,Y) ) ) ).
tff(abs_pos,axiom,
! [X: $int] : $lesseq(0,abs(X)) ).
tff(div,type,
div: ( $int * $int ) > $int ).
tff(mod,type,
mod: ( $int * $int ) > $int ).
tff(div_mod,axiom,
! [X: $int,Y: $int] :
( ( Y != 0 )
=> ( X = $sum($product(Y,div(X,Y)),mod(X,Y)) ) ) ).
tff(div_bound,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(0,Y) )
=> ( $lesseq(0,div(X,Y))
& $lesseq(div(X,Y),X) ) ) ).
tff(mod_bound,axiom,
! [X: $int,Y: $int] :
( ( Y != 0 )
=> ( $less($uminus(abs(Y)),mod(X,Y))
& $less(mod(X,Y),abs(Y)) ) ) ).
tff(div_sign_pos,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(0,Y) )
=> $lesseq(0,div(X,Y)) ) ).
tff(div_sign_neg,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(0,Y) )
=> $lesseq(div(X,Y),0) ) ).
tff(mod_sign_pos,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& ( Y != 0 ) )
=> $lesseq(0,mod(X,Y)) ) ).
tff(mod_sign_neg,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& ( Y != 0 ) )
=> $lesseq(mod(X,Y),0) ) ).
tff(rounds_toward_zero,axiom,
! [X: $int,Y: $int] :
( ( Y != 0 )
=> $lesseq(abs($product(div(X,Y),Y)),abs(X)) ) ).
tff(div_1,axiom,
! [X: $int] : div(X,1) = X ).
tff(mod_1,axiom,
! [X: $int] : mod(X,1) = 0 ).
tff(div_inf,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(X,Y) )
=> ( div(X,Y) = 0 ) ) ).
tff(mod_inf,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(X,Y) )
=> ( mod(X,Y) = X ) ) ).
tff(div_mult,axiom,
! [X: $int,Y: $int,Z: $int] :
( ( $less(0,X)
& $lesseq(0,Y)
& $lesseq(0,Z) )
=> ( div($sum($product(X,Y),Z),X) = $sum(Y,div(Z,X)) ) ) ).
tff(mod_mult,axiom,
! [X: $int,Y: $int,Z: $int] :
( ( $less(0,X)
& $lesseq(0,Y)
& $lesseq(0,Z) )
=> ( mod($sum($product(X,Y),Z),X) = mod(Z,X) ) ) ).
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(wP_parameter_fast_exp_imperative,conjecture,
! [X: $int,N: $int] :
( $lesseq(0,N)
=> ! [E: $int,P: $int,R: $int] :
( ( $lesseq(0,E)
& ( $product(R,power(P,E)) = power(X,N) ) )
=> ( ~ $less(0,E)
=> ( R = power(X,N) ) ) ) ) ).
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