TSTP Solution File: NUM925_2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:43:00 EDT 2023
% Result : Theorem 16.67s 4.90s
% Output : Refutation 18.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 767
% Syntax : Number of formulae : 1472 ( 510 unt; 64 typ; 0 def)
% Number of atoms : 3307 (1090 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 19623 ( 225 ~; 49 |; 316 &;17499 @)
% ( 195 <=>;1339 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 23 con; 0-2 aty)
% Number of variables : 2544 ( 0 ^;2516 !; 28 ?;2544 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(fun_int_bool_type,type,
fun_int_bool: $tType ).
thf(fun_int_int_type,type,
fun_int_int: $tType ).
thf(fun_int_fun_int_bool_type,type,
fun_int_fun_int_bool: $tType ).
thf(fun_nat_bool_type,type,
fun_nat_bool: $tType ).
thf(fun_nat_int_type,type,
fun_nat_int: $tType ).
thf(fun_nat_nat_type,type,
fun_nat_nat: $tType ).
thf(fun_nat_real_type,type,
fun_nat_real: $tType ).
thf(fun_nat_fun_nat_bool_type,type,
fun_nat_fun_nat_bool: $tType ).
thf(fun_real_bool_type,type,
fun_real_bool: $tType ).
thf(fun_real_real_type,type,
fun_real_real: $tType ).
thf(fun_re413263731l_bool_type,type,
fun_re413263731l_bool: $tType ).
thf(one_one_int_type,type,
one_one_int: int ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(one_one_real_type,type,
one_one_real: real ).
thf(plus_plus_int_type,type,
plus_plus_int: int > fun_int_int ).
thf(plus_plus_nat_type,type,
plus_plus_nat: nat > fun_nat_nat ).
thf(plus_plus_real_type,type,
plus_plus_real: real > fun_real_real ).
thf(times_times_int_type,type,
times_times_int: int > int > int ).
thf(zero_zero_int_type,type,
zero_zero_int: int ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(zero_zero_real_type,type,
zero_zero_real: real ).
thf(if_nat_type,type,
if_nat: bool > nat > fun_nat_nat ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_int_type,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
thf(number267125858f_real_type,type,
number267125858f_real: int > real ).
thf(succ_type,type,
succ: int > int ).
thf(semiri1621563631at_int_type,type,
semiri1621563631at_int: fun_nat_int ).
thf(semiri984289939at_nat_type,type,
semiri984289939at_nat: fun_nat_nat ).
thf(semiri132038758t_real_type,type,
semiri132038758t_real: fun_nat_real ).
thf(sqrt_type,type,
sqrt: real > real ).
thf(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
thf(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
thf(ord_less_real_type,type,
ord_less_real: fun_re413263731l_bool ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: fun_int_fun_int_bool ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: fun_re413263731l_bool ).
thf(power_power_int_type,type,
power_power_int: int > fun_nat_int ).
thf(power_power_nat_type,type,
power_power_nat: nat > fun_nat_nat ).
thf(power_power_real_type,type,
power_power_real: real > fun_nat_real ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(hAPP_int_bool_type,type,
hAPP_int_bool: fun_int_bool > int > bool ).
thf(hAPP_int_int_type,type,
hAPP_int_int: fun_int_int > int > int ).
thf(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: fun_int_fun_int_bool > int > fun_int_bool ).
thf(hAPP_nat_bool_type,type,
hAPP_nat_bool: fun_nat_bool > nat > bool ).
thf(hAPP_nat_int_type,type,
hAPP_nat_int: fun_nat_int > nat > int ).
thf(hAPP_nat_nat_type,type,
hAPP_nat_nat: fun_nat_nat > nat > nat ).
thf(hAPP_nat_real_type,type,
hAPP_nat_real: fun_nat_real > nat > real ).
thf(hAPP_n1699378549t_bool_type,type,
hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).
thf(hAPP_real_bool_type,type,
hAPP_real_bool: fun_real_bool > real > bool ).
thf(hAPP_real_real_type,type,
hAPP_real_real: fun_real_real > real > real ).
thf(hAPP_r1134773055l_bool_type,type,
hAPP_r1134773055l_bool: fun_re413263731l_bool > real > fun_real_bool ).
thf(hBOOL_type,type,
hBOOL: bool > $o ).
thf(m1_type,type,
m1: int ).
thf(n_type,type,
n: nat ).
thf(t_type,type,
t: int ).
thf(tn_type,type,
tn: nat ).
thf(246,axiom,
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_not__one__less__zero) ).
thf(1586,plain,
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(166,axiom,
! [A: nat] :
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ A )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_power__one) ).
thf(1337,plain,
! [A: nat] :
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_of__nat__less__imp__less) ).
thf(1411,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(533,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(2612,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(204,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1454,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(377,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( power_power_nat @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_power2__eq__imp__eq) ).
thf(2072,plain,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( power_power_nat @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(684,axiom,
! [A: int] :
( ( bit0 @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
thf(3167,plain,
! [A: int] :
( ( bit0 @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(44,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_add__mono) ).
thf(846,plain,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(332,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_add__strict__mono) ).
thf(1899,plain,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(318,axiom,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_add__right__cancel) ).
thf(1840,plain,
! [A: real,B: real,C: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(68,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( sqrt @ A ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_real__sqrt__gt__1__iff) ).
thf(941,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( sqrt @ A ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( sqrt @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(125,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_le__neq__implies__less) ).
thf(1168,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(460,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_real ) )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_sum__power2__le__zero__iff) ).
thf(2341,plain,
! [A: real,B: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_real ) )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(348,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_less__imp__of__nat__less) ).
thf(1956,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(232,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_le0) ).
thf(1549,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(444,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_rel__simps_I46_J) ).
thf(2280,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(234,axiom,
! [A: int,B: int] :
( ( A = B )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_order__eq__refl) ).
thf(1554,plain,
! [A: int,B: int] :
( ( A = B )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(273,axiom,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_ex__least__nat__less) ).
thf(1686,plain,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(431,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Numeral1__eq1__nat) ).
thf(2250,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(578,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_of__nat__add) ).
thf(2776,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(101,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_power__one__right) ).
thf(1073,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(366,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
& ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_less__imp__add__positive) ).
thf(2014,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
& ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(282,axiom,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_power__le__imp__le__exp) ).
thf(1728,plain,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(639,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
<=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_sum__power2__gt__zero__iff) ).
thf(3012,plain,
! [A: real,B: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) )
& ( ( ( A != zero_zero_real )
| ( B != zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(228,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_mono__nat__linear__lb) ).
thf(1533,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(197,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_trans__le__add2) ).
thf(1437,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(127,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_power__eq__0__iff) ).
thf(1173,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(466,axiom,
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_one__power2) ).
thf(2363,plain,
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(131,axiom,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_power__strict__decreasing) ).
thf(1200,plain,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(288,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_add__mono) ).
thf(1750,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(76,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_zero__less__double__add__iff__zero__less__single__add) ).
thf(977,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(628,axiom,
! [A: real,B: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_realpow__two__sum__zero__iff) ).
thf(2976,plain,
! [A: real,B: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(19,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_power__le__imp__le__exp) ).
thf(762,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_add__less__imp__less__left) ).
thf(1005,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(420,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_of__nat__0__less__iff) ).
thf(2210,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(621,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_of__nat__eq__iff) ).
thf(2940,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(188,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_real__le__refl) ).
thf(1406,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(386,axiom,
! [A: fun_int_bool] :
( ! [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
<=> ! [B: nat] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_transfer__int__nat__quantifiers_I1_J) ).
thf(2104,plain,
! [A: fun_int_bool] :
( ( ! [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
=> ! [B: nat] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ! [B: nat] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ! [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(497,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_add__le__cancel__left) ).
thf(2495,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(471,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add__numeral__0) ).
thf(2381,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(622,axiom,
( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_nat__1__add__1) ).
thf(2947,plain,
( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(430,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_add__left__mono) ).
thf(2248,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(389,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_add__nonneg__pos) ).
thf(2114,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(118,axiom,
! [A: real,B: real,C: real] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_ord__eq__le__trans) ).
thf(1142,plain,
! [A: real,B: real,C: real] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(278,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_zle__antisym) ).
thf(1705,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(265,axiom,
! [A: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ A )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_double__eq__0__iff) ).
thf(1655,plain,
! [A: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ A )
= zero_zero_real )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(635,axiom,
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__add__one__is__two) ).
thf(3004,plain,
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(411,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2184,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(620,axiom,
! [A: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ A )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_double__eq__0__iff) ).
thf(2933,plain,
! [A: int] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ A )
= zero_zero_int )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(396,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_one__neq__zero) ).
thf(2141,plain,
one_one_int != zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(563,axiom,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( hAPP_nat_int @ ( power_power_int @ C ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_power__inject__exp) ).
thf(2712,plain,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( ( hAPP_nat_int @ ( power_power_int @ C ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ ( power_power_int @ C ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(492,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_semiring__add__number__of) ).
thf(2476,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(490,axiom,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__nat__number__of) ).
thf(2459,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(261,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_add__0__right) ).
thf(1640,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(398,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zero__is__num__zero) ).
thf(2146,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(531,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zadd__left__commute) ).
thf(2607,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(554,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_semiring__norm_I112_J) ).
thf(2686,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(646,axiom,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ B ) @ A )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
thf(3044,plain,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ B ) @ A )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(285,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_add__right__imp__eq) ).
thf(1735,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(671,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_zero__le__double__add__iff__zero__le__single__add) ).
thf(3121,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(61,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_zero__reorient) ).
thf(913,plain,
! [A: nat] :
( ( ( zero_zero_nat = A )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( zero_zero_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_add__leD2) ).
thf(1222,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(65,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_ord__le__eq__trans) ).
thf(930,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(464,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_add__strict__mono) ).
thf(2360,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(666,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__Pls) ).
thf(3103,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(702,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(3236,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(566,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_rel__simps_I22_J) ).
thf(2723,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(42,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_add__0) ).
thf(841,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_add__lessD1) ).
thf(1046,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(342,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_le__antisym) ).
thf(1935,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_of__nat__le__iff) ).
thf(1650,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(183,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_le__special_I2_J) ).
thf(1386,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(407,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_not__one__le__zero) ).
thf(2173,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(504,axiom,
! [A: nat,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_power__strict__mono) ).
thf(2516,plain,
! [A: nat,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(351,axiom,
! [A: nat,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_power__strict__mono) ).
thf(1967,plain,
! [A: nat,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_add__nonneg__eq__0__iff) ).
thf(1254,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) )
& ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A )
= zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(329,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_nat__add__left__commute) ).
thf(1887,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(484,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I44_J) ).
thf(2432,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(336,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_power__mono) ).
thf(1914,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(143,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_nat__add__assoc) ).
thf(1243,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(511,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( A != zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_zero__less__power2) ).
thf(2548,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( A != zero_zero_real ) )
& ( ( A != zero_zero_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(629,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_zadd__left__mono) ).
thf(2985,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(184,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_nat__add__left__cancel__le) ).
thf(1391,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(26,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_one__neq__zero) ).
thf(782,plain,
one_one_real != zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(199,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_add__leE) ).
thf(1441,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(608,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_rel__simps_I29_J) ).
thf(2886,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(170,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_add__neg__neg) ).
thf(1359,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(334,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1904,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(223,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_order__antisym__conv) ).
thf(1518,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(277,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_add__nonpos__nonpos) ).
thf(1703,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(642,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_int__one__le__iff__zero__less) ).
thf(3029,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(674,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(3131,plain,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(548,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_one__le__power) ).
thf(2667,plain,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(27,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_le__add1) ).
thf(785,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(574,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zless__add1__eq) ).
thf(2755,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(561,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_add__nonpos__nonpos) ).
thf(2708,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(422,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_semiring__numeral__0__eq__0) ).
thf(2217,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(496,axiom,
! [A: nat,B: nat,C: bool] :
( ( ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( if_nat @ C @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( if_nat @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_int__if__cong) ).
thf(2488,plain,
! [A: nat,B: nat,C: bool] :
( ( ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( if_nat @ C @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( if_nat @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(66,axiom,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_power__increasing) ).
thf(934,plain,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(358,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_add__right__mono) ).
thf(1992,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_power__strict__decreasing) ).
thf(949,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(304,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_zless__le) ).
thf(1792,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(195,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_le__refl) ).
thf(1430,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(335,axiom,
! [A: real] :
( ( zero_zero_real
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_double__zero__sym) ).
thf(1907,plain,
! [A: real] :
( ( ( zero_zero_real
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( zero_zero_real
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(499,axiom,
( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__power2) ).
thf(2501,plain,
( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(552,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_pos__add__strict) ).
thf(2682,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(314,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1826,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(180,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_order__trans) ).
thf(1379,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(576,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_int__0) ).
thf(2767,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(85,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_add__le__less__mono) ).
thf(1013,plain,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(186,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_order__antisym__conv) ).
thf(1398,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(296,axiom,
( ( hAPP_nat_real @ semiri132038758t_real @ zero_zero_nat )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_of__nat__0) ).
thf(1773,plain,
( ( hAPP_nat_real @ semiri132038758t_real @ zero_zero_nat )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(350,axiom,
! [A: int,B: int,C: int] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_xt1_I3_J) ).
thf(1963,plain,
! [A: int,B: int,C: int] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(319,axiom,
! [A: real,B: real] :
( ( A
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) )
<=> ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_add__0__iff) ).
thf(1847,plain,
! [A: real,B: real] :
( ( ( A
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) )
=> ( B = zero_zero_real ) )
& ( ( B = zero_zero_real )
=> ( A
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_le__eq__less__or__eq) ).
thf(1319,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(330,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_xt1_I3_J) ).
thf(1890,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(211,axiom,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_realpow__pos__nth) ).
thf(1479,plain,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(253,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1609,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(74,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_order__antisym) ).
thf(969,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(168,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_less__nat__zero__code) ).
thf(1347,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_of__nat__power) ).
thf(1572,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(489,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_int__less__0__conv) ).
thf(2456,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(409,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rel__simps_I49_J) ).
thf(2178,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(457,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2324,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_trans__less__add2) ).
thf(789,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(202,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_nat__power__less__imp__less) ).
thf(1450,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(382,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2090,plain,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(165,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_add__imp__eq) ).
thf(1334,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(617,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_add__mono) ).
thf(2925,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(121,axiom,
! [A: nat,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_power__mono) ).
thf(1151,plain,
! [A: nat,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(182,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ D ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1383,plain,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ D ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_of__nat__add) ).
thf(1051,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(58,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_order__refl) ).
thf(905,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(157,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_nat__add__left__cancel) ).
thf(1302,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(267,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_add__strict__increasing) ).
thf(1664,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(610,axiom,
( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zero__power2) ).
thf(2893,plain,
( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(491,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_add__left__cancel) ).
thf(2469,plain,
! [A: int,B: int,C: int] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(270,axiom,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_power__decreasing) ).
thf(1677,plain,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(370,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_linorder__neqE__nat) ).
thf(2034,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(128,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_zero__le__imp__of__nat) ).
thf(1183,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(152,axiom,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_add__left__imp__eq) ).
thf(1283,plain,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(591,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_semiring__1__add__number__of) ).
thf(2833,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_real @ semiri132038758t_real @ A )
= ( hAPP_nat_real @ semiri132038758t_real @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_of__nat__eq__iff) ).
thf(877,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_real @ semiri132038758t_real @ A )
= ( hAPP_nat_real @ semiri132038758t_real @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_real @ semiri132038758t_real @ A )
= ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(9,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_add__strict__increasing2) ).
thf(734,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_add__less__mono1) ).
thf(866,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(256,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_less__imp__le__nat) ).
thf(1622,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(680,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_power2__le__imp__le) ).
thf(3157,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(225,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_add__nonneg__pos) ).
thf(1526,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(363,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ B ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(2002,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ B ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(572,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_semiring__numeral__1__eq__1) ).
thf(2750,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(475,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I16_J) ).
thf(2392,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(524,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit0 @ A ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_number__of1) ).
thf(2586,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit0 @ A ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(653,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_power2__less__imp__less) ).
thf(3068,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(179,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_add__neg__nonpos) ).
thf(1377,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(564,axiom,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_power__increasing) ).
thf(2718,plain,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(418,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_add__strict__right__mono) ).
thf(2205,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(323,axiom,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_not__add__less1) ).
thf(1863,plain,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(251,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1604,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(664,axiom,
! [A: int] :
( ( bit1 @ A )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
thf(3097,plain,
! [A: int] :
( ( bit1 @ A )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(638,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_pos2) ).
thf(3011,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(519,axiom,
! [A: int,B: int] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add__number__of__eq) ).
thf(2574,plain,
! [A: int,B: int] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(404,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2164,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(391,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_int__int__eq) ).
thf(2118,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(300,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1783,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(536,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_zero__less__int__conv) ).
thf(2621,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(122,axiom,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_nat__less__cases) ).
thf(1153,plain,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(688,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_even__less__0__iff) ).
thf(3186,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(209,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_xt1_I6_J) ).
thf(1470,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(279,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_less__imp__of__nat__less) ).
thf(1708,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(159,axiom,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_add__right__imp__eq) ).
thf(1311,plain,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(650,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_semiring__1__add__number__of) ).
thf(3054,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(546,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_semiring__numeral__0__eq__0) ).
thf(2660,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(325,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_zero__le__power) ).
thf(1868,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(376,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
<=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_sum__power2__gt__zero__iff) ).
thf(2061,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) )
& ( ( ( A != zero_zero_int )
| ( B != zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(362,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_power__increasing) ).
thf(2000,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(283,axiom,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_add__imp__eq) ).
thf(1730,plain,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(123,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1163,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(525,axiom,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_power__less__imp__less__base) ).
thf(2589,plain,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(14,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( sqrt @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_real__sqrt__gt__zero) ).
thf(746,plain,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( sqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(482,axiom,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_power__le__imp__le__exp) ).
thf(2428,plain,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(36,axiom,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_zero__less__two) ).
thf(825,plain,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(93,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_xt1_I4_J) ).
thf(1042,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(244,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_Nat_Oadd__0__right) ).
thf(1580,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_xt1_I4_J) ).
thf(862,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(240,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_order__refl) ).
thf(1570,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(35,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I17_J) ).
thf(820,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(268,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1666,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(175,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_add__less__le__mono) ).
thf(1370,plain,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(369,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_add__left__mono) ).
thf(2032,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(507,axiom,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
<=> ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_number__of__reorient) ).
thf(2528,plain,
! [A: int,B: nat] :
( ( ( ( number_number_of_nat @ A )
= B )
=> ( B
= ( number_number_of_nat @ A ) ) )
& ( ( B
= ( number_number_of_nat @ A ) )
=> ( ( number_number_of_nat @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(142,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_double__add__less__zero__iff__single__add__less__zero) ).
thf(1238,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_ord__eq__le__trans) ).
thf(1021,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(24,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_order__trans) ).
thf(778,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(193,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_add__less__imp__less__right) ).
thf(1423,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(173,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_of__nat__0__le__iff) ).
thf(1365,plain,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(589,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_number__of__add) ).
thf(2820,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(347,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_less__or__eq__imp__le) ).
thf(1951,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(205,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_xt1_I4_J) ).
thf(1457,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_one__less__power) ).
thf(830,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(302,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_ord__le__eq__trans) ).
thf(1787,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(134,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__add__one) ).
thf(1210,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(453,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_int__0__less__1) ).
thf(2313,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(151,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_real__le__trans) ).
thf(1281,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(388,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_of__nat__0) ).
thf(2112,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(577,axiom,
! [A: int] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_eq__number__of__0) ).
thf(2769,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( ( number_number_of_nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(109,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__int__code_I13_J) ).
thf(1106,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(689,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3191,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(343,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zless__linear) ).
thf(1938,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(91,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_le__special_I3_J) ).
thf(1032,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(317,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_less__irrefl__nat) ).
thf(1837,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(311,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_of__nat__less__0__iff) ).
thf(1819,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(257,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1624,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(90,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
<=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_le__number__of__eq__not__less) ).
thf(1027,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(458,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
<=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_le__nat__number__of) ).
thf(2327,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ) )
& ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(18,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_less__0__number__of) ).
thf(757,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(648,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_power2__le__imp__le) ).
thf(3050,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(259,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_add_Ocomm__neutral) ).
thf(1634,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(425,axiom,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_real @ semiri132038758t_real @ ( number_number_of_nat @ A ) )
= ( number267125858f_real @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_real @ semiri132038758t_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_of__nat__number__of__lemma) ).
thf(2228,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_real @ semiri132038758t_real @ ( number_number_of_nat @ A ) )
= ( number267125858f_real @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_real @ semiri132038758t_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__is__0) ).
thf(1350,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(306,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( if_nat @ fFalse @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).
thf(1804,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( if_nat @ fFalse @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(611,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_add__Bit1__Bit0) ).
thf(2895,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(178,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_real__add__left__mono) ).
thf(1375,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(520,axiom,
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_one__power2) ).
thf(2577,plain,
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(110,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_add__pos__pos) ).
thf(1111,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(556,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
thf(2692,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(106,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_add__le__imp__le__left) ).
thf(1096,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(538,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
thf(2631,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(599,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_semiring__numeral__1__eq__1) ).
thf(2858,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(656,axiom,
( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_semiring__one__add__one__is__two) ).
thf(3078,plain,
( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(703,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_less__int__code_I15_J) ).
thf(3237,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(113,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_order__antisym__conv) ).
thf(1118,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(661,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_less__int__code_I14_J) ).
thf(3087,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(13,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_real__lbound__gt__zero) ).
thf(742,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(449,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_zero__le__power2) ).
thf(2300,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(293,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1762,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(384,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_add__pos__nonneg) ).
thf(2100,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(593,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_add__nonneg__nonneg) ).
thf(2841,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(163,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_add__left__imp__eq) ).
thf(1328,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(696,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_add__strict__increasing2) ).
thf(3218,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(7,axiom,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A )
& ! [D: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ D ) )
& ( ( hAPP_nat_real @ ( power_power_real @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_realpow__pos__nth__unique) ).
thf(725,plain,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A )
& ! [D: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ D ) )
& ( ( hAPP_nat_real @ ( power_power_real @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(557,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_add__less__cancel__right) ).
thf(2694,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(194,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_le__number__of) ).
thf(1425,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(239,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_power__one__right) ).
thf(1567,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(53,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_add__0__left) ).
thf(884,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(171,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_add__strict__increasing2) ).
thf(1361,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(633,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_of__nat__less__imp__less) ).
thf(3000,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(603,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_mult__Bit1) ).
thf(2868,plain,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(201,axiom,
! [A: int,B: int,C: int] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_ord__eq__le__trans) ).
thf(1446,plain,
! [A: int,B: int,C: int] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(254,axiom,
! [A: real,B: real] :
( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_linorder__le__cases) ).
thf(1612,plain,
! [A: real,B: real] :
( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(580,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_double__add__le__zero__iff__single__add__le__zero) ).
thf(2781,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(513,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_add__less__le__mono) ).
thf(2561,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(694,axiom,
! [A: int] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ one_one_real )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__special_I3_J) ).
thf(3210,plain,
! [A: int] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ one_one_real )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(663,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3094,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(206,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_xt1_I6_J) ).
thf(1461,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(416,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_add__le__imp__le__left) ).
thf(2196,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(428,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_add__number__of__eq) ).
thf(2240,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(308,axiom,
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_not__one__le__zero) ).
thf(1810,plain,
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(303,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_zero__le__one) ).
thf(1791,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(136,axiom,
! [A: real] :
( ( one_one_real = A )
<=> ( A = one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_one__reorient) ).
thf(1214,plain,
! [A: real] :
( ( ( one_one_real = A )
=> ( A = one_one_real ) )
& ( ( A = one_one_real )
=> ( one_one_real = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(690,axiom,
( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_transfer__int__nat__numerals_I4_J) ).
thf(3194,plain,
( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(133,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1207,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(380,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_zadd__0__right) ).
thf(2085,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(704,axiom,
! [A: real,B: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sum__power2__eq__zero__iff) ).
thf(3242,plain,
! [A: real,B: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(313,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ tn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_tn0) ).
thf(1825,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ tn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_of__nat__power) ).
thf(997,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(145,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_even__less__0__iff) ).
thf(1249,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_add__pos__pos) ).
thf(738,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(353,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_le__number__of__eq__not__less) ).
thf(1974,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(522,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(2581,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(501,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_of__nat__le__iff) ).
thf(2505,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(698,axiom,
! [A: int,B: int] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_power2__eq__imp__eq) ).
thf(3222,plain,
! [A: int,B: int] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(516,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_quartic__square__square) ).
thf(2566,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(356,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_less__zeroE) ).
thf(1984,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(81,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_less__mono__imp__le__mono) ).
thf(1002,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(601,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add__Bit0__Bit1) ).
thf(2862,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(281,axiom,
! [A: nat] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_one__reorient) ).
thf(1720,plain,
! [A: nat] :
( ( ( one_one_nat = A )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( one_one_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(258,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_le__iff__add) ).
thf(1627,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
& ( ? [C: nat] :
( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(487,axiom,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_power__increasing__iff) ).
thf(2450,plain,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(392,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_less__special_I2_J) ).
thf(2125,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(247,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_one__le__power) ).
thf(1588,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(508,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_add__less__imp__less__left) ).
thf(2536,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(672,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_power2__less__imp__less) ).
thf(3126,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(551,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_zero__less__one) ).
thf(2681,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(230,axiom,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_eq__number__of) ).
thf(1539,plain,
! [A: int,B: int] :
( ( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(592,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_le__special_I4_J) ).
thf(2836,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(528,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_nat__numeral__1__eq__1) ).
thf(2598,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(652,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(3059,plain,
! [A: int,B: int] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) )
& ( ( ( A = zero_zero_int )
& ( B = zero_zero_int ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(148,axiom,
! [A: bool,B: bool,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ B )
<=> ( hBOOL @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ B ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_conj__le__cong) ).
thf(1266,plain,
! [A: bool,B: bool,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) ) )
=> ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ A ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(473,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_number__of__add) ).
thf(2387,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(316,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_power__inject__exp) ).
thf(1831,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(595,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_semiring__norm_I110_J) ).
thf(2851,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(429,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rel__simps_I12_J) ).
thf(2243,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(462,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_of__nat__1) ).
thf(2355,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(341,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1932,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(250,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_rel__simps_I34_J) ).
thf(1599,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_power__strict__increasing__iff) ).
thf(1246,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(668,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_of__nat__less__two__power) ).
thf(3109,plain,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(354,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_linorder__le__cases) ).
thf(1979,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(682,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_add__neg__nonpos) ).
thf(3162,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(292,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_nat__add__commute) ).
thf(1759,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(132,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( sqrt @ A ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_real__sqrt__gt__0__iff) ).
thf(1202,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( sqrt @ A ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( sqrt @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(699,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_power2__less__imp__less) ).
thf(3225,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(62,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(921,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(237,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_less__add__one) ).
thf(1563,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_add__nonpos__neg) ).
thf(1054,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(153,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_one__neq__zero) ).
thf(1286,plain,
one_one_nat != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(100,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_add__increasing) ).
thf(1071,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(615,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_zero__less__double__add__iff__zero__less__single__add) ).
thf(2915,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(221,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_zero__less__two) ).
thf(1515,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(360,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_add__nonneg__nonneg) ).
thf(1996,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(413,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_zero__le__power) ).
thf(2189,plain,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(631,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_add__left__imp__eq) ).
thf(2995,plain,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(547,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_of__nat__less__iff) ).
thf(2662,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(129,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_power__0__left) ).
thf(1185,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(150,axiom,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( hAPP_nat_real @ ( power_power_real @ B ) @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_field__power__not__zero) ).
thf(1278,plain,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( hAPP_nat_real @ ( power_power_real @ B ) @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(263,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_trans__le__add1) ).
thf(1648,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_of__nat__less__imp__less) ).
thf(750,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(512,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_rel__simps_I32_J) ).
thf(2556,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(212,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__int__code_I16_J) ).
thf(1483,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(287,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_order__antisym) ).
thf(1747,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(339,axiom,
( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_of__nat__1) ).
thf(1927,plain,
( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(530,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_less__eq__int__code_I14_J) ).
thf(2602,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(569,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_two__realpow__ge__one) ).
thf(2734,plain,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(669,axiom,
! [A: nat,B: nat] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zadd__int) ).
thf(3111,plain,
! [A: nat,B: nat] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(177,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_zero__less__one) ).
thf(1374,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(469,axiom,
( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zero__power2) ).
thf(2376,plain,
( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(426,axiom,
! [A: int,B: int,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ B ) ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add__number__of__left) ).
thf(2235,plain,
! [A: int,B: int,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ B ) ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(397,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_add__neg__neg) ).
thf(2144,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1146,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(290,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_of__nat__add) ).
thf(1754,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(448,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rel__simps_I51_J) ).
thf(2292,plain,
! [A: int,B: int] :
( ( ( ( bit1 @ A )
= ( bit1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit1 @ A )
= ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(433,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_semiring__add__number__of) ).
thf(2253,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(441,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ m1 ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mn) ).
thf(2275,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ m1 ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(654,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_add__numeral__0__right) ).
thf(3070,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(83,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1007,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(337,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_add__nonpos__neg) ).
thf(1916,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(8,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_of__nat__0__le__iff) ).
thf(732,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(583,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_less__eq__int__code_I15_J) ).
thf(2791,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(582,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_add__le__less__mono) ).
thf(2789,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(22,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ one_one_real )
= ( number267125858f_real @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_semiring__number__of__add__1) ).
thf(772,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ one_one_real )
= ( number267125858f_real @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(289,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add__less__mono) ).
thf(1752,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(276,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_trans__less__add1) ).
thf(1701,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(588,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zadd__0) ).
thf(2817,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_of__nat__less__iff) ).
thf(1124,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(213,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_add__strict__right__mono) ).
thf(1488,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(695,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_le__special_I1_J) ).
thf(3213,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(701,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_int__1) ).
thf(3234,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(373,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_add__0__left) ).
thf(2048,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(658,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(3081,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(340,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_add_Ocomm__neutral) ).
thf(1929,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_less__not__refl3) ).
thf(826,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
<=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_zero__less__power__nat__eq) ).
thf(711,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(402,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_tpos) ).
thf(2161,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(217,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_not__less0) ).
thf(1503,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(67,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( sqrt @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_real__sqrt__lt__0__iff) ).
thf(936,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( sqrt @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( sqrt @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(609,axiom,
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_one__power2) ).
thf(2891,plain,
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(28,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_zle__refl) ).
thf(787,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(693,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_add__less__imp__less__right) ).
thf(3208,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(560,axiom,
( one_one_int
= ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_transfer__int__nat__numerals_I2_J) ).
thf(2706,plain,
( one_one_int
= ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(294,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__special_I3_J) ).
thf(1765,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( A
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_add__0__iff) ).
thf(804,plain,
! [A: nat,B: nat] :
( ( ( A
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
=> ( B = zero_zero_nat ) )
& ( ( B = zero_zero_nat )
=> ( A
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(138,axiom,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_zero__less__one) ).
thf(1224,plain,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(685,axiom,
! [A: fun_int_bool,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_int__gr__induct) ).
thf(3170,plain,
! [A: fun_int_bool,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(640,axiom,
! [A: int] :
( ( succ @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_succ__def) ).
thf(3023,plain,
! [A: int] :
( ( succ @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(269,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( ( hAPP_real_real @ ( plus_plus_real @ B ) @ A )
= zero_zero_real )
<=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_add__nonneg__eq__0__iff) ).
thf(1669,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( ( ( hAPP_real_real @ ( plus_plus_real @ B ) @ A )
= zero_zero_real )
=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) )
& ( ( ( B = zero_zero_real )
& ( A = zero_zero_real ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ B ) @ A )
= zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(415,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ one_one_int )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_add__special_I3_J) ).
thf(2193,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ one_one_int )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(301,axiom,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_zero__le__one) ).
thf(1786,plain,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(634,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_nat__number__of__Pls) ).
thf(3002,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(284,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_add__strict__left__mono) ).
thf(1733,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(399,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ D ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(2148,plain,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ D ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(455,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_zero__le__imp__of__nat) ).
thf(2319,plain,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(506,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(2521,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(57,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_add__less__cancel__right) ).
thf(900,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(540,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2637,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(224,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_add__le__mono1) ).
thf(1524,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(445,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ A ) ) @ one_one_nat )
= ( number_number_of_nat @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_semiring__number__of__add__1) ).
thf(2284,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ A ) ) @ one_one_nat )
= ( number_number_of_nat @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(215,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ A )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_power__one) ).
thf(1492,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(667,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_power__0) ).
thf(3106,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(549,axiom,
! [A: nat,B: int] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_power__eq__0__iff__number__of) ).
thf(2669,plain,
! [A: nat,B: int] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(390,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_numeral__1__eq__1) ).
thf(2116,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(305,axiom,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).
thf(1801,plain,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(598,axiom,
! [A: nat,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_power__mono) ).
thf(2856,plain,
! [A: nat,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(352,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_rel__simps_I31_J) ).
thf(1969,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(502,axiom,
! [A: int] :
( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__special_I2_J) ).
thf(2510,plain,
! [A: int] :
( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(20,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_add__le__cancel__right) ).
thf(764,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(509,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_add1__zle__eq) ).
thf(2538,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(189,axiom,
! [A: real,B: nat,C: real] :
( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ B )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_power__eq__imp__eq__base) ).
thf(1408,plain,
! [A: real,B: nat,C: real] :
( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ B )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(400,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_odd__less__0) ).
thf(2151,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(679,axiom,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_sum__power2__ge__zero) ).
thf(3155,plain,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(479,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_add__0__right) ).
thf(2415,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(331,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_of__nat__0__less__iff) ).
thf(1894,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(630,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_less__nat__number__of) ).
thf(2987,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(613,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_add__less__cancel__left) ).
thf(2906,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(95,axiom,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_power__increasing__iff) ).
thf(1048,plain,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_add__strict__mono) ).
thf(736,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(470,axiom,
! [A: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_power2__less__0) ).
thf(2378,plain,
! [A: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(274,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_nat__zero__less__power__iff) ).
thf(1690,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( B = zero_zero_nat ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( B = zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(604,axiom,
! [A: nat] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ A )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_power__one) ).
thf(2871,plain,
! [A: nat] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(198,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_zle__linear) ).
thf(1439,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(55,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__number__of__int__code) ).
thf(890,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(327,axiom,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_not__add__less2) ).
thf(1877,plain,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(587,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_rel__simps_I27_J) ).
thf(2812,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(532,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_semiring__norm_I110_J) ).
thf(2610,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(454,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_rel__simps_I21_J) ).
thf(2314,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(655,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(3073,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(438,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_add__number__of__left) ).
thf(2267,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(436,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ~ ! [B: nat] :
( A
!= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_nonneg__int__cases) ).
thf(2261,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ~ ! [B: nat] :
( A
!= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(45,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_add__pos__nonneg) ).
thf(848,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(643,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_le__special_I2_J) ).
thf(3034,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(21,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_zero__neq__one) ).
thf(769,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(432,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_zero__less__two) ).
thf(2252,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(443,axiom,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_power__strict__decreasing) ).
thf(2278,plain,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_add__le__imp__le__left) ).
thf(1381,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(99,axiom,
! [A: real,B: nat] :
( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ B )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_power__eq__0__iff) ).
thf(1061,plain,
! [A: real,B: nat] :
( ( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) )
=> ( ( hAPP_nat_real @ ( power_power_real @ A ) @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(34,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_less__eq__real__def) ).
thf(811,plain,
! [A: real,B: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(410,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zadd__strict__right__mono) ).
thf(2182,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(675,axiom,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_zadd__power2) ).
thf(3133,plain,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_add__neg__neg) ).
thf(858,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(527,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_bin__less__0__simps_I3_J) ).
thf(2593,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(56,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_add__le__cancel__left) ).
thf(895,plain,
! [A: real,B: real,C: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(636,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_add__Pls__right) ).
thf(3006,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_pos__add__strict) ).
thf(1149,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_le__number__of) ).
thf(964,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(605,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_rel__simps_I10_J) ).
thf(2874,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(562,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_semiring__numeral__1__eq__1) ).
thf(2710,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(614,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rel__simps_I39_J) ).
thf(2911,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(461,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_zless__int) ).
thf(2350,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(275,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_add__neg__nonpos) ).
thf(1699,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_add__le__cancel__left) ).
thf(959,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( if_nat @ fTrue @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).
thf(1113,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( if_nat @ fTrue @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(368,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_exp__eq__1) ).
thf(2022,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = one_one_nat )
| ( B = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(474,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).
thf(2390,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(401,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_rel__simps_I15_J) ).
thf(2156,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(419,axiom,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_power__strict__increasing__iff) ).
thf(2207,plain,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(63,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_less__special_I4_J) ).
thf(922,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ one_one_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(60,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_rel__simps_I19_J) ).
thf(912,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(126,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_power__less__imp__less__base) ).
thf(1171,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(378,axiom,
! [A: int] :
( ( succ @ ( bit1 @ A ) )
= ( bit0 @ ( succ @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_succ__Bit1) ).
thf(2075,plain,
! [A: int] :
( ( succ @ ( bit1 @ A ) )
= ( bit0 @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(480,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_add__numeral__0__right) ).
thf(2418,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(185,axiom,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_one__le__power) ).
thf(1396,plain,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(485,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) @ A )
!= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_odd__nonzero) ).
thf(2439,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) @ A )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(626,axiom,
! [A: real,B: int] :
( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_power__eq__0__iff__number__of) ).
thf(2962,plain,
! [A: real,B: int] :
( ( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) )
& ( ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) )
=> ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(467,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_int ) )
<=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_sum__power2__le__zero__iff) ).
thf(2365,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_int ) )
=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) )
& ( ( ( A = zero_zero_int )
& ( B = zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(374,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_power__one__right) ).
thf(2051,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(494,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_rel__simps_I5_J) ).
thf(2481,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(226,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_linorder__neqE__linordered__idom) ).
thf(1528,plain,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_nat__less__le) ).
thf(868,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(25,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_le__add2) ).
thf(780,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(262,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__number__of) ).
thf(1643,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(681,axiom,
! [A: real,B: real] :
( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_power2__eq__imp__eq) ).
thf(3159,plain,
! [A: real,B: real] :
( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_xt1_I5_J) ).
thf(1015,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(297,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_add__less__imp__less__right) ).
thf(1775,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(80,axiom,
! [A: int,B: int] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_linorder__le__cases) ).
thf(1000,plain,
! [A: int,B: int] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(573,axiom,
! [A: int] :
( ( number_number_of_int @ ( succ @ A ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_number__of__succ) ).
thf(2752,plain,
! [A: int] :
( ( number_number_of_int @ ( succ @ A ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(637,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_semiring__numeral__0__eq__0) ).
thf(3009,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(245,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1583,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(624,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( hAPP_int_int @ ( plus_plus_int @ B ) @ A )
= zero_zero_int )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_add__nonneg__eq__0__iff) ).
thf(2952,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( ( hAPP_int_int @ ( plus_plus_int @ B ) @ A )
= zero_zero_int )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) )
& ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ B ) @ A )
= zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(266,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_order__refl) ).
thf(1662,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(124,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_add__le__imp__le__right) ).
thf(1166,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(544,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_add__0) ).
thf(2652,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(192,axiom,
! [A: int] :
( ( number267125858f_real @ ( succ @ A ) )
= ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_number__of__succ) ).
thf(1420,plain,
! [A: int] :
( ( number267125858f_real @ ( succ @ A ) )
= ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(500,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_number__of__Pls) ).
thf(2503,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(678,axiom,
! [A: int,B: int] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_power__eq__0__iff__number__of) ).
thf(3146,plain,
! [A: int,B: int] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) )
& ( ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(553,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_zero__less__power) ).
thf(2684,plain,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ A )
= ( hAPP_nat_nat @ semiri984289939at_nat @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_of__nat__eq__iff) ).
thf(1340,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ A )
= ( hAPP_nat_nat @ semiri984289939at_nat @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ semiri984289939at_nat @ A )
= ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(210,axiom,
! [A: real,B: real,C: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_add__left__cancel) ).
thf(1472,plain,
! [A: real,B: real,C: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(349,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_add__le__cancel__right) ).
thf(1958,plain,
! [A: real,B: real,C: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(364,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_le__0__eq) ).
thf(2005,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(191,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_add__right__cancel) ).
thf(1413,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(102,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_nat__add__left__cancel__less) ).
thf(1076,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(375,axiom,
! [A: nat] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= zero_zero_int )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_int__eq__0__conv) ).
thf(2054,plain,
! [A: nat] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= zero_zero_int )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_order__antisym) ).
thf(722,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(64,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(927,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(371,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_power__0__left) ).
thf(2037,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_xt1_I5_J) ).
thf(1081,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(618,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_of__nat__power) ).
thf(2927,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(87,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( ( sqrt @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_real__sqrt__not__eq__zero) ).
thf(1018,plain,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( ( sqrt @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(434,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_zadd__zless__mono) ).
thf(2256,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(515,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2564,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(40,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_plus__nat_Oadd__0) ).
thf(836,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(233,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_real__zero__not__eq__one) ).
thf(1551,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(503,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_add_Ocomm__neutral) ).
thf(2513,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(231,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_power__strict__increasing) ).
thf(1547,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(295,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_power__0) ).
thf(1770,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_add__nonpos__nonpos) ).
thf(1516,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1,conjecture,
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(705,plain,
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(139,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_of__nat__0__less__iff) ).
thf(1225,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(365,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
| ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_real__le__linear) ).
thf(2012,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
| ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(344,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_less__not__refl2) ).
thf(1941,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(408,axiom,
! [A: nat,B: nat,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zadd__int__left) ).
thf(2175,plain,
! [A: nat,B: nat,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(299,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_zero__neq__one) ).
thf(1780,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(478,axiom,
! [A: int] :
( ( one_one_int = A )
<=> ( A = one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_one__reorient) ).
thf(2407,plain,
! [A: int] :
( ( ( one_one_int = A )
=> ( A = one_one_int ) )
& ( ( A = one_one_int )
=> ( one_one_int = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(565,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( A = zero_zero_int )
| ( A = one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_int__pos__lt__two__imp__zero__or__one) ).
thf(2720,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( A = zero_zero_int )
| ( A = one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(227,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_power__strict__mono) ).
thf(1531,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(140,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_add__less__cancel__left) ).
thf(1230,plain,
! [A: real,B: real,C: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ D )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_less__add__eq__less) ).
thf(1098,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ D )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(607,axiom,
! [A: fun_int_bool,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ B ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_int__ge__induct) ).
thf(2882,plain,
! [A: fun_int_bool,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ B ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(476,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_zero__le__power2) ).
thf(2397,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_power__less__imp__less__exp) ).
thf(1025,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(659,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zadd__assoc) ).
thf(3082,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(54,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_xt1_I5_J) ).
thf(887,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(550,axiom,
! [A: nat] :
( ( number267125858f_real @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_real @ semiri132038758t_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_number__of__int) ).
thf(2678,plain,
! [A: nat] :
( ( number267125858f_real @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_real @ semiri132038758t_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(505,axiom,
! [A: nat,B: nat] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(2518,plain,
! [A: nat,B: nat] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(657,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
thf(3080,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(517,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_add__numeral__0) ).
thf(2569,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(383,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_rel__simps_I48_J) ).
thf(2092,plain,
! [A: int,B: int] :
( ( ( ( bit0 @ A )
= ( bit0 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit0 @ A )
= ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(357,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__special_I1_J) ).
thf(1987,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(196,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_add__less__cancel__right) ).
thf(1432,plain,
! [A: real,B: real,C: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(641,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_add__Bit0__Bit0) ).
thf(3026,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(161,axiom,
! [A: real,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_power__less__imp__less__base) ).
thf(1317,plain,
! [A: real,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(333,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_semiring__1__add__number__of) ).
thf(1901,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(271,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_pos__add__strict) ).
thf(1679,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(686,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_int__le__0__conv) ).
thf(3174,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_add__less__cancel__left) ).
thf(907,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(156,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_add__left__mono) ).
thf(1300,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(203,axiom,
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_not__one__less__zero) ).
thf(1452,plain,
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(260,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_add__0__left) ).
thf(1637,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(670,axiom,
! [A: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_eq__0__number__of) ).
thf(3114,plain,
! [A: int] :
( ( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( zero_zero_nat
= ( number_number_of_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(555,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rel__simps_I50_J) ).
thf(2688,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(616,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__special_I4_J) ).
thf(2920,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(30,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
<=> ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ B ) ) @ ( number267125858f_real @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_le__number__of__eq__not__less) ).
thf(791,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
=> ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ B ) ) @ ( number267125858f_real @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ B ) ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_eq__imp__le) ).
thf(1262,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(141,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1235,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(442,axiom,
( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
thf(2276,plain,
( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(423,axiom,
! [A: fun_int_bool] :
( ? [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
<=> ? [B: nat] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_transfer__int__nat__quantifiers_I2_J) ).
thf(2219,plain,
! [A: fun_int_bool] :
( ( ? [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
=> ? [B: nat] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ? [B: nat] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ? [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(495,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_zero__zle__int) ).
thf(2486,plain,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(71,axiom,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
<=> ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_number__of__reorient) ).
thf(951,plain,
! [A: int,B: real] :
( ( ( ( number267125858f_real @ A )
= B )
=> ( B
= ( number267125858f_real @ A ) ) )
& ( ( B
= ( number267125858f_real @ A ) )
=> ( ( number267125858f_real @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(286,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_real__less__def) ).
thf(1738,plain,
! [A: real,B: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(645,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_int__power) ).
thf(3041,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(187,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_zle__trans) ).
thf(1404,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(498,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(2500,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(510,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_rel__simps_I33_J) ).
thf(2543,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(218,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_add__le__imp__le__right) ).
thf(1506,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(521,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_one__is__num__one) ).
thf(2579,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(567,axiom,
! [A: int] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_number__of__Bit0) ).
thf(2728,plain,
! [A: int] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_add__right__mono) ).
thf(1372,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(523,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_less__imp__of__nat__less) ).
thf(2584,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(229,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_real__le__antisym) ).
thf(1536,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(355,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1981,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(463,axiom,
! [A: int,B: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_not__sum__power2__lt__zero) ).
thf(2357,plain,
! [A: int,B: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(594,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_power__0__left) ).
thf(2843,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(105,axiom,
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_not__one__le__zero) ).
thf(1094,plain,
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(117,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_add__le__mono) ).
thf(1140,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(600,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_add__increasing2) ).
thf(2860,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(623,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_number__of__Bit1) ).
thf(2949,plain,
! [A: int] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(602,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_of__nat__less__0__iff) ).
thf(2865,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(677,axiom,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_nat__1__add__number__of) ).
thf(3139,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(493,axiom,
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_semiring__one__add__one__is__two) ).
thf(2479,plain,
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(381,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_number__of__Pls) ).
thf(2088,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(346,axiom,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_zero__le__power) ).
thf(1949,plain,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(379,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
<=> ? [C: nat] :
( B
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_zle__iff__zadd) ).
thf(2078,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) ) )
& ( ? [C: nat] :
( B
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(452,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ B ) ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_semiring__add__number__of) ).
thf(2310,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ B ) ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(421,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_numeral__1__eq__1) ).
thf(2215,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(324,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_add__strict__right__mono) ).
thf(1866,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(307,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1807,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(644,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_add__le__imp__le__right) ).
thf(3039,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(361,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_xt1_I6_J) ).
thf(1998,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(537,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_zle__int) ).
thf(2626,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(338,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) ) ) )
<=> ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_zero__less__power__nat__eq__number__of) ).
thf(1918,plain,
! [A: nat,B: int] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) ) ) )
=> ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) )
& ( ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat )
<=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_nat__power__eq__0__iff) ).
thf(1084,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) )
& ( ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(372,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_add__0__right) ).
thf(2045,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(662,axiom,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_power__less__imp__less__exp) ).
thf(3092,plain,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(310,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_add__nonneg__pos) ).
thf(1817,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(625,axiom,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_power__strict__increasing) ).
thf(2960,plain,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(571,axiom,
! [A: real] :
( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__eq__power2) ).
thf(2743,plain,
! [A: real] :
( ( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(412,axiom,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_power__decreasing) ).
thf(2187,plain,
! [A: int,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(387,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
thf(2110,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(84,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_power__0) ).
thf(1010,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(451,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_le__special_I3_J) ).
thf(2305,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(242,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_power__eq__imp__eq__base) ).
thf(1575,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(154,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_less__eq__int__code_I16_J) ).
thf(1289,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(43,axiom,
( ( hAPP_nat_real @ semiri132038758t_real @ one_one_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_of__nat__1) ).
thf(844,plain,
( ( hAPP_nat_real @ semiri132038758t_real @ one_one_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(424,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_add__nonpos__neg) ).
thf(2226,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(542,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_add__le__cancel__right) ).
thf(2643,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(486,axiom,
! [A: int] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_zero__eq__power2) ).
thf(2443,plain,
! [A: int] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(15,axiom,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_zero__less__power) ).
thf(748,plain,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(597,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_zero__le__one) ).
thf(2855,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(394,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_plus__numeral__code_I9_J) ).
thf(2135,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(219,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_less__number__of) ).
thf(1508,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(627,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_bin__less__0__simps_I4_J) ).
thf(2971,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(320,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( sqrt @ A ) ) @ one_one_real ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_real__sqrt__lt__1__iff) ).
thf(1854,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( sqrt @ A ) ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ one_one_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( sqrt @ A ) ) @ one_one_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(393,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_double__add__less__zero__iff__single__add__less__zero) ).
thf(2130,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(676,axiom,
! [A: int] :
( ( succ @ ( bit0 @ A ) )
= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_succ__Bit0) ).
thf(3136,plain,
! [A: int] :
( ( succ @ ( bit0 @ A ) )
= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(235,axiom,
! [A: real,B: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1558,plain,
! [A: real,B: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ B )
= ( hAPP_real_real @ ( plus_plus_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(660,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_zless__imp__add1__zle) ).
thf(3085,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(149,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_add__strict__increasing) ).
thf(1276,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(526,axiom,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_transfer__int__nat__numerals_I3_J) ).
thf(2591,plain,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(248,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_power__0__left__number__of) ).
thf(1590,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(405,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_add__imp__eq) ).
thf(2167,plain,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(440,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_power2__ge__self) ).
thf(2273,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(596,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_bin__less__0__simps_I1_J) ).
thf(2853,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(447,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_semiring__norm_I113_J) ).
thf(2290,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_add__eq__self__zero) ).
thf(946,plain,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(108,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_less__eq__number__of__int__code) ).
thf(1101,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(590,axiom,
! [A: int,B: nat] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ B )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_power__eq__0__iff) ).
thf(2823,plain,
! [A: int,B: nat] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ B )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(697,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_of__nat__less__two__power) ).
thf(3220,plain,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(575,axiom,
! [A: int] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_number__of__Bit1) ).
thf(2764,plain,
! [A: int] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(312,axiom,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_power__strict__increasing__iff) ).
thf(1822,plain,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(322,axiom,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_power__strict__increasing) ).
thf(1861,plain,
! [A: real,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(584,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_power__0__left__number__of) ).
thf(2796,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(477,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( A != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_zero__less__power2) ).
thf(2399,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( A != zero_zero_int ) )
& ( ( A != zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(155,axiom,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( hAPP_nat_real @ ( power_power_real @ C ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_power__inject__exp) ).
thf(1294,plain,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( ( hAPP_nat_real @ ( power_power_real @ C ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_real @ ( power_power_real @ C ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(417,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_add__right__cancel) ).
thf(2198,plain,
! [A: int,B: int,C: int] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(130,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_nat__add__right__cancel) ).
thf(1193,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(135,axiom,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_one__less__power) ).
thf(1212,plain,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(252,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_zero__less__power) ).
thf(1607,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(220,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_add__nonneg__nonneg) ).
thf(1513,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(39,axiom,
! [A: real,B: real,C: real] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_xt1_I3_J) ).
thf(832,plain,
! [A: real,B: real,C: real] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(158,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_add__increasing) ).
thf(1309,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(200,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_order__trans) ).
thf(1444,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(359,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_add__strict__left__mono) ).
thf(1994,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(579,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_add__strict__increasing) ).
thf(2779,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(687,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rel__simps_I4_J) ).
thf(3181,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(472,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_int__0__neq__1) ).
thf(2384,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(581,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ one_one_int )
= ( number_number_of_int @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_semiring__number__of__add__1) ).
thf(2786,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ one_one_int )
= ( number_number_of_int @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(543,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ? [B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_zero__less__imp__eq__int) ).
thf(2648,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ? [B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(298,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_power__increasing__iff) ).
thf(1777,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(465,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(2362,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(403,axiom,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( sqrt @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_real__sqrt__sum__squares__ge__zero) ).
thf(2162,plain,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( sqrt @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(255,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
<=> ( B
= ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_number__of__reorient) ).
thf(1614,plain,
! [A: int,B: int] :
( ( ( ( number_number_of_int @ A )
= B )
=> ( B
= ( number_number_of_int @ A ) ) )
& ( ( B
= ( number_number_of_int @ A ) )
=> ( ( number_number_of_int @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(481,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_rel__simps_I38_J) ).
thf(2421,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(112,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_less__eq__nat_Osimps_I1_J) ).
thf(1116,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(468,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_not__one__less__zero) ).
thf(2374,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(446,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_add__special_I2_J) ).
thf(2287,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(450,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
thf(2302,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(243,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_add__less__imp__less__left) ).
thf(1578,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(665,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ? [B: nat] :
( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_zero__le__imp__eq__int) ).
thf(3100,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ? [B: nat] :
( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(570,axiom,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ A ) ) @ one_one_nat )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ A ) ) @ one_one_nat )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_nat__number__of__add__1) ).
thf(2736,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ A ) ) @ one_one_nat )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( number_number_of_nat @ A ) ) @ one_one_nat )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(291,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I2_J) ).
thf(1757,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(692,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_zle__add1__eq__le) ).
thf(3203,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(683,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3164,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(619,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( succ @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_add__Bit1__Bit1) ).
thf(2930,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( succ @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(435,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_add__right__imp__eq) ).
thf(2258,plain,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_add__left__cancel) ).
thf(1133,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(385,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_add__pos__pos) ).
thf(2102,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_of__nat__less__iff) ).
thf(752,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(539,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_number__of2) ).
thf(2636,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(321,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_add__le__less__mono) ).
thf(1859,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(32,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_of__nat__less__0__iff) ).
thf(801,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(216,axiom,
! [A: real] :
( ( zero_zero_real = A )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_zero__reorient) ).
thf(1495,plain,
! [A: real] :
( ( ( zero_zero_real = A )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( zero_zero_real = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(459,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_power__0__left__number__of) ).
thf(2334,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(518,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_add__increasing) ).
thf(2572,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(98,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_zero__le__double__add__iff__zero__le__single__add) ).
thf(1056,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(280,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_nat__neq__iff) ).
thf(1710,plain,
! [A: nat,B: nat] :
( ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(691,axiom,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ A ) )
= ( number_number_of_int @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_of__nat__number__of__lemma) ).
thf(3196,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ A ) )
= ( number_number_of_int @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(535,axiom,
( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__add__one__is__two) ).
thf(2619,plain,
( ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(5,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_zero__le__imp__of__nat) ).
thf(720,plain,
! [A: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_less__eq__int__code_I13_J) ).
thf(796,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(172,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_add__increasing2) ).
thf(1363,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(160,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_gr0I) ).
thf(1314,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(236,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_add__leD1) ).
thf(1561,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(559,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_add__strict__left__mono) ).
thf(2704,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_add__increasing2) ).
thf(839,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(12,axiom,
( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
thf(740,plain,
( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(78,axiom,
! [A: bool,B: bool,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ B )
<=> ( hBOOL @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ B ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_imp__le__cong) ).
thf(987,plain,
! [A: bool,B: bool,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) ) )
=> ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ A ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(483,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_le__imp__0__less) ).
thf(2430,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(437,axiom,
( ( succ @ pls )
= ( bit1 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_succ__Pls) ).
thf(2265,plain,
( ( succ @ pls )
= ( bit1 @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(46,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_eq__number__of) ).
thf(850,plain,
! [A: int,B: int] :
( ( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(558,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__special_I3_J) ).
thf(2699,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(439,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2270,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(395,axiom,
! [A: nat] :
( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_number__of__int) ).
thf(2138,plain,
! [A: nat] :
( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(586,axiom,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_sum__power2__ge__zero) ).
thf(2810,plain,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(568,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2731,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(673,axiom,
! [A: real,B: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_not__sum__power2__lt__zero) ).
thf(3128,plain,
! [A: real,B: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(315,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_le__trans) ).
thf(1829,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(115,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_ord__le__eq__trans) ).
thf(1129,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(651,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_less__add__one) ).
thf(3057,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(585,axiom,
! [A: int,B: int] :
( ( A
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) )
<=> ( B = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_add__0__iff) ).
thf(2803,plain,
! [A: int,B: int] :
( ( ( A
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) )
=> ( B = zero_zero_int ) )
& ( ( B = zero_zero_int )
=> ( A
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_power__decreasing) ).
thf(860,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(529,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_power2__le__imp__le) ).
thf(2600,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(612,axiom,
! [A: int] :
( ( zero_zero_int = A )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_zero__reorient) ).
thf(2898,plain,
! [A: int] :
( ( ( zero_zero_int = A )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( zero_zero_int = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(249,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_add__pos__nonneg) ).
thf(1597,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(77,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_double__add__le__zero__iff__single__add__le__zero) ).
thf(982,plain,
! [A: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(328,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_add__gr__0) ).
thf(1880,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(164,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_add__0) ).
thf(1331,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(514,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n0) ).
thf(2563,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(345,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_gr__implies__not0) ).
thf(1945,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(272,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_less__special_I2_J) ).
thf(1681,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(367,axiom,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_ex__least__nat__le) ).
thf(2018,plain,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(534,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ~ ! [B: nat] :
( A
!= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_nonneg__eq__int) ).
thf(2615,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ~ ! [B: nat] :
( A
!= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(406,axiom,
! [A: nat] :
( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_number__of__int) ).
thf(2170,plain,
! [A: nat] :
( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Nat__Onat_T) ).
thf(708,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(545,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__special_I1_J) ).
thf(2655,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(606,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_zero__neq__one) ).
thf(2879,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(541,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zpower__int) ).
thf(2640,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(456,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_number__of__Bit0) ).
thf(2321,plain,
! [A: int] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(700,axiom,
! [A: int] :
( ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_double__zero__sym) ).
thf(3227,plain,
! [A: int] :
( ( ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(174,axiom,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_linorder__neqE__linordered__idom) ).
thf(1367,plain,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(207,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_of__nat__le__iff) ).
thf(1463,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(632,axiom,
( zero_zero_int
= ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_transfer__int__nat__numerals_I1_J) ).
thf(2998,plain,
( zero_zero_int
= ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_nat__le__linear) ).
thf(1565,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(427,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_one__less__power) ).
thf(2238,plain,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(214,axiom,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_power__less__imp__less__exp) ).
thf(1490,plain,
! [A: nat,B: nat,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(92,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_le__special_I1_J) ).
thf(1037,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(23,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_less__not__refl) ).
thf(775,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(488,axiom,
! [A: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_power2__less__0) ).
thf(2453,plain,
! [A: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(649,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_of__nat__0__le__iff) ).
thf(3052,plain,
! [A: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(414,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_add__right__mono) ).
thf(2191,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(309,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_rel__simps_I14_J) ).
thf(1812,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(208,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_add__less__le__mono) ).
thf(1468,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(647,axiom,
! [A: int,B: nat,C: int] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ B )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_power__eq__imp__eq__base) ).
thf(3047,plain,
! [A: int,B: nat,C: int] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ B )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(326,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_neq0__conv) ).
thf(1870,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(75,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_le__special_I4_J) ).
thf(972,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ one_one_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(3251,plain,
$false,
inference(e,[status(thm)],[1586,1337,1411,2612,1454,2072,3167,846,1899,1840,941,1168,2341,1956,1549,2280,1554,1686,2250,2776,1073,2014,1728,3012,1533,1437,1173,2363,1200,1750,977,2976,762,1005,2210,2940,1406,2104,2495,2381,2947,2248,2114,1142,1705,1655,3004,2184,2933,2141,2712,2476,2459,1640,2146,2607,2686,3044,1735,3121,913,1222,930,2360,3103,3236,2723,841,1046,1935,1650,1386,2173,2516,1967,1254,1887,2432,1914,1243,2548,2985,1391,782,1441,2886,1359,1904,1518,1703,3029,3131,2667,785,2755,2708,2217,2488,934,1992,949,1792,1430,1907,2501,2682,1826,1379,2767,1013,1398,1773,1963,1847,1319,1890,1479,1609,969,1347,1572,2456,2178,2324,789,1450,2090,1334,2925,1151,1383,1051,905,1302,1664,2893,2469,1677,2034,1183,1283,2833,877,734,866,1622,3157,1526,2002,2750,2392,2586,3068,1377,2718,2205,1863,1604,3097,3011,2574,2164,2118,1783,2621,1153,3186,1470,1708,1311,3054,2660,1868,2061,2000,1730,1163,2589,746,2428,825,1042,1580,862,1570,820,1666,1370,2032,2528,1238,1021,778,1423,1365,2820,1951,1457,830,1787,1210,2313,1281,2112,2769,1106,3191,1938,1032,1837,1819,1624,1027,2327,757,3050,1634,2228,1350,1804,2895,1375,2577,1111,2692,1096,2631,2858,3078,3237,1118,3087,742,2300,1762,2100,2841,1328,3218,725,2694,1425,1567,884,1361,3000,2868,1446,1612,2781,2561,3210,3094,1461,2196,2240,1810,1791,1214,3194,1207,2085,3242,1825,997,1249,738,1974,2581,2505,3222,2566,1984,1002,2862,1720,1627,2450,2125,1588,2536,3126,2681,1539,2836,2598,3059,1266,2387,1831,2851,2243,2355,1932,1599,1246,3109,1979,3162,1759,1202,3225,921,1563,1054,1286,1071,2915,1515,1996,2189,2995,2662,1185,1278,1648,750,2556,1483,1747,1927,2602,2734,3111,1374,2376,2235,2144,1146,1754,2292,2253,2275,3070,1007,1916,732,2791,2789,772,1752,1701,2817,1124,1488,3213,3234,2048,3081,1929,826,711,2161,1503,936,2891,787,3208,2706,1765,804,1224,3170,3023,1669,2193,1786,3002,1733,2148,2319,2521,900,2637,1524,2284,1492,3106,2669,2116,1801,2856,1969,2510,764,2538,1408,2151,3155,2415,1894,2987,2906,1048,736,2378,1690,2871,1439,890,1877,2812,2610,2314,3073,2267,2261,848,3034,769,2252,2278,1381,1061,811,2182,3133,858,2593,895,3006,1149,964,2874,2710,2911,2350,1699,959,1113,2022,2390,2156,2207,922,912,1171,2075,2418,1396,2439,2962,2365,2051,2481,1528,868,780,1643,3159,1015,1775,1000,2752,3009,1583,2952,1662,1166,2652,1420,2503,3146,2684,1340,1472,1958,2005,1413,1076,2054,722,927,2037,1081,2927,1018,2256,2564,836,1551,2513,1547,1770,1516,705,1225,2012,1941,2175,1780,2407,2720,1531,1230,1098,2882,2397,1025,3082,887,2678,2518,3080,2569,2092,1987,1432,3026,1317,1901,1679,3174,907,1300,1452,1637,3114,2688,2920,791,1262,1235,2276,2219,2486,951,1738,3041,1404,2500,2543,1506,2579,2728,1372,2584,1536,1981,2357,2843,1094,1140,2860,2949,2865,3139,2479,2088,1949,2078,2310,2215,1866,1807,3039,1998,2626,1918,1084,2045,3092,1817,2960,2743,2187,2110,1010,2305,1575,1289,844,2226,2643,2443,748,2855,2135,1508,2971,1854,2130,3136,1558,3085,1276,2591,1590,2167,2273,2853,2290,946,1101,2823,3220,2764,1822,1861,2796,2399,1294,2198,1193,1212,1607,1513,832,1309,1444,1994,2779,3181,2384,2786,2648,1777,2362,2162,1614,2421,1116,2374,2287,2302,1578,3100,2736,1757,3203,3164,2930,2258,1133,2102,752,2636,1859,801,1495,2334,2572,1056,1710,3196,2619,720,796,1363,1314,1561,2704,839,740,987,2430,2265,850,2699,2270,2138,2810,2731,3128,1829,1129,3057,2803,860,2600,2898,1597,982,1880,1331,2563,1945,1681,2018,2615,2170,708,2655,2879,2640,2321,3227,1367,1463,2998,1565,2238,1490,1037,775,2453,3052,2191,1812,1468,3047,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% 0.14/0.13 % Command : run_Leo-III %s %d
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu May 18 17:46:08 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.82/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.13 % [INFO] Parsing done (304ms).
% 1.79/1.15 % [INFO] Running in sequential loop mode.
% 2.59/1.39 % [INFO] eprover registered as external prover.
% 2.59/1.39 % [INFO] cvc4 registered as external prover.
% 2.59/1.39 % [INFO] Scanning for conjecture ...
% 3.16/1.54 % [INFO] Found a conjecture and 702 axioms. Running axiom selection ...
% 3.83/1.71 % [INFO] Axiom selection finished. Selected 702 axioms (removed 0 axioms).
% 4.92/2.00 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.92/2.02 % [INFO] Type checking passed.
% 4.92/2.02 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.26/2.32 % [INFO] [Domain constraints] Detected constraint on bool
% 6.26/2.32 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 16.67/4.89 % External prover 'e' found a proof!
% 16.67/4.89 % [INFO] Killing All external provers ...
% 16.67/4.89 % Time passed: 4412ms (effective reasoning time: 3742ms)
% 16.67/4.89 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 16.67/4.90 % Axioms used in derivation (702): fact_686_order__antisym__conv, fact_3_sum__power2__eq__zero__iff, fact_529_zle__iff__zadd, fact_548_add__neg__nonpos, fact_541_add__nonneg__pos, fact_475_add__nonneg__eq__0__iff, fact_97_Bit0__Pls, help_If_3_1_If_000tc__Nat__Onat_T, fact_271_power__inject__exp, fact_527_zero__zle__int, fact_467_zero__le__double__add__iff__zero__le__single__add, fact_482_add__increasing2, fact_2_sum__power2__eq__zero__iff, fact_261_not__one__less__zero, fact_288_of__nat__less__0__iff, fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_454_power__decreasing, fact_159_one__less__power, fact_48_rel__simps_I2_J, fact_665_xt1_I5_J, fact_21_quartic__square__square, fact_184_linorder__neqE__nat, fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_236_of__nat__less__iff, fact_440_zle__trans, fact_651_real__le__antisym, fact_615_less__or__eq__imp__le, fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_63_even__less__0__iff, fact_327_add__left__cancel, fact_372_add__less__imp__less__left, fact_29_n0, fact_378_add__strict__mono, fact_305_double__add__less__zero__iff__single__add__less__zero, fact_270_less__add__one, fact_24_power__0__left__number__of, fact_422_add__mono, fact_582_number__of__succ, fact_110_number__of__Pls, fact_453_le__special_I3_J, fact_381_add__strict__left__mono, fact_660_linorder__le__cases, fact_439_zle__linear, fact_419_add__left__mono, fact_313_add__imp__eq, fact_176_number__of__is__id, fact_497_zero__le__one, fact_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_391_add__less__cancel__right, fact_103_Bit0__def, fact_640_zle__int, fact_557_eq__0__number__of, fact_4_one__power2, fact_65_zadd__assoc, fact_692_mult__Bit1, fact_208_linorder__neqE__linordered__idom, fact_506_power__mono, fact_255_Nat__Transfer_Otransfer__int__nat__functions_I4_J, fact_172_real__zero__not__eq__one, fact_511_zero__le__imp__of__nat, fact_116_add__numeral__0__right, fact_446_of__nat__le__iff, fact_519_rel__simps_I21_J, fact_500_le__number__of__eq__not__less, fact_280_power__strict__increasing, fact_349_add__0__iff, fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_292_of__nat__0, fact_41_nat__number__of__Pls, fact_626_real__less__def, fact_697_real__sqrt__lt__1__iff, fact_407_nat__1__add__number__of, fact_635_add__leD2, fact_466_le__special_I4_J, fact_129_odd__nonzero, fact_350_add__0__iff, fact_61_rel__simps_I51_J, fact_30_zless__linear, fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_238_less__imp__of__nat__less, fact_447_zless__le, fact_659_linorder__le__cases, fact_173_less__not__refl, fact_32_plus__numeral__code_I9_J, fact_437_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_485_add__nonpos__nonpos, fact_413_add__le__cancel__left, fact_622_eq__imp__le, fact_293_of__nat__0, fact_550_add__neg__nonpos, fact_36_zpower__int, fact_525_transfer__int__nat__quantifiers_I2_J, fact_522_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_682_ord__eq__le__trans, fact_425_add__le__imp__le__right, fact_79_bin__less__0__simps_I1_J, fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_279_power__less__imp__less__exp, fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_559_rel__simps_I5_J, fact_83_int__less__0__conv, fact_39_zadd__int, fact_389_add__less__cancel__left, fact_514_of__nat__0__le__iff, fact_272_power__inject__exp, fact_360_add__0__right, fact_655_order__refl, fact_387_add__less__cancel__left, fact_169_int__gr__induct, fact_526_transfer__int__nat__quantifiers_I1_J, fact_132_number__of__int, fact_433_rel__simps_I34_J, fact_15_add__special_I3_J, fact_471_add__nonneg__nonneg, fact_145_semiring__numeral__1__eq__1, fact_157_one__less__power, fact_375_add__less__imp__less__right, fact_111_semiring__norm_I112_J, fact_457_power__increasing__iff, fact_256_pos__add__strict, fact_140_not__sum__power2__lt__zero, fact_78_bin__less__0__simps_I4_J, fact_689_real__lbound__gt__zero, fact_595_power2__eq__imp__eq, fact_213_plus__nat_Oadd__0, fact_459_power__increasing__iff, fact_40_int__1, fact_179_nat__add__left__commute, fact_540_add__nonneg__pos, fact_251_of__nat__power, fact_584_add__Bit1__Bit1, fact_532_semiring__1__add__number__of, fact_542_add__strict__increasing, fact_632_trans__le__add2, fact_171_less__zeroE, fact_481_add__increasing2, fact_22_power__0__left__number__of, fact_365_add__0, fact_182_nat__add__right__cancel, fact_480_add__increasing2, fact_181_nat__add__left__cancel, fact_361_double__zero__sym, fact_487_add__less__le__mono, fact_673_xt1_I4_J, fact_352_add_Ocomm__neutral, fact_631_trans__le__add1, fact_281_power__strict__increasing, fact_505_power__mono, fact_656_order__refl, fact_14_add__special_I3_J, fact_88_odd__less__0, fact_52_add__nat__number__of, fact_100_add__Pls__right, fact_198_less__nat__zero__code, fact_204_Nat__Transfer_Otransfer__int__nat__relations_I2_J, fact_606_sum__power2__le__zero__iff, fact_183_nat__add__left__cancel__less, fact_544_add__strict__increasing, fact_217_of__nat__eq__iff, fact_6_one__power2, fact_504_power__mono, fact_524_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_11_zero__eq__power2, fact_331_ab__semigroup__add__class_Oadd__ac_I1_J, fact_189_trans__less__add2, fact_611_nonneg__int__cases, fact_443_le__number__of, fact_20_semiring__one__add__one__is__two, fact_649_real__le__linear, fact_658_linorder__le__cases, fact_237_of__nat__less__iff, fact_594_power2__le__imp__le, fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_398_add__neg__neg, fact_158_one__less__power, fact_71_less__special_I1_J, fact_444_of__nat__le__iff, fact_54_nat__numeral__1__eq__1, fact_175_not__add__less2, fact_25_semiring__norm_I110_J, fact_530_semiring__1__add__number__of, fact_465_le__special_I4_J, fact_552_add__nonpos__neg, fact_214_power__one__right, fact_508_one__le__power, fact_432_less__eq__int__code_I16_J, fact_614_le__0__eq, fact_364_add__0, fact_112_semiring__norm_I112_J, fact_99_int__0__neq__1, fact_515_of__nat__0__le__iff, fact_358_add__0__right, fact_556_power__less__imp__less__base, fact_72_less__special_I1_J, fact_125_number__of__add, fact_371_add__0__left, fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_106_semiring__numeral__0__eq__0, fact_605_sum__power2__le__zero__iff, fact_647_mono__nat__linear__lb, fact_617_less__imp__le__nat, fact_177_nat__neq__iff, fact_311_add__right__imp__eq, fact_285_power__eq__0__iff, fact_563_rel__simps_I33_J, fact_239_less__imp__of__nat__less, fact_576_power__eq__imp__eq__base, fact_351_add__0__iff, fact_318_add__left__imp__eq, fact_567_succ__Pls, fact_685_order__antisym__conv, fact_405_tpos, fact_316_add__left__imp__eq, fact_221_int__if__cong, fact_113_add__numeral__0, fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_531_semiring__1__add__number__of, fact_690_real__sqrt__sum__squares__ge__zero, fact_135_power2__less__0, fact_174_not__add__less1, fact_252_of__nat__power, fact_396_nat__power__eq__0__iff, fact_282_power__strict__increasing, fact_624_le__antisym, fact_499_le__number__of__eq__not__less, fact_646_nonneg__eq__int, fact_49_less__int__code_I13_J, fact_411_add__le__cancel__left, fact_190_add__less__mono1, fact_456_power__decreasing, fact_150_of__nat__less__two__power, fact_266_zero__less__power, fact_287_of__nat__less__0__iff, fact_161_power__0__left, fact_558_eq__number__of__0, fact_8_zero__power2, fact_246_of__nat__add, fact_546_add__strict__increasing2, fact_406_nat__number__of__add__1, fact_206_zless__int, fact_356_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_579_semiring__add__number__of, fact_93_rel__simps_I50_J, fact_94_rel__simps_I49_J, fact_242_of__nat__less__imp__less, fact_117_power__eq__0__iff__number__of, fact_247_of__nat__1, fact_62_rel__simps_I48_J, fact_66_zadd__left__commute, fact_452_le__special_I3_J, fact_283_power__eq__0__iff, fact_486_add__less__le__mono, fact_426_add__le__imp__le__left, fact_441_zle__antisym, fact_613_less__eq__nat_Osimps_I1_J, fact_561_rel__simps_I15_J, fact_226_one__neq__zero, fact_693_real__sqrt__gt__zero, fact_538_add__pos__nonneg, fact_1_t1, fact_449_less__eq__number__of__int__code, fact_235_of__nat__less__iff, fact_399_add__neg__neg, fact_180_nat__add__assoc, fact_134_zero__less__power2, fact_89_double__eq__0__iff, fact_612_le0, fact_223_zero__less__int__conv, fact_670_order__antisym, fact_118_power__eq__0__iff__number__of, fact_230_field__power__not__zero, fact_96_rel__simps_I38_J, fact_303_zero__less__double__add__iff__zero__less__single__add, fact_53_one__is__num__one, fact_608_number__of1, fact_460_power__le__imp__le__exp, fact_56_eq__number__of, fact_652_int__ge__induct, fact_551_add__nonpos__neg, fact_385_add__strict__right__mono, fact_580_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_680_xt1_I3_J, fact_5_one__power2, fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_586_power__strict__mono, fact_593_power2__le__imp__le, fact_323_add__right__cancel, fact_639_Nat__Transfer_Otransfer__int__nat__relations_I3_J, fact_148_mn, fact_147_semiring__numeral__1__eq__1, fact_120_add__number__of__left, fact_154_of__nat__0__less__iff, fact_678_ord__le__eq__trans, fact_59_number__of__reorient, fact_332_ab__semigroup__add__class_Oadd__ac_I1_J, fact_216_power__one__right, fact_102_add__Bit0__Bit0, fact_578_semiring__add__number__of, fact_616_le__neq__implies__less, fact_67_zadd__commute, fact_114_add__numeral__0, fact_599_of__nat__number__of__lemma, fact_562_less__int__code_I14_J, fact_461_power__le__imp__le__exp, fact_82_zless__add1__eq, fact_196_gr__implies__not0, fact_520_rel__simps_I27_J, fact_295_transfer__int__nat__numerals_I1_J, fact_630_nat__add__left__cancel__le, fact_263_zero__less__one, fact_91_rel__simps_I46_J, fact_153_realpow__two__sum__zero__iff, fact_545_add__strict__increasing2, fact_37_int__power, fact_684_ord__eq__le__trans, fact_225_one__neq__zero, fact_307_zero__reorient, fact_377_add__less__imp__less__right, fact_291_power__0, fact_31_less__number__of__int__code, fact_400_add__pos__pos, fact_149_of__nat__less__two__power, fact_695_real__sqrt__lt__0__iff, fact_625_less__eq__real__def, fact_623_le__trans, fact_664_xt1_I5_J, fact_192_less__add__eq__less, fact_12_add__special_I2_J, fact_18_semiring__one__add__one__is__two, fact_81_int__0__less__1, fact_600_power2__less__imp__less, fact_23_power__0__left__number__of, fact_668_order__trans, fact_163_power__strict__decreasing, fact_392_add__less__cancel__right, fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_386_add__strict__right__mono, fact_304_zero__less__double__add__iff__zero__less__single__add, fact_259_not__one__less__zero, fact_543_add__strict__increasing, fact_681_xt1_I3_J, fact_45_nat__1__add__1, fact_128_Bit1__def, fact_536_add__pos__nonneg, fact_666_xt1_I5_J, fact_382_add__strict__left__mono, fact_648_real__le__refl, fact_73_rel__simps_I12_J, fact_414_add__right__mono, fact_123_add__number__of__eq, fact_492_not__one__le__zero, fact_501_zero__le__power, fact_535_semiring__number__of__add__1, fact_442_le__number__of, fact_598_of__nat__number__of__lemma, fact_289_power__0, fact_265_zero__less__power, fact_609_number__of2, fact_592_power2__le__imp__le, fact_369_add__0__left, fact_509_one__le__power, fact_92_rel__simps_I39_J, fact_373_add__less__imp__less__left, fact_517_rel__simps_I32_J, fact_105_zadd__0, fact_472_add__nonneg__nonneg, fact_521_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_126_add__Bit1__Bit0, fact_571_add1__zle__eq, fact_90_double__eq__0__iff, fact_698_real__sqrt__gt__1__iff, fact_200_add__gr__0, fact_38_zadd__int__left, fact_638_real__add__left__mono, fact_644_imp__le__cong, fact_489_add__le__less__mono, fact_264_zero__less__one, fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_233_power__one, fact_428_add__le__imp__le__left, fact_108_semiring__numeral__0__eq__0, fact_121_add__number__of__left, fact_463_le__special_I2_J, fact_202_not__less0, fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_322_add__right__cancel, fact_621_nat__le__linear, fact_227_zero__neq__one, fact_654_less__mono__imp__le__mono, fact_362_double__zero__sym, fact_119_power__eq__0__iff__number__of, fact_87_less__special_I2_J, fact_359_add__0__right, fact_28_numeral__1__eq__1, fact_379_add__strict__mono, fact_229_zero__neq__one, fact_418_add__left__mono, fact_510_zero__le__imp__of__nat, fact_101_add__Pls, fact_205_zero__less__power__nat__eq__number__of, fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_683_ord__eq__le__trans, fact_618_le__eq__less__or__eq, fact_455_power__decreasing, fact_55_Numeral1__eq1__nat, fact_408_add__le__cancel__right, fact_429_power__increasing, fact_569_succ__Bit1, fact_553_add__nonpos__neg, fact_195_gr0I, fact_95_rel__simps_I44_J, fact_232_power__one, fact_523_zadd__zless__mono, fact_19_semiring__one__add__one__is__two, fact_35_zero__is__num__zero, fact_445_of__nat__le__iff, fact_636_add__leD1, fact_7_zero__power2, fact_607_int__pos__lt__two__imp__zero__or__one, fact_581_le__imp__0__less, fact_253_transfer__int__nat__numerals_I2_J, fact_688_order__eq__refl, fact_417_add__left__mono, fact_315_add__imp__eq, fact_257_pos__add__strict, fact_267_zero__less__power, fact_641_le__nat__number__of, fact_653_ex__least__nat__le, fact_577_semiring__add__number__of, fact_676_ord__le__eq__trans, fact_663_xt1_I6_J, fact_675_xt1_I4_J, fact_434_rel__simps_I19_J, fact_70_less__special_I3_J, fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_207_less__nat__number__of, fact_146_semiring__numeral__1__eq__1, fact_435_less__eq__int__code_I13_J, fact_144_number__of__Bit1, fact_243_of__nat__less__imp__less, fact_133_zero__less__power2, fact_312_add__right__imp__eq, fact_507_one__le__power, fact_143_number__of__Bit1, fact_17_one__add__one__is__two, fact_260_not__one__less__zero, fact_483_add__nonpos__nonpos, fact_661_xt1_I6_J, fact_168_zero__less__two, fact_494_not__one__le__zero, fact_634_add__le__mono, fact_310_add__right__imp__eq, fact_57_eq__number__of, fact_138_sum__power2__gt__zero__iff, fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_597_power2__eq__imp__eq, fact_142_number__of__Bit0, fact_268_less__add__one, fact_249_of__nat__1, fact_496_zero__le__one, fact_353_add_Ocomm__neutral, fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_601_power2__less__imp__less, fact_314_add__imp__eq, fact_241_of__nat__less__imp__less, fact_490_add__le__less__mono, fact_50_rel__simps_I14_J, fact_13_add__special_I2_J, fact_516_rel__simps_I22_J, fact_662_xt1_I6_J, fact_643_conj__le__cong, fact_273_power__inject__exp, fact_210_add__eq__self__zero, fact_436_rel__simps_I31_J, fact_602_power2__less__imp__less, fact_383_add__strict__left__mono, fact_384_add__strict__right__mono, fact_269_less__add__one, fact_402_add__pos__pos, fact_224_one__neq__zero, fact_76_rel__simps_I10_J, fact_276_power__strict__increasing__iff, fact_694_real__sqrt__not__eq__zero, fact_565_int__one__le__iff__zero__less, fact_403_realpow__pos__nth__unique, fact_696_real__sqrt__gt__0__iff, fact_211_add__is__0, fact_165_power__strict__decreasing, fact_619_nat__less__le, fact_493_not__one__le__zero, fact_416_add__right__mono, fact_415_add__right__mono, fact_477_add__increasing, fact_412_add__le__cancel__left, fact_98_Pls__def, fact_244_of__nat__add, fact_370_add__0__left, fact_478_add__increasing, fact_603_sum__power2__ge__zero, fact_74_less__int__code_I15_J, fact_191_add__less__mono, fact_679_xt1_I3_J, fact_596_power2__eq__imp__eq, fact_355_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_464_le__special_I2_J, fact_136_power2__less__0, fact_203_zero__less__power__nat__eq, fact_537_add__pos__nonneg, fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_107_semiring__numeral__0__eq__0, fact_194_nat__less__cases, fact_115_add__numeral__0__right, fact_627_le__add2, fact_43_int__eq__0__conv, fact_363_add__0, fact_137_sum__power2__gt__zero__iff, fact_245_of__nat__add, fact_570_zle__add1__eq__le, fact_308_zero__reorient, fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_610_zero__le__imp__eq__int, fact_637_add__leE, fact_185_less__irrefl__nat, fact_167_zero__less__two, fact_671_order__antisym, fact_46_less__int__code_I16_J, fact_220_Nat__Transfer_Otransfer__int__nat__relations_I1_J, fact_212_Nat_Oadd__0__right, fact_215_power__one__right, fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_152_transfer__int__nat__numerals_I4_J, fact_296_pos2, fact_193_add__lessD1, fact_201_neq0__conv, fact_219_of__nat__eq__iff, fact_306_double__add__less__zero__iff__single__add__less__zero, fact_277_power__less__imp__less__exp, fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_518_less__eq__int__code_I14_J, fact_104_zadd__0__right, fact_421_add__mono, fact_450_le__special_I1_J, fact_374_add__less__imp__less__left, fact_462_power__le__imp__le__exp, fact_80_bin__less__0__simps_I3_J, fact_317_add__left__imp__eq, fact_691_zadd__power2, fact_33_less__number__of, fact_42_semiring__norm_I113_J, fact_162_power__0__left, fact_549_add__neg__nonpos, fact_430_power__increasing, help_If_1_1_If_000tc__Nat__Onat_T, fact_299_exp__eq__1, fact_77_rel__simps_I4_J, fact_503_zero__le__power, fact_667_order__trans, fact_354_add_Ocomm__neutral, fact_590_zero__le__power2, fact_572_zless__imp__add1__zle, fact_431_power__increasing, fact_401_add__pos__pos, fact_347_one__reorient, fact_491_add__le__less__mono, fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_178_nat__add__commute, fact_346_one__reorient, fact_473_add__nonneg__nonneg, fact_669_order__trans, fact_390_add__less__cancel__right, fact_186_less__not__refl2, fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_156_of__nat__0__less__iff, fact_68_int__int__eq, fact_657_order__refl, fact_27_numeral__1__eq__1, fact_44_int__0, fact_275_power__strict__increasing__iff, fact_109_number__of__Pls, fact_469_double__add__le__zero__iff__single__add__le__zero, fact_628_le__add1, fact_218_of__nat__eq__iff, fact_427_add__le__imp__le__left, fact_170_tn0, fact_380_add__strict__mono, fact_687_order__antisym__conv, fact_502_zero__le__power, fact_420_add__mono, fact_86_less__special_I2_J, fact_566_int__le__0__conv, fact_458_power__increasing__iff, fact_513_of__nat__0__le__iff, fact_64_even__less__0__iff, fact_573_succ__def, fact_69_less__special_I3_J, fact_187_less__not__refl3, fact_677_ord__le__eq__trans, fact_122_add__number__of__eq, fact_620_le__refl, fact_672_order__antisym, fact_248_of__nat__1, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_9_zero__power2, fact_642_two__realpow__ge__one, fact_533_semiring__number__of__add__1, fact_587_power__strict__mono, fact_286_of__nat__less__0__iff, fact_376_add__less__imp__less__right, fact_325_add__left__cancel, fact_262_zero__less__one, fact_568_succ__Bit0, fact_10_zero__eq__power2, fact_141_number__of__Bit0, fact_155_of__nat__0__less__iff, fact_333_ab__semigroup__add__class_Oadd__ac_I1_J, fact_348_one__reorient, fact_199_nat__zero__less__power__iff, fact_534_semiring__number__of__add__1, fact_51_zadd__strict__right__mono, fact_151_transfer__int__nat__numerals_I3_J, fact_297_zero__less__imp__eq__int, fact_274_power__strict__increasing__iff, fact_34_less__number__of, fact_591_zero__le__power2, fact_231_field__power__not__zero, fact_495_zero__le__one, fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_60_number__of__reorient, fact_633_add__le__mono1, fact_290_power__0, fact_188_trans__less__add1, fact_309_zero__reorient, fact_410_add__le__cancel__right, fact_139_not__sum__power2__lt__zero, fact_564_less__eq__int__code_I15_J, fact_404_realpow__pos__nth, fact_555_power__less__imp__less__base, fact_488_add__less__le__mono, fact_512_zero__le__imp__of__nat, fact_468_zero__le__double__add__iff__zero__le__single__add, fact_674_xt1_I4_J, fact_298_less__imp__add__positive, fact_127_add__Bit0__Bit1, fact_85_less__special_I4_J, fact_397_add__neg__neg, fact_498_le__number__of__eq__not__less, fact_131_number__of__int, fact_479_add__increasing, fact_554_power__less__imp__less__base, fact_294_of__nat__0, fact_539_add__nonneg__pos, fact_258_pos__add__strict, fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_326_add__left__cancel, fact_575_power__eq__imp__eq__base, fact_574_power__eq__imp__eq__base, fact_0_n1pos, fact_240_less__imp__of__nat__less, fact_438_zle__refl, fact_278_power__less__imp__less__exp, help_If_2_1_If_000tc__Nat__Onat_T, fact_84_less__special_I4_J, fact_324_add__right__cancel, fact_451_le__special_I1_J, fact_470_double__add__le__zero__iff__single__add__le__zero, fact_75_rel__simps_I16_J, fact_209_linorder__neqE__linordered__idom, fact_476_add__nonneg__eq__0__iff, fact_164_power__strict__decreasing, fact_547_add__strict__increasing2, fact_160_power__0__left, fact_423_add__le__imp__le__right, fact_629_le__iff__add, fact_589_power2__ge__self, fact_448_zadd__left__mono, fact_16_one__add__one__is__two, fact_197_nat__power__less__imp__less, fact_604_sum__power2__ge__zero, fact_484_add__nonpos__nonpos, fact_222_less__0__number__of, fact_166_zero__less__two, fact_58_number__of__reorient, fact_250_of__nat__power, fact_130_number__of__int, fact_26_semiring__norm_I110_J, fact_474_add__nonneg__eq__0__iff, fact_388_add__less__cancel__left, fact_583_number__of__succ, fact_528_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_254_Nat__Transfer_Otransfer__int__nat__functions_I1_J, fact_585_power__strict__mono, fact_47_rel__simps_I17_J, fact_124_number__of__add, fact_645_ex__least__nat__less, fact_284_power__eq__0__iff, fact_409_add__le__cancel__right, fact_424_add__le__imp__le__right, fact_650_real__le__trans, fact_234_power__one, fact_228_zero__neq__one, fact_560_rel__simps_I29_J
% 16.67/4.90 % No. of inferences in proof: 1408
% 16.67/4.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4412 ms resp. 3742 ms w/o parsing
% 18.22/5.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.22/5.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------