TSTP Solution File: NUM926_3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM926_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 11:43:28 EDT 2023
% Result : Theorem 25.04s 7.02s
% Output : Refutation 26.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1285
% Syntax : Number of formulae : 2485 ( 908 unt; 87 typ; 0 def)
% Number of atoms : 6073 (1915 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 41702 ( 566 ~; 176 |; 651 &;37461 @)
% ( 254 <=>;2594 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 25 con; 0-2 aty)
% Number of variables : 5197 ( 0 ^;5141 !; 56 ?;5197 :)
% 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_bool_bool_type,type,
fun_bool_bool: $tType ).
thf(fun_bo1549164019l_bool_type,type,
fun_bo1549164019l_bool: $tType ).
thf(fun_int_bool_type,type,
fun_int_bool: $tType ).
thf(fun_int_int_type,type,
fun_int_int: $tType ).
thf(fun_in531499254l_bool_type,type,
fun_in531499254l_bool: $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(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(cOMBC_int_int_bool_type,type,
cOMBC_int_int_bool: fun_int_fun_int_bool > int > fun_int_bool ).
thf(div_mod_int_type,type,
div_mod_int: int > fun_int_int ).
thf(div_mod_nat_type,type,
div_mod_nat: nat > fun_nat_nat ).
thf(minus_minus_int_type,type,
minus_minus_int: int > fun_int_int ).
thf(minus_minus_nat_type,type,
minus_minus_nat: nat > fun_nat_nat ).
thf(minus_minus_real_type,type,
minus_minus_real: real > fun_real_real ).
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 > fun_int_int ).
thf(times_times_nat_type,type,
times_times_nat: nat > fun_nat_nat ).
thf(times_times_real_type,type,
times_times_real: real > fun_real_real ).
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(multInv_type,type,
multInv: int > int > int ).
thf(d22set_type,type,
d22set: int > fun_int_bool ).
thf(zfact_type,type,
zfact: int > int ).
thf(zcong_type,type,
zcong: int > int > fun_int_bool ).
thf(zprime_type,type,
zprime: fun_int_bool ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(min_type,type,
min: 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(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(product_Pair_int_int_type,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(legendre_type,type,
legendre: int > int > int ).
thf(quadRes_type,type,
quadRes: int > fun_int_bool ).
thf(sr_type,type,
sr: int > fun_int_bool ).
thf(standardRes_type,type,
standardRes: int > int > int ).
thf(dvd_dvd_int_type,type,
dvd_dvd_int: fun_int_fun_int_bool ).
thf(dvd_dvd_nat_type,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
thf(dvd_dvd_real_type,type,
dvd_dvd_real: fun_re413263731l_bool ).
thf(twoSqu820444569sum2sq_type,type,
twoSqu820444569sum2sq: fun_int_bool ).
thf(twoSqu949963151sum2sq_type,type,
twoSqu949963151sum2sq: product_prod_int_int > int ).
thf(inv_type,type,
inv: int > int > int ).
thf(wset_type,type,
wset: int > int > fun_int_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(member_int_type,type,
member_int: int > fun_int_bool > bool ).
thf(m_type,type,
m: int ).
thf(s1_type,type,
s1: int ).
thf(s_type,type,
s: int ).
thf(t_type,type,
t: int ).
thf(128,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_wset__less) ).
thf(1586,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(741,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_87_add1__zle__eq) ).
thf(3883,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)],[741]) ).
thf(189,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 @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ B ) @ A )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_mod__pos__neg__trivial) ).
thf(1823,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 @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) @ zero_zero_int ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ B ) @ A )
= ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1089,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ zero_zero_int ) @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_mult__zero__left) ).
thf(5136,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ zero_zero_int ) @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(178,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_rel__simps_I8_J) ).
thf(1767,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(604,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_less__not__refl) ).
thf(3397,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(446,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_mult__zero__right) ).
thf(2787,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(368,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_Nat_Odiff__le__self) ).
thf(2480,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(751,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(3927,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(956,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_593_power__0__left__number__of) ).
thf(4682,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)],[956]) ).
thf(32,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 @ zero_zero_real ) @ D ) )
=> ( ( 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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_mult__mono) ).
thf(1295,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 @ zero_zero_real ) @ D ) )
=> ( ( 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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1158,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_semiring__mult__2) ).
thf(5385,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(297,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_dvd__mult__cancel) ).
thf(2199,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(516,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_88_zle__add1__eq__le) ).
thf(3021,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)],[516]) ).
thf(1194,axiom,
! [A: int,B: nat,C: nat] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(5509,plain,
! [A: int,B: nat,C: nat] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(808,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( D = B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_zcong__eq__trans) ).
thf(4188,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( D = B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(759,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) @ one_one_int ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ one_one_int ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_zcong__zpower__zmult) ).
thf(3962,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) @ one_one_int ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ one_one_int ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(207,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_561_eq__0__number__of) ).
thf(1879,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)],[207]) ).
thf(1169,axiom,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ s ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ s ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ s ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_s0p) ).
thf(5422,plain,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ s ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ s ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ s ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(267,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_446_power2__le__imp__le) ).
thf(2094,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)],[267]) ).
thf(754,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(3944,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(69,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_305_power__increasing__iff) ).
thf(1411,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)],[69]) ).
thf(325,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_819_comm__mult__strict__left__mono) ).
thf(2306,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(523,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_Residues_Oaux) ).
thf(3053,plain,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(879,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_33_one__add__one__is__two) ).
thf(4450,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)],[879]) ).
thf(885,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_semiring__mult__2__right) ).
thf(4464,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(332,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_335_power__0__left) ).
thf(2336,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)],[332]) ).
thf(273,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_dvd__mult) ).
thf(2109,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1003,axiom,
! [A: real,B: real] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_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 ) ) ) ) ) ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_real__sum__squared__expand) ).
thf(4824,plain,
! [A: real,B: real] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_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 ) ) ) ) ) ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(234,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_one__dvd) ).
thf(1995,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(752,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_mult__0__right) ).
thf(3930,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(802,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_power__mult__distrib) ).
thf(4169,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(715,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_mult__nonneg__nonpos) ).
thf(3798,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_add__diff__inverse) ).
thf(1559,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(970,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ ( bit0 @ A ) ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_zmod__number__of__Bit0) ).
thf(4729,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ ( bit0 @ A ) ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(170,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_nat__mult__dvd__cancel__disj_H) ).
thf(1729,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(807,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_431_less__special_I3_J) ).
thf(4183,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)],[807]) ).
thf(484,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_rel__simps_I23_J) ).
thf(2921,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(627,axiom,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( standardRes @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_StandardRes__prop1) ).
thf(3477,plain,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( standardRes @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(653,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( times_times_real @ C ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(3566,plain,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( times_times_real @ C ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1056,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_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(5028,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)],[1056]) ).
thf(221,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_934_diff__diff__left) ).
thf(1956,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1046,axiom,
! [A: int] :
( ( min
= ( bit1 @ A ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_rel__simps_I43_J) ).
thf(4992,plain,
! [A: int] :
( ( ( min
= ( bit1 @ A ) )
=> ( min = A ) )
& ( ( min = A )
=> ( min
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(114,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 @ zero_zero_int ) @ 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 @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_mult__mono_H) ).
thf(1549,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 @ zero_zero_int ) @ 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 @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(116,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_437_le__imp__0__less) ).
thf(1554,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)],[116]) ).
thf(1029,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_mult__number__of__left) ).
thf(4904,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(375,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_dvd_Ole__imp__less__or__eq) ).
thf(2512,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(848,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_zcong__zpower) ).
thf(4339,plain,
! [A: nat,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(774,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 ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_pos__mod__conj) ).
thf(4075,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 ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(732,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_zdvd__zmod__imp__zdvd) ).
thf(3858,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(371,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_996_le__add1) ).
thf(2495,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)],[371]) ).
thf(1117,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_250_number__of__add) ).
thf(5242,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)],[1117]) ).
thf(379,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_power__le__dvd) ).
thf(2527,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(514,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3012,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(269,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_mult__pos__neg) ).
thf(2099,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(940,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_353_add__0__iff) ).
thf(4623,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)],[940]) ).
thf(1145,axiom,
hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(5348,plain,
hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(198,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_mult__nonneg__nonpos2) ).
thf(1855,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1,conjecture,
? [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 ) ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [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 ) ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1200,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 ) ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(261,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_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_331_dvd__power__same) ).
thf(2077,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_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)],[261]) ).
thf(684,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 ) @ B ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_mod__neg__neg__trivial) ).
thf(3681,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 ) @ B ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(6,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 @ ( times_times_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_864_real__mult__order) ).
thf(1211,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 @ ( times_times_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(770,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ 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 @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( inv @ B @ A ) ) @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_inv__is__inv) ).
thf(3990,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ 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 @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( inv @ B @ A ) ) @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(529,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_885_minus__nat_Odiff__0) ).
thf(3072,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(299,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 @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_diff__less__mono) ).
thf(2210,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 @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(276,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_167_le__special_I4_J) ).
thf(2117,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)],[276]) ).
thf(132,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 @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_mult__pos__pos) ).
thf(1596,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 @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1111,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_31_add__special_I3_J) ).
thf(5225,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)],[1111]) ).
thf(454,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(2808,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(746,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( ( 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 @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_mult__le__cancel2) ).
thf(3905,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( ( 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 @ A ) @ C ) ) ) )
& ( ( ( 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 @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(704,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 ) @ ( standardRes @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1196_StandardRes__lbound) ).
thf(3762,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 ) @ ( standardRes @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(903,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ C ) ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_MultInv__zcong__prop1) ).
thf(4515,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ C ) ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(79,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_500_power__strict__increasing) ).
thf(1443,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)],[79]) ).
thf(442,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ one_one_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_nat__mult__1) ).
thf(2776,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ one_one_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(496,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_53_le__number__of) ).
thf(2953,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)],[496]) ).
thf(397,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_divides__div__not) ).
thf(2590,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1131,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_135_eq__number__of) ).
thf(5297,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)],[1131]) ).
thf(493,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_76_zadd__left__mono) ).
thf(2947,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)],[493]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_add__diff__assoc2) ).
thf(1569,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(217,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_left__add__mult__distrib) ).
thf(1939,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(758,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_304_power__increasing__iff) ).
thf(3959,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)],[758]) ).
thf(747,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 @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ B ) )
<=> ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_875_dvd__mult__cancel1) ).
thf(3912,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 @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ B ) )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(535,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_nat__mult__commute) ).
thf(3098,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(240,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_55_zadd__zless__mono) ).
thf(2014,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)],[240]) ).
thf(1101,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_442_zero__eq__power2) ).
thf(5173,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)],[1101]) ).
thf(275,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ 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 @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) @ one_one_int ) @ B ) )
=> ( ( A = one_one_int )
| ( A
= ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_zcong__square__zless) ).
thf(2114,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ 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 @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) @ one_one_int ) @ B ) )
=> ( ( A = one_one_int )
| ( A
= ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(24,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 ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_mult__right__mono__neg) ).
thf(1269,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 ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(226,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_86_zless__imp__add1__zle) ).
thf(1971,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)],[226]) ).
thf(937,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(4614,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(107,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_881_real__le__linear) ).
thf(1533,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)],[107]) ).
thf(1115,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_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(5237,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)],[1115]) ).
thf(977,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_power2__eq__square) ).
thf(4747,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(928,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_semiring__norm_I112_J) ).
thf(4592,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(942,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ pls ) @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_mult__Pls) ).
thf(4633,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ pls ) @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(153,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_402_int__0__less__1) ).
thf(1655,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)],[153]) ).
thf(974,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_mult__numeral__1__right) ).
thf(4739,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(402,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ 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 @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_mult__less__cancel1) ).
thf(2607,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ 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 @ 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 @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(39,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ E ) )
=> ( ( 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 )
= one_one_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ D ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_convex__bound__lt) ).
thf(1310,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ E ) )
=> ( ( 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 )
= one_one_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ D ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1129,axiom,
! [A: int,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(5288,plain,
! [A: int,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(785,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_zero__less__diff) ).
thf(4110,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( minus_minus_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 @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(360,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_nat__le__add__iff1) ).
thf(2448,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(283,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( member_int @ A @ ( d22set @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_d22set__le) ).
thf(2141,plain,
! [A: int,B: int] :
( ( hBOOL @ ( member_int @ A @ ( d22set @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(665,axiom,
! [A: real,B: nat] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ A )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_power__commutes) ).
thf(3616,plain,
! [A: real,B: nat] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ A )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(689,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_diff__diff__cancel) ).
thf(3693,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(407,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_986_le__eq__less__or__eq) ).
thf(2627,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)],[407]) ).
thf(629,axiom,
! [A: int,B: int,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( minus_minus_real @ ( number267125858f_real @ B ) ) @ C ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_add__number__of__diff1) ).
thf(3481,plain,
! [A: int,B: int,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( minus_minus_real @ ( number267125858f_real @ B ) ) @ C ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( number267125858f_real @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(819,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_886_diff__self__eq__0) ).
thf(4247,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(285,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1026_nat__mult__1__right) ).
thf(2146,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(336,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_gcd__lcm__complete__lattice__nat_Oless__top) ).
thf(2360,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) ) )
=> ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(729,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1169_zmult2__lemma__aux1) ).
thf(3848,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_971_mult__is__0) ).
thf(1705,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_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 @ ( times_times_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(184,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( hBOOL @ ( member_int @ B @ ( d22set @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_d22set__mem) ).
thf(1788,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( hBOOL @ ( member_int @ B @ ( d22set @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(568,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 @ 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_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_zcong__zless__imp__eq) ).
thf(3217,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 @ 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_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(815,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_381_power__strict__decreasing) ).
thf(4234,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)],[815]) ).
thf(1059,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_421_number__of__Bit0) ).
thf(5037,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)],[1059]) ).
thf(248,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ zero_zero_real ) @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2035,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ zero_zero_real ) @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1008,axiom,
~ ! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int )
!= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(4839,plain,
~ ! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int )
!= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(1022,axiom,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ t ) )
=> ? [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 ) ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(4884,plain,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ t ) )
=> ? [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 ) ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(429,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2740,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1093,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_eq__number__of__Pls__Min) ).
thf(5146,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(204,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 @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_mult__nonpos__nonneg) ).
thf(1872,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 @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(876,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_number__of__diff) ).
thf(4435,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(657,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_dvd__mult__right) ).
thf(3577,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(796,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 @ ( times_times_real @ ( number267125858f_real @ B ) ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_semiring__mult__number__of) ).
thf(4142,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 @ ( times_times_real @ ( number267125858f_real @ B ) ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(64,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_zero__le__square) ).
thf(1391,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(78,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_mult__neg__pos) ).
thf(1441,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(696,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_940_le__trans) ).
thf(3730,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)],[696]) ).
thf(1031,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 @ ( times_times_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_semiring__mult__number__of) ).
thf(4916,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 @ ( times_times_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(623,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ B @ A ) @ zero_zero_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_MultInv__prop3) ).
thf(3466,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ B @ A ) @ zero_zero_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(934,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_17_one__power2) ).
thf(4607,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)],[934]) ).
thf(347,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_1004_add__leD1) ).
thf(2400,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)],[347]) ).
thf(102,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_mult__strict__right__mono) ).
thf(1518,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1147,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_semiring__mult__2) ).
thf(5352,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(593,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_443_zero__le__power2) ).
thf(3350,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)],[593]) ).
thf(426,axiom,
! [A: nat] :
( ( A != one_one_nat )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_gcd__lcm__complete__lattice__nat_Obot__less) ).
thf(2723,plain,
! [A: nat] :
( ( ( A != one_one_nat )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) ) )
=> ( A != one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(437,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_75_zadd__strict__right__mono) ).
thf(2763,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)],[437]) ).
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 ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_add__leD2) ).
thf(1782,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)],[181]) ).
thf(387,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2548,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1188,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ one_one_int ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_inv__not__p__minus__1__aux) ).
thf(5486,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ one_one_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(640,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 @ zero_zero_int ) @ D ) )
=> ( ( 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 @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_777_mult__mono) ).
thf(3513,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 @ zero_zero_int ) @ D ) )
=> ( ( 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 @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(955,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_comm__semiring__class_Odistrib) ).
thf(4679,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(755,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_957_not__less0) ).
thf(3947,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)],[755]) ).
thf(790,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 ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_mult__right__mono__neg) ).
thf(4124,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 ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(795,axiom,
! [A: int,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
| ( A = one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_dvd__power) ).
thf(4137,plain,
! [A: int,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
| ( A = one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(168,axiom,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_mod__mod__is__mod) ).
thf(1724,plain,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(381,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2531,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(886,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 @ B ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_power__Suc__less) ).
thf(4467,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 @ B ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(13,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_367_power__mono) ).
thf(1228,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)],[13]) ).
thf(89,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_mult__strict__right__mono__neg) ).
thf(1482,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(721,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
& ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ zero_zero_int ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_zcong__zprime__prod__zero__contra) ).
thf(3820,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
& ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ zero_zero_int ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(68,axiom,
! [A: nat,B: real,C: nat,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_power__le__dvd) ).
thf(1409,plain,
! [A: nat,B: real,C: nat,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(764,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_300_power__le__imp__le__exp) ).
thf(3976,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)],[764]) ).
thf(920,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_478_sum__power2__le__zero__iff) ).
thf(4563,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)],[920]) ).
thf(417,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_nat__diff__add__eq1) ).
thf(2667,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(43,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 @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_real__mult__le__cancel__iff1) ).
thf(1323,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 @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_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 ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(316,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_self__quotient__aux1) ).
thf(2274,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(708,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_dvd_Oless__imp__le) ).
thf(3776,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(190,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_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(1826,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)],[190]) ).
thf(608,axiom,
! [A: real,B: real] :
( ( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_divisors__zero) ).
thf(3410,plain,
! [A: real,B: real] :
( ( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(717,axiom,
! [A: nat,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_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_330_dvd__power__same) ).
thf(3803,plain,
! [A: nat,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_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)],[717]) ).
thf(520,axiom,
! [A: fun_int_fun_int_bool,B: int,C: int] :
( ( hAPP_int_bool @ ( cOMBC_int_int_bool @ A @ B ) @ C )
= ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).
thf(3043,plain,
! [A: fun_int_fun_int_bool,B: int,C: int] :
( ( hAPP_int_bool @ ( cOMBC_int_int_bool @ A @ B ) @ C )
= ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1182,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ one_one_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(5461,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(560,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_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3195,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)],[560]) ).
thf(518,axiom,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1129_pow__divides__eq__nat) ).
thf(3029,plain,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(542,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_diff__less) ).
thf(3131,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1040,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ C @ A ) ) ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_MultInvPair__distinct) ).
thf(4956,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ C @ A ) ) ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(521,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_zcong__zero__equiv__div) ).
thf(3046,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(687,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_368_zero__less__power) ).
thf(3689,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)],[687]) ).
thf(435,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_nat__less__add__iff1) ).
thf(2755,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(633,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_mult__neg__pos) ).
thf(3495,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(982,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_prime__g__5) ).
thf(4761,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(526,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 @ C ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_int__le__induct) ).
thf(3061,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 @ C ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(46,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_432_less__special_I3_J) ).
thf(1330,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)],[46]) ).
thf(200,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ E ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_zcong__zmult__prop1) ).
thf(1860,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(22,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_494_power__strict__increasing__iff) ).
thf(1264,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)],[22]) ).
thf(40,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_dvdI) ).
thf(1313,plain,
! [A: real,B: real,C: real] :
( ( A
= ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,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 @ zero_zero_real ) @ 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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_mult__mono_H) ).
thf(1279,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 @ zero_zero_real ) @ 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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(852,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_919_dvd_Oeq__refl) ).
thf(4349,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(1103,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_rel__simps_I48_J) ).
thf(5182,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)],[1103]) ).
thf(728,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_963_plus__nat_Oadd__0) ).
thf(3845,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(533,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique) ).
thf(3089,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(431,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_475_sum__power2__ge__zero) ).
thf(2745,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)],[431]) ).
thf(394,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_dvd__antisym) ).
thf(2571,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(853,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_489_power__increasing) ).
thf(4353,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)],[853]) ).
thf(291,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I19_J) ).
thf(2169,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(938,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( minus_minus_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_diff__bin__simps_I7_J) ).
thf(4617,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( minus_minus_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(253,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_nat__le__add__iff2) ).
thf(2049,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(138,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1609,plain,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(66,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) )
=> ( ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_zero__less__mult__pos2) ).
thf(1398,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) )
=> ( ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1065,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_311_power__eq__0__iff) ).
thf(5052,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)],[1065]) ).
thf(824,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_937_le__refl) ).
thf(4265,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(506,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_mult__strict__right__mono__neg) ).
thf(2989,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(1113,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_semiring__norm_I110_J) ).
thf(5231,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(353,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) @ D ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ B ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_combine__common__factor) ).
thf(2420,plain,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) @ D ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ B ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1148,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_semiring__mult__2) ).
thf(5355,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(62,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_one__dvd) ).
thf(1379,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ one_one_real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(600,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_977_trans__less__add1) ).
thf(3385,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)],[600]) ).
thf(1120,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(5256,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1105,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) )
!= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_crossproduct__noteq) ).
thf(5193,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ( C != D )
& ( A != B ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) )
!= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ A ) ) ) )
& ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) )
!= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ A ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(439,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_68_less__int__code_I13_J) ).
thf(2767,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)],[439]) ).
thf(896,axiom,
! [A: int] :
( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
<=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1172_neq__one__mod__two) ).
thf(4492,plain,
! [A: int] :
( ( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ) )
& ( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(51,axiom,
! [A: real,B: real] :
( ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_order__le__neq__implies__less) ).
thf(1347,plain,
! [A: real,B: real] :
( ( 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)],[51]) ).
thf(123,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_zdiv__mono2__neg__lemma) ).
thf(1572,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(1186,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__mult__2__right) ).
thf(5480,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(826,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_zcong__shift) ).
thf(4270,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(745,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_40_zle__antisym) ).
thf(3902,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)],[745]) ).
thf(675,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_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(3657,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)],[675]) ).
thf(698,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_66_rel__simps_I34_J) ).
thf(3734,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)],[698]) ).
thf(377,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_dvd__mult) ).
thf(2520,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(150,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_83_rel__simps_I33_J) ).
thf(1641,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)],[150]) ).
thf(692,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_382_power__strict__decreasing) ).
thf(3708,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)],[692]) ).
thf(900,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(4507,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(866,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_39_zle__trans) ).
thf(4400,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)],[866]) ).
thf(1190,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_int @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ C ) ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_left__diff__distrib__number__of) ).
thf(5493,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_int @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ C ) ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( number_number_of_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(15,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_685_less__eq__real__def) ).
thf(1232,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)],[15]) ).
thf(821,axiom,
! [A: nat] :
~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_dvd_Oless__irrefl) ).
thf(4253,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1042,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= one_one_int )
<=> ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_zmult__eq__1__iff) ).
thf(4967,plain,
! [A: int,B: int] :
( ( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= one_one_int )
=> ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) )
& ( ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) )
=> ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(575,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(3268,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(573,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_one__neq__zero) ).
thf(3258,plain,
one_one_nat != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(980,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_16_one__power2) ).
thf(4756,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)],[980]) ).
thf(712,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_157_rel__simps_I21_J) ).
thf(3788,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)],[712]) ).
thf(35,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_691_real__add__left__mono) ).
thf(1302,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)],[35]) ).
thf(265,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 @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_mult__le__mono) ).
thf(2090,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 @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(147,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_dvd__mult__right) ).
thf(1632,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(680,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_dvd__reduce) ).
thf(3670,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(553,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) )
!= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_crossproduct__noteq) ).
thf(3163,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( C != D )
& ( A != B ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) )
!= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ A ) ) ) )
& ( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) )
!= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ A ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(361,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_rel__simps_I28_J) ).
thf(2451,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(968,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_219_power2__ge__self) ).
thf(4724,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)],[968]) ).
thf(786,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ 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 @ A ) @ B ) )
=> ( ( inv @ B @ ( inv @ B @ A ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_inv__inv) ).
thf(4115,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ 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 @ A ) @ B ) )
=> ( ( inv @ B @ ( inv @ B @ A ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1150,axiom,
! [A: nat] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= one_one_int )
| ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= ( number_number_of_int @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_neg__one__power) ).
thf(5360,plain,
! [A: nat] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= one_one_int )
| ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= ( number_number_of_int @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(801,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= A ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_mod__if) ).
thf(4162,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= A ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(875,axiom,
! [A: nat] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ A )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_power__one) ).
thf(4432,plain,
! [A: nat] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(362,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_dvd__mult__left) ).
thf(2456,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(239,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_355_add__0__iff) ).
thf(2007,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)],[239]) ).
thf(294,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_crossproduct__noteq) ).
thf(2178,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( C != D )
& ( A != B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) ) )
& ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(868,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_336_power__0__left) ).
thf(4411,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)],[868]) ).
thf(92,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_302_power__le__imp__le__exp) ).
thf(1489,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)],[92]) ).
thf(960,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(4696,plain,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(811,axiom,
! [A: int,B: nat,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ B ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_nat__number__of__mult__left) ).
thf(4205,plain,
! [A: int,B: nat,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ B ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(404,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_81_rel__simps_I5_J) ).
thf(2616,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)],[404]) ).
thf(220,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ D ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
<=> ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_crossproduct__eq) ).
thf(1946,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ D ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
=> ( ( A = C )
| ( B = D ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ D ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(864,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 @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_diff__le__mono2) ).
thf(4396,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 @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(329,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_add__numeral__0__right) ).
thf(2324,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(245,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 @ zero_zero_nat ) @ 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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_mult__mono_H) ).
thf(2027,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 @ zero_zero_nat ) @ 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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1074,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_four__x__squared) ).
thf(5084,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(923,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_power2__eq__square) ).
thf(4578,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(530,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_diff__is__0__eq) ).
thf(3075,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_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 @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(773,axiom,
! [A: real,B: nat,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ C )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(4072,plain,
! [A: real,B: nat,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ C )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_dvd_Oless__le) ).
thf(1811,plain,
! [A: nat,B: nat] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( A != B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(645,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_zcong__trans) ).
thf(3527,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(625,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 @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_mod__less__divisor) ).
thf(3473,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 @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(767,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ E ) )
=> ( ( 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 )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_convex__bound__lt) ).
thf(3983,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ E ) )
=> ( ( 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 )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(159,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_930_nat__add__left__cancel) ).
thf(1682,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)],[159]) ).
thf(1010,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ t ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(4847,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ t ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(644,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_363_zero__le__power) ).
thf(3525,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)],[644]) ).
thf(277,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_69_rel__simps_I14_J) ).
thf(2122,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)],[277]) ).
thf(191,axiom,
! [A: real,B: real,C: int] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( minus_minus_real @ A ) @ B ) ) @ ( number267125858f_real @ C ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ C ) ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_left__diff__distrib__number__of) ).
thf(1828,plain,
! [A: real,B: real,C: int] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( minus_minus_real @ A ) @ B ) ) @ ( number267125858f_real @ C ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ C ) ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(486,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_51_less__number__of) ).
thf(2925,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)],[486]) ).
thf(229,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_rel__simps_I3_J) ).
thf(1978,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(321,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_diff__add__0) ).
thf(2291,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(794,axiom,
! [A: real,B: nat,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_power__mult) ).
thf(4134,plain,
! [A: real,B: nat,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(654,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_255_number__of__Bit1) ).
thf(3569,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)],[654]) ).
thf(1134,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_rel__simps_I50_J) ).
thf(5311,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(1018,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_one__is__num__one) ).
thf(4871,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(749,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_921_dvd_Oless__le__not__le) ).
thf(3923,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(582,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) @ D ) )
=> ( ( ( ( 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 ) @ D ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ D ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ zero_zero_int ) ) ) ) )
=> ( ( B != zero_zero_int )
=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_divmod__int__rel__mod__eq) ).
thf(3290,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) @ D ) )
=> ( ( ( ( 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 ) @ D ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ D ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ zero_zero_int ) ) ) ) )
=> ( ( B != zero_zero_int )
=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(995,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) ) ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1134_neg__zmod__mult__2) ).
thf(4798,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) ) ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1121,axiom,
! [A: int] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_rel__simps_I42_J) ).
thf(5259,plain,
! [A: int] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(30,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ 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 @ B ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_mult__less__cancel__left__disj) ).
thf(1283,plain,
! [A: real,B: real,C: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ 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 @ B ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ 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 @ B ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1062,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_number__of__mult) ).
thf(5045,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(768,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_dvd__add) ).
thf(3986,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(528,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_dvd_Oord__eq__le__trans) ).
thf(3068,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(8,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_785_comm__mult__left__mono) ).
thf(1215,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(694,axiom,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
<=> ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_number__of__reorient) ).
thf(3712,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)],[694]) ).
thf(1080,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_246_add__number__of__left) ).
thf(5101,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)],[1080]) ).
thf(719,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_582_power__eq__0__iff__number__of) ).
thf(3808,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)],[719]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_le__add__diff__inverse) ).
thf(2002,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(962,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_248_add__number__of__eq) ).
thf(4701,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)],[962]) ).
thf(499,axiom,
! [A: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_not__square__less__zero) ).
thf(2965,plain,
! [A: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_dvd__trans) ).
thf(1600,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(599,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_592_power__0__left__number__of) ).
thf(3378,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)],[599]) ).
thf(1156,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__numeral__0) ).
thf(5379,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(699,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_zcong__scalar2) ).
thf(3739,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1078,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of) ).
thf(5096,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(611,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ~ ( hBOOL @ ( member_int @ A @ ( wset @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) @ B ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ C @ B ) ) )
=> ( ( A = C )
| ( A
= ( inv @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_wset__mem__imp__or) ).
thf(3421,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ~ ( hBOOL @ ( member_int @ A @ ( wset @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) @ B ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ C @ B ) ) )
=> ( ( A = C )
| ( A
= ( inv @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(637,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 @ dvd_dvd_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_315_le__imp__power__dvd) ).
thf(3505,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 @ dvd_dvd_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)],[637]) ).
thf(208,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_49_le__number__of__eq__not__less) ).
thf(1886,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)],[208]) ).
thf(899,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_253_Bit1__def) ).
thf(4504,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)],[899]) ).
thf(143,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_zcong__id) ).
thf(1622,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(778,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_790_mult__left__mono) ).
thf(4087,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(440,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_1064_number__of2) ).
thf(2772,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)],[440]) ).
thf(551,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ? [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_zprime__factor__exists) ).
thf(3157,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ? [B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(104,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_dvd__0__right) ).
thf(1526,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(682,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 @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_mult__less__cancel__left__pos) ).
thf(3676,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 @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ 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 @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(50,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_dvd__mult__right) ).
thf(1345,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(320,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_72_rel__simps_I31_J) ).
thf(2286,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)],[320]) ).
thf(409,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_966_less__eq__nat_Osimps_I1_J) ).
thf(2639,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)],[409]) ).
thf(271,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ zero_zero_real ) @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_mult__zero__left) ).
thf(2103,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ zero_zero_real ) @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(433,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_mult__strict__left__mono) ).
thf(2750,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(660,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_dvd_Oorder__trans) ).
thf(3588,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1025,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_145_zadd__assoc) ).
thf(4892,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)],[1025]) ).
thf(832,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_1002_add__le__mono) ).
thf(4285,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)],[832]) ).
thf(162,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
<=> ( ( A = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_nat__mult__dvd__cancel__disj) ).
thf(1696,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
=> ( ( A = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) )
& ( ( ( A = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(889,axiom,
! [A: int] :
( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ min ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_zmod__minus1__right) ).
thf(4475,plain,
! [A: int] :
( ( hAPP_int_int @ ( div_mod_int @ A ) @ ( number_number_of_int @ min ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(228,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_nat__less__add__iff2) ).
thf(1975,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(892,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ C @ A ) @ ( multInv @ C @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_MultInv__prop1) ).
thf(4483,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ C @ A ) @ ( multInv @ C @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(639,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_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(3510,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)],[639]) ).
thf(485,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_1059_number__of1) ).
thf(2922,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)],[485]) ).
thf(480,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_428_odd__less__0) ).
thf(2910,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)],[480]) ).
thf(365,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ zero_zero_int ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_zcong__zmult__prop3) ).
thf(2473,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ zero_zero_int ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(412,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ B ) @ A )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_le__mod__geq) ).
thf(2646,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ B ) @ A )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1176,axiom,
! [A: int,B: int,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(5443,plain,
! [A: int,B: int,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1069,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_286_semiring__one__add__one__is__two) ).
thf(5070,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)],[1069]) ).
thf(1130,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_493_power__inject__exp) ).
thf(5291,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)],[1130]) ).
thf(252,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_mult__pos__neg) ).
thf(2047,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(922,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_zprime__power__zdvd__cancel__left) ).
thf(4576,plain,
! [A: nat,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(410,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 @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_mod__le__divisor) ).
thf(2641,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 @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(683,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_mult__nonpos__nonneg) ).
thf(3679,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(201,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_820_comm__mult__strict__left__mono) ).
thf(1863,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(616,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) @ zero_zero_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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_q__neg__lemma) ).
thf(3435,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) @ zero_zero_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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(4,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_883_real__le__antisym) ).
thf(1206,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)],[4]) ).
thf(933,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_450_power2__eq__imp__eq) ).
thf(4604,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)],[933]) ).
thf(1052,axiom,
! [A: int] :
( ( ( bit1 @ A )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_rel__simps_I47_J) ).
thf(5012,plain,
! [A: int] :
( ( ( ( bit1 @ A )
= min )
=> ( A = min ) )
& ( ( A = min )
=> ( ( bit1 @ A )
= min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(636,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_zcong__zdiff) ).
thf(3503,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ B ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(583,axiom,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_mult__eq__if) ).
thf(3303,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(979,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( minus_minus_int @ ( number_number_of_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_add__number__of__diff1) ).
thf(4753,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( minus_minus_int @ ( number_number_of_int @ B ) ) @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(395,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_dvd_Oeq__iff) ).
thf(2574,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(695,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_divides__antisym) ).
thf(3720,plain,
! [A: nat,B: nat] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1165,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_semiring__norm_I113_J) ).
thf(5411,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(37,axiom,
! [A: nat,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_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_329_dvd__power__same) ).
thf(1306,plain,
! [A: nat,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_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)],[37]) ).
thf(909,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(4531,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(1174,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ D @ C ) ) ) @ C ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_aux______2) ).
thf(5438,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ D @ C ) ) ) @ C ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(558,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_nat__dvd__1__iff__1) ).
thf(3186,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(48,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_485_one__le__power) ).
thf(1338,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)],[48]) ).
thf(1091,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_447_power2__le__imp__le) ).
thf(5142,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)],[1091]) ).
thf(859,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_comm__semiring__class_Odistrib) ).
thf(4370,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(428,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_878_less__zeroE) ).
thf(2737,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)],[428]) ).
thf(405,axiom,
! [A: real,B: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ one_one_real ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2621,plain,
! [A: real,B: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ one_one_real ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(447,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_451_power2__less__0) ).
thf(2790,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)],[447]) ).
thf(479,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_73_less__number__of__int__code) ).
thf(2905,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)],[479]) ).
thf(340,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_974_not__add__less1) ).
thf(2382,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)],[340]) ).
thf(803,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 @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_neg__mod__conj) ).
thf(4172,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 @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(441,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2773,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1128,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_rel__simps_I44_J) ).
thf(5281,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1047,axiom,
( ( legendre @ ( number_number_of_int @ min ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(4999,plain,
( ( legendre @ ( number_number_of_int @ min ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(236,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( 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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ D ) ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1195_mod__lemma) ).
thf(2000,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( 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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ D ) ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(149,axiom,
! [A: int,B: int,C: int] :
( ( C != zero_zero_int )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_zdvd__mono) ).
thf(1636,plain,
! [A: int,B: int,C: int] :
( ( C != zero_zero_int )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1064,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(5049,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(574,axiom,
! [A: int,B: int] :
( ( ( standardRes @ A @ B )
= zero_zero_int )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1189_StandardRes__eq__zcong) ).
thf(3261,plain,
! [A: int,B: int] :
( ( ( ( standardRes @ A @ B )
= zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( ( standardRes @ A @ B )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(355,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 @ one_one_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_power__gt1__lemma) ).
thf(2428,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 @ one_one_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(453,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ one_one_real ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_real__mult__1) ).
thf(2805,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ one_one_real ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(309,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(2249,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(385,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_dvd__0__right) ).
thf(2541,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(736,axiom,
! [A: int,B: int,C: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_zcong__zmult__self) ).
thf(3867,plain,
! [A: int,B: int,C: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(9,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_mult__dvd__mono) ).
thf(1217,plain,
! [A: real,B: real,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(91,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 @ dvd_dvd_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_314_le__imp__power__dvd) ).
thf(1487,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 @ dvd_dvd_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)],[91]) ).
thf(1152,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( d22set @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( wset @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_d22set__eq__wset) ).
thf(5366,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( d22set @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( wset @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(142,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 @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_Int2_Ozcong__zero) ).
thf(1619,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 @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(564,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_960_add__eq__self__zero) ).
thf(3207,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)],[564]) ).
thf(580,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_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_sum__squares__ge__zero) ).
thf(3286,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_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1131_divides__le) ).
thf(1274,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1107,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_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 ) ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_diff__square) ).
thf(5206,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_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 ) ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(126,axiom,
! [A: int,B: fun_int_bool] :
( ! [C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_d22set__induct__old) ).
thf(1580,plain,
! [A: int,B: fun_int_bool] :
( ! [C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(317,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_zcong__zprime__prod__zero) ).
thf(2277,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1020,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_332_field__power__not__zero) ).
thf(4878,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)],[1020]) ).
thf(1195,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ D ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ B ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_combine__common__factor) ).
thf(5512,plain,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) @ D ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ B ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(935,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_mult__numeral__1) ).
thf(4609,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1045,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(4989,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1146,axiom,
! [A: int,B: int] :
( ( standardRes @ A @ B )
= ( hAPP_int_int @ ( div_mod_int @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_StandardRes__def) ).
thf(5349,plain,
! [A: int,B: int] :
( ( standardRes @ A @ B )
= ( hAPP_int_int @ ( div_mod_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(1180,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ A )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(5455,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ A )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(98,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_dvd__add) ).
thf(1502,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( plus_plus_real @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(850,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_mult__nonneg__nonpos2) ).
thf(4344,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(780,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_997_le__iff__add) ).
thf(4091,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)],[780]) ).
thf(990,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_power__less__power__Suc) ).
thf(4785,plain,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(897,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ B @ A ) ) @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_MultInv__prop2) ).
thf(4499,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ B @ A ) ) @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(247,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_928_nat__add__left__commute) ).
thf(2032,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)],[247]) ).
thf(1000,axiom,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ s1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(4821,plain,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ s1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(280,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_369_zero__less__power) ).
thf(2132,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)],[280]) ).
thf(1007,axiom,
! [A: real,B: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(4836,plain,
! [A: real,B: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(591,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 ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_diff__less__mono2) ).
thf(3339,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 ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(709,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_dvd_Ole__neq__trans) ).
thf(3778,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(367,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ zero_zero_int ) @ A ) )
=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_dvd__0__left) ).
thf(2477,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ zero_zero_int ) @ A ) )
=> ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(469,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_553_one__less__power) ).
thf(2872,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)],[469]) ).
thf(663,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_591_power__0__left__number__of) ).
thf(3600,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)],[663]) ).
thf(154,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_zdvd__zmod) ).
thf(1656,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(330,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_873_realpow__pos__nth__unique) ).
thf(2327,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)],[330]) ).
thf(29,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_mult__nonneg__nonpos) ).
thf(1281,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(213,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( ( inv @ B @ A )
!= zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_inv__not__0) ).
thf(1910,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( ( inv @ B @ A )
!= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(497,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_le__cube) ).
thf(2958,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(73,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) @ zero_zero_real ) )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_sum__squares__le__zero__iff) ).
thf(1423,plain,
! [A: real,B: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) @ 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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(576,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_rel__simps_I6_J) ).
thf(3271,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(359,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_448_power2__eq__imp__eq) ).
thf(2445,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)],[359]) ).
thf(835,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(4295,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(830,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_zero__neq__one) ).
thf(4280,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(436,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) )
<=> ( 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_1007_le__diff__conv) ).
thf(2758,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(766,axiom,
! [A: real,B: real,C: int] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( number267125858f_real @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ C ) ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_left__distrib__number__of) ).
thf(3980,plain,
! [A: real,B: real,C: int] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( number267125858f_real @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ C ) ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(135,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 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_less__diff__iff) ).
thf(1602,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 ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(57,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_370_zero__less__power) ).
thf(1365,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)],[57]) ).
thf(809,axiom,
! [A: real,B: real] :
( ( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_mult__eq__0__iff) ).
thf(4192,plain,
! [A: real,B: real] :
( ( ( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
| ( B = zero_zero_real ) )
=> ( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(418,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) @ zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_zmult2__lemma__aux2) ).
thf(2670,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) @ zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(606,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( 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 ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_zdvd__bounds) ).
thf(3403,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( 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 ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(391,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 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_le__add__diff) ).
thf(2565,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 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(561,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_422_number__of__Bit0) ).
thf(3198,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)],[561]) ).
thf(799,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_876_le0) ).
thf(4155,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)],[799]) ).
thf(585,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_490_power__increasing) ).
thf(3314,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)],[585]) ).
thf(527,axiom,
! [A: int,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( minus_minus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_right__diff__distrib__number__of) ).
thf(3065,plain,
! [A: int,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( minus_minus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(651,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( div_mod_int @ A ) @ C ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_zcong__zmod) ).
thf(3556,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( div_mod_int @ A ) @ C ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( div_mod_int @ A ) @ C ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(259,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_zmult__zless__mono2) ).
thf(2068,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(144,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
= ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1624,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
= ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(867,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_514_nat__zero__less__power__iff) ).
thf(4402,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)],[867]) ).
thf(193,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 @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ B ) )
<=> ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_dvd__mult__cancel2) ).
thf(1836,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 @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ B ) )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(333,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
<=> ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_mult__cancel1) ).
thf(2344,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) )
& ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(370,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_mult__0) ).
thf(2492,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(783,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_divisors__zero) ).
thf(4104,plain,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(148,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_wset__mem) ).
thf(1634,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(971,axiom,
! [A: int,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_power__even__eq) ).
thf(4732,plain,
! [A: int,B: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(303,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ 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 @ B ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_mult__less__cancel__left__disj) ).
thf(2228,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ 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 @ B ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ 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 @ B ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(1140,axiom,
( ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_int @ min ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(5330,plain,
( ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_int @ min ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(1196,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_162_less__special_I4_J) ).
thf(5515,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)],[1196]) ).
thf(111,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 @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_mult__neg__pos) ).
thf(1541,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 @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(231,axiom,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( ( zfact @ A )
= one_one_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( ( zfact @ A )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( zfact @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_zfact_Osimps) ).
thf(1983,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( ( zfact @ A )
= one_one_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( ( zfact @ A )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( zfact @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(725,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_mult__less__cancel__right__disj) ).
thf(3831,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(179,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_383_even__less__0__iff) ).
thf(1772,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)],[179]) ).
thf(734,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(3862,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(45,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_379_power__decreasing) ).
thf(1328,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)],[45]) ).
thf(502,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1041_mult__le__cancel1) ).
thf(2973,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_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_eq_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(225,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_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(1970,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)],[225]) ).
thf(466,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_dvd_Oless__imp__not__eq) ).
thf(2858,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1073,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_254_number__of__Bit1) ).
thf(5081,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)],[1073]) ).
thf(673,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( inv @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1079_inv__g__1) ).
thf(3650,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( inv @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1114,axiom,
! [A: int,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) @ zero_zero_int ) )
=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_even__power__le__0__imp__0) ).
thf(5233,plain,
! [A: int,B: nat] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) @ zero_zero_int ) )
=> ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(618,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_420_le__nat__number__of) ).
thf(3440,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)],[618]) ).
thf(510,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_1000_trans__le__add2) ).
thf(3001,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)],[510]) ).
thf(307,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_zprime__zdvd__zmult__better) ).
thf(2245,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(52,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 ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_mult__left__mono__neg) ).
thf(1350,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 ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(789,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_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(4123,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)],[789]) ).
thf(55,axiom,
! [A: real,B: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_not__sum__squares__lt__zero) ).
thf(1360,plain,
! [A: real,B: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(177,axiom,
! [A: int,B: int,C: nat] :
( ( C != zero_zero_nat )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_pow__divides__eq__int) ).
thf(1762,plain,
! [A: int,B: int,C: nat] :
( ( C != zero_zero_nat )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(609,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_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(3413,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)],[609]) ).
thf(338,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_zdvd__zdiffD) ).
thf(2377,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(1124,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_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(5270,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)],[1124]) ).
thf(951,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ B @ A ) ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_Int2_Oaux____1) ).
thf(4668,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ B @ A ) ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(902,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_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(4512,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)],[902]) ).
thf(1050,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat__mult__2) ).
thf(5006,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(992,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_semiring__numeral__1__eq__1) ).
thf(4789,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(913,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_452_power2__less__0) ).
thf(4544,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)],[913]) ).
thf(874,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_zmult__assoc) ).
thf(4429,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(943,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_29_add__special_I2_J) ).
thf(4636,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)],[943]) ).
thf(96,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_dvd__mult__left) ).
thf(1498,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(422,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_907_dvd_Oless__not__sym) ).
thf(2694,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(959,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_zmod__zmult1__eq) ).
thf(4693,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(374,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(2509,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(158,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_313_power__eq__0__iff) ).
thf(1672,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)],[158]) ).
thf(555,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_65_less__eq__int__code_I16_J) ).
thf(3176,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)],[555]) ).
thf(1027,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_480_not__sum__power2__lt__zero) ).
thf(4898,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)],[1027]) ).
thf(243,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_871_two__realpow__ge__one) ).
thf(2023,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)],[243]) ).
thf(1071,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(5075,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1043,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(4983,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(565,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_dvd__diffD) ).
thf(3210,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1082,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) )
= ( hAPP_int_int @ ( minus_minus_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_642_zspecial__product) ).
thf(5107,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) )
= ( hAPP_int_int @ ( minus_minus_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)],[1082]) ).
thf(83,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_364_zero__le__power) ).
thf(1461,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)],[83]) ).
thf(249,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_gcd__lcm__complete__lattice__nat_Otop__le) ).
thf(2038,plain,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1016,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_p0) ).
thf(4867,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(973,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_205_add__Bit0__Bit0) ).
thf(4736,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)],[973]) ).
thf(444,axiom,
! [A: real,B: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ B )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ one_one_real ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2781,plain,
! [A: real,B: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ B )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ one_one_real ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_dvd__add) ).
thf(1567,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(954,axiom,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_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_650_zdiff__power2) ).
thf(4676,plain,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_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)],[954]) ).
thf(94,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_mod__less__eq__dividend) ).
thf(1493,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(450,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_374_power__less__imp__less__base) ).
thf(2798,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)],[450]) ).
thf(846,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_one__neq__zero) ).
thf(4333,plain,
one_one_real != zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(757,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_152_rel__simps_I4_J) ).
thf(3954,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)],[757]) ).
thf(546,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_dvd__mult2) ).
thf(3141,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(584,axiom,
! [A: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ min ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_power__m1__even) ).
thf(3311,plain,
! [A: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ min ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1057,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_wset__inv__mem__mem) ).
thf(5031,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(547,axiom,
! [A: real,B: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_zero__le__even__power_H) ).
thf(3143,plain,
! [A: real,B: nat] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(224,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_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_1037_nat__0__less__mult__iff) ).
thf(1964,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_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 @ ( times_times_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(218,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_301_power__le__imp__le__exp) ).
thf(1942,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)],[218]) ).
thf(1191,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(5496,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(667,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_dvd_Oless__asym) ).
thf(3622,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(870,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_499_power__less__imp__less__exp) ).
thf(4421,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)],[870]) ).
thf(839,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ A )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(4315,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ A ) @ A )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1183,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
<=> ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_crossproduct__eq) ).
thf(5464,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( ( A = C )
| ( B = D ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(978,axiom,
! [A: int,B: int,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_power__mult__distrib) ).
thf(4750,plain,
! [A: int,B: int,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1143,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_mult__zero__right) ).
thf(5337,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1122,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_pos__zmult__eq__1__iff__lemma) ).
thf(5263,plain,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(70,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_472_power2__less__imp__less) ).
thf(1414,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)],[70]) ).
thf(296,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(2196,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(305,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_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2240,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)],[305]) ).
thf(194,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_979_add__less__mono1) ).
thf(1842,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)],[194]) ).
thf(976,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(4744,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(403,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_diff__add__inverse) ).
thf(2613,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1014,axiom,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ B ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(4861,plain,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ B ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(293,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( hAPP_real_real @ ( times_times_real @ A ) @ C )
= ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_real__mult__right__cancel) ).
thf(2172,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( ( hAPP_real_real @ ( times_times_real @ A ) @ C )
= ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_real_real @ ( times_times_real @ A ) @ C )
= ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(388,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_339_power__strict__mono) ).
thf(2551,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)],[388]) ).
thf(263,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_dvd__triv__right) ).
thf(2085,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(139,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_486_one__le__power) ).
thf(1612,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)],[139]) ).
thf(413,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_218_semiring__add__number__of) ).
thf(2649,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)],[413]) ).
thf(500,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_less__irrefl__nat) ).
thf(2968,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1125,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_476_sum__power2__ge__zero) ).
thf(5273,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)],[1125]) ).
thf(861,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( ( inv @ B @ A )
!= ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_inv__not__p__minus__1) ).
thf(4384,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( ( inv @ B @ A )
!= ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(463,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_add__mult__distrib) ).
thf(2845,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(706,axiom,
! [A: int,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_realpow__minus__mult) ).
thf(3770,plain,
! [A: int,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(306,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 @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_mult__less__mono1) ).
thf(2243,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 @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(818,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_number__of__diff) ).
thf(4244,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) )
= ( hAPP_real_real @ ( minus_minus_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(364,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_415_less__nat__number__of) ).
thf(2465,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)],[364]) ).
thf(1005,axiom,
! [A: int] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_rel__simps_I45_J) ).
thf(4829,plain,
! [A: int] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(186,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_768_nat__power__eq__0__iff) ).
thf(1799,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)],[186]) ).
thf(788,axiom,
! [A: int] :
( ( hAPP_int_int @ ( div_mod_int @ A ) @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_zmod__self) ).
thf(4120,plain,
! [A: int] :
( ( hAPP_int_int @ ( div_mod_int @ A ) @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(957,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_semiring__norm_I110_J) ).
thf(4689,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
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 @ dvd_dvd_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_316_le__imp__power__dvd) ).
thf(2272,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 @ dvd_dvd_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)],[315]) ).
thf(488,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_realpow__minus__mult) ).
thf(2932,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(129,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_786_comm__mult__left__mono) ).
thf(1588,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(383,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_diffs0__imp__equal) ).
thf(2536,plain,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_mod__mult__distrib) ).
thf(1297,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(649,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
<=> ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_mult__cancel2) ).
thf(3541,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
=> ( ( A = C )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = C )
| ( B = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1154,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_147_zadd__commute) ).
thf(5374,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)],[1154]) ).
thf(1094,axiom,
! [A: int] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__eq__square__number__of) ).
thf(5149,plain,
! [A: int] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(110,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 @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_zcong__not__zero) ).
thf(1539,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 @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(81,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 @ 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 @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_split__mult__pos__le) ).
thf(1456,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 @ 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 @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(478,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_169_le__special_I2_J) ).
thf(2900,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)],[478]) ).
thf(342,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_dvd__mult2) ).
thf(2387,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(192,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_150_rel__simps_I16_J) ).
thf(1831,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)],[192]) ).
thf(1036,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_sum__squares__eq__zero__iff) ).
thf(4934,plain,
! [A: int,B: int] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) )
= 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_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(372,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ D ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_crossproduct__eq) ).
thf(2497,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ D ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( ( A = C )
| ( B = D ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ D ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(814,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_941_le__antisym) ).
thf(4231,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)],[814]) ).
thf(197,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_diff__add__assoc) ).
thf(1852,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(669,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_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_769_divides__exp) ).
thf(3628,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_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)],[669]) ).
thf(205,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 @ B ) @ A ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_mod__pos__pos__trivial) ).
thf(1874,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 @ B ) @ A ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1132,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( bit1 @ A ) ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_mult__Bit1) ).
thf(5305,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( bit1 @ A ) ) @ B )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(703,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_divides__mul__r) ).
thf(3760,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(761,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_dvd_Oless__le__trans) ).
thf(3967,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(467,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_890_less__not__refl2) ).
thf(2862,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)],[467]) ).
thf(254,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_857_pos__add__strict) ).
thf(2052,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)],[254]) ).
thf(369,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_1061_imp__le__cong) ).
thf(2482,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)],[369]) ).
thf(17,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_mult__left__mono) ).
thf(1246,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(164,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_841_mult__pos__neg2) ).
thf(1715,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 @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1039,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_28_add__special_I2_J) ).
thf(4953,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)],[1039]) ).
thf(166,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( member_int @ B @ ( wset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_wset__mem__mem) ).
thf(1720,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( member_int @ B @ ( wset @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1153,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_166_le__special_I4_J) ).
thf(5369,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)],[1153]) ).
thf(823,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_dvd_Oantisym__conv) ).
thf(4259,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(562,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_153_rel__simps_I22_J) ).
thf(3201,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)],[562]) ).
thf(65,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_54_le__number__of) ).
thf(1393,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)],[65]) ).
thf(145,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ C @ B ) @ ( multInv @ C @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_MultInv__prop5) ).
thf(1627,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ C @ B ) @ ( multInv @ C @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(567,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_dvd_Oless__imp__not__less) ).
thf(3215,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1118,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_584_power__eq__0__iff__number__of) ).
thf(5245,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)],[1118]) ).
thf(1100,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_power3__eq__cube) ).
thf(5170,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(41,axiom,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ zero_zero_real ) @ A ) )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_dvd__0__left) ).
thf(1318,plain,
! [A: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ zero_zero_real ) @ A ) )
=> ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(571,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(3225,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(16,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_50_le__number__of__eq__not__less) ).
thf(1241,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)],[16]) ).
thf(989,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_pos__zmod__mult__2) ).
thf(4782,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1167,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_1108_int__gr__induct) ).
thf(5415,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)],[1167]) ).
thf(256,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_965_le__0__eq) ).
thf(2057,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)],[256]) ).
thf(726,axiom,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_dvd__triv__left) ).
thf(3841,plain,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1087,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= zero_zero_int )
<=> ? [C: int] :
( A
= ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_zmod__eq__0__iff) ).
thf(5126,plain,
! [A: int,B: int] :
( ( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= zero_zero_int )
=> ? [C: int] :
( A
= ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) )
& ( ? [C: int] :
( A
= ( hAPP_int_int @ ( times_times_int @ B ) @ C ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(681,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_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(3675,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)],[681]) ).
thf(921,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( minus_minus_int @ A ) @ B )
= C )
=> ( A
= ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_Int2_Oaux1) ).
thf(4572,plain,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( minus_minus_int @ A ) @ B )
= C )
=> ( A
= ( hAPP_int_int @ ( plus_plus_int @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(915,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_487_one__le__power) ).
thf(4550,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)],[915]) ).
thf(798,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_560_eq__number__of__0) ).
thf(4148,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)],[798]) ).
thf(75,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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_sum__squares__ge__zero) ).
thf(1434,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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(199,axiom,
! [A: real,B: real] :
( ( B != zero_zero_real )
=> ( ( A != zero_zero_real )
=> ( ( hAPP_real_real @ ( times_times_real @ B ) @ A )
!= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_no__zero__divisors) ).
thf(1857,plain,
! [A: real,B: real] :
( ( B != zero_zero_real )
=> ( ( A != zero_zero_real )
=> ( ( hAPP_real_real @ ( times_times_real @ B ) @ A )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(668,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ C ) @ ( hAPP_real_real @ ( times_times_real @ E ) @ A ) )
!= ( hAPP_real_real @ ( plus_plus_real @ D ) @ ( hAPP_real_real @ ( times_times_real @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_add__scale__eq__noteq) ).
thf(3624,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( hAPP_real_real @ ( plus_plus_real @ C ) @ ( hAPP_real_real @ ( times_times_real @ E ) @ A ) )
!= ( hAPP_real_real @ ( plus_plus_real @ D ) @ ( hAPP_real_real @ ( times_times_real @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1076,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_power__even__eq) ).
thf(5090,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(812,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_37_zless__le) ).
thf(4212,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)],[812]) ).
thf(1024,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(4889,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(557,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ C ) ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_zdiff__zmod__left) ).
thf(3183,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ C ) ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(472,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_number__of__Pls) ).
thf(2883,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(554,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_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3173,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)],[554]) ).
thf(85,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_52_less__number__of) ).
thf(1466,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)],[85]) ).
thf(348,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( 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 @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_zmult2__lemma__aux3) ).
thf(2402,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( 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 @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1168,axiom,
! [A: int] :
( ( bit0 @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Bit0__def) ).
thf(5419,plain,
! [A: int] :
( ( bit0 @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(481,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 @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_mult__le__mono2) ).
thf(2915,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 @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(448,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_980_add__less__mono) ).
thf(2793,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)],[448]) ).
thf(1108,axiom,
( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( number_number_of_int @ min ) ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) )
!= one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(5209,plain,
( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( number_number_of_int @ min ) ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) )
!= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(156,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_492_power__inject__exp) ).
thf(1663,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)],[156]) ).
thf(354,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_149_less__int__code_I15_J) ).
thf(2423,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)],[354]) ).
thf(380,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ C @ D ) ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ C @ D ) ) ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1075_aux______1) ).
thf(2529,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ C @ D ) ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ C @ D ) ) ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(676,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_diff__commute) ).
thf(3660,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1139,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_power3__eq__cube) ).
thf(5327,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(344,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_mod__geq) ).
thf(2391,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(222,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_mult__nonneg__nonpos) ).
thf(1959,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(396,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_zcong__eq__zdvd__prop) ).
thf(2585,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1063,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_int @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(5048,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_int @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(742,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_dvd__power__le) ).
thf(3888,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(578,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_961_add__is__0) ).
thf(3274,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)],[578]) ).
thf(686,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_zdiff__zmod__right) ).
thf(3686,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(690,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_976_nat__add__left__cancel__less) ).
thf(3696,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)],[690]) ).
thf(881,axiom,
( ( t = one_one_int )
=> ? [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 ) ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(4453,plain,
( ( t = one_one_int )
=> ? [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 ) ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(313,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_995_le__add2) ).
thf(2260,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)],[313]) ).
thf(1187,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ E ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_zdvd__period) ).
thf(5483,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ E ) ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ E ) ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1032,axiom,
! [A: real,B: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_power__even__eq) ).
thf(4919,plain,
! [A: real,B: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(596,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_36_zle__linear) ).
thf(3358,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)],[596]) ).
thf(286,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( ( B != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_divides__rev) ).
thf(2149,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( ( B != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(929,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_zprime__power__zdvd__cancel__right) ).
thf(4594,plain,
! [A: nat,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(10,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 @ ( hAPP_real_real @ ( minus_minus_real @ A ) @ B ) ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_real__le__eq__diff) ).
thf(1219,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 @ ( hAPP_real_real @ ( minus_minus_real @ A ) @ B ) ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( minus_minus_real @ A ) @ B ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(664,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_583_power__eq__0__iff__number__of) ).
thf(3607,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)],[664]) ).
thf(743,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_1030_add__gr__0) ).
thf(3890,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)],[743]) ).
thf(1127,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_int__0__neq__1) ).
thf(5278,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(877,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_zero__neq__one) ).
thf(4438,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(173,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 @ zero_zero_nat ) @ D ) )
=> ( ( 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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_mult__mono) ).
thf(1747,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 @ zero_zero_nat ) @ D ) )
=> ( ( 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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(60,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_340_power__strict__mono) ).
thf(1374,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)],[60]) ).
thf(931,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_semiring__numeral__0__eq__0) ).
thf(4599,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1037,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_rel__simps_I38_J) ).
thf(4943,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(601,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_add__scale__eq__noteq) ).
thf(3387,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(700,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_869_exp__eq__1) ).
thf(3741,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)],[700]) ).
thf(849,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_955_less__nat__zero__code) ).
thf(4341,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)],[849]) ).
thf(215,axiom,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_mult__nat__number__of) ).
thf(1916,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(490,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_939_eq__imp__le) ).
thf(2938,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)],[490]) ).
thf(1161,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_505_int__pos__lt__two__imp__zero__or__one) ).
thf(5395,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)],[1161]) ).
thf(1067,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_numeral__1__eq__1) ).
thf(5065,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1085,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_146_zadd__left__commute) ).
thf(5121,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)],[1085]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1132_mult__left__cancel) ).
thf(1652,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(281,axiom,
! [A: int,B: int,C: int] :
( ( A
= ( hAPP_int_int @ ( times_times_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_dvdI) ).
thf(2134,plain,
! [A: int,B: int,C: int] :
( ( A
= ( hAPP_int_int @ ( times_times_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1184,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_249_number__of__add) ).
thf(5474,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)],[1184]) ).
thf(302,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_962_Nat_Oadd__0__right) ).
thf(2225,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(831,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_mult__left__mono) ).
thf(4283,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(182,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 ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_pos__zmult__pos) ).
thf(1784,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 ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(295,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ( hAPP_int_int @ ( times_times_int @ B ) @ A )
= one_one_int )
<=> ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_pos__zmult__eq__1__iff) ).
thf(2188,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ( ( hAPP_int_int @ ( times_times_int @ B ) @ A )
= one_one_int )
=> ( ( B = one_one_int )
& ( A = one_one_int ) ) )
& ( ( ( B = one_one_int )
& ( A = one_one_int ) )
=> ( ( hAPP_int_int @ ( times_times_int @ B ) @ A )
= one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1068,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( minus_minus_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) )
= ( bit1 @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_diff__bin__simps_I9_J) ).
thf(5067,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( minus_minus_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) )
= ( bit1 @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(532,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_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 @ B ) @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_self__quotient__aux2) ).
thf(3086,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_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 @ B ) @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(175,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_989_less__or__eq__imp__le) ).
thf(1752,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)],[175]) ).
thf(579,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_diff__is__0__eq_H) ).
thf(3283,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(241,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_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(2016,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)],[241]) ).
thf(577,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ 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 ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_zero__less__mult__pos) ).
thf(3272,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ 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 ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(996,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_137_number__of__reorient) ).
thf(4801,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)],[996]) ).
thf(1079,axiom,
! [A: int,B: int,C: int] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_Euler_Oaux____1) ).
thf(5099,plain,
! [A: int,B: int,C: int] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(108,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 @ ( times_times_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_mult__pos__pos) ).
thf(1535,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 @ ( times_times_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(507,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_dvd__refl) ).
thf(2991,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(661,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3590,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(843,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 @ ( minus_minus_nat @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_less__imp__diff__less) ).
thf(4328,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 @ ( minus_minus_nat @ B ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(927,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ B @ A ) ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_Int2_Oaux____2) ).
thf(4590,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ B @ A ) ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(103,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_491_power__inject__exp) ).
thf(1520,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)],[103]) ).
thf(936,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_474_power2__less__imp__less) ).
thf(4612,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)],[936]) ).
thf(981,axiom,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ B ) ) @ C ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_neg__one__power__eq__mod__m) ).
thf(4758,plain,
! [A: nat,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ B ) ) @ C ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(12,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_mult__pos__neg) ).
thf(1226,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1054,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= zero_zero_int )
=> ? [C: int] :
( A
= ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_zmod__eq__0D) ).
thf(5022,plain,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= zero_zero_int )
=> ? [C: int] :
( A
= ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(570,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_rel__simps_I20_J) ).
thf(3223,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(893,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_power__0) ).
thf(4485,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(707,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_add__mult__distrib2) ).
thf(3773,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(246,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2029,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(589,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= A )
<=> ( C
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_le__imp__diff__is__add) ).
thf(3330,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= A )
=> ( C
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) )
& ( ( C
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(235,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1997,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(983,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_semiring__mult__2__right) ).
thf(4764,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(1104,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_mult__2) ).
thf(5190,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(710,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_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3783,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)],[710]) ).
thf(1178,axiom,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ min ) @ ( bit0 @ A ) )
= ( bit1 @ ( hAPP_int_int @ ( minus_minus_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_diff__bin__simps_I5_J) ).
thf(5449,plain,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ min ) @ ( bit0 @ A ) )
= ( bit1 @ ( hAPP_int_int @ ( minus_minus_int @ min ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1013,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_441_zero__eq__power2) ).
thf(4854,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)],[1013]) ).
thf(610,axiom,
! [A: int,B: fun_int_bool] :
( ( hBOOL @ ( member_int @ A @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_mem__def) ).
thf(3416,plain,
! [A: int,B: fun_int_bool] :
( ( ( hBOOL @ ( member_int @ A @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ B @ A ) )
=> ( hBOOL @ ( member_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1097,axiom,
hBOOL @ ( hAPP_int_bool @ zprime @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_p) ).
thf(5158,plain,
hBOOL @ ( hAPP_int_bool @ zprime @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(907,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_216_semiring__add__number__of) ).
thf(4526,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)],[907]) ).
thf(911,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ C ) @ ( hAPP_int_int @ ( times_times_int @ E ) @ A ) )
!= ( hAPP_int_int @ ( plus_plus_int @ D ) @ ( hAPP_int_int @ ( times_times_int @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq) ).
thf(4537,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( hAPP_int_int @ ( plus_plus_int @ C ) @ ( hAPP_int_int @ ( times_times_int @ E ) @ A ) )
!= ( hAPP_int_int @ ( plus_plus_int @ D ) @ ( hAPP_int_int @ ( times_times_int @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(714,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_power__le__dvd) ).
thf(3796,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(183,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( zfact @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) @ ( number_number_of_int @ min ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_Wilson__Russ) ).
thf(1786,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( zfact @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) @ ( number_number_of_int @ min ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(918,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_zmult__commute) ).
thf(4558,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(157,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ F ) @ D ) )
=> ( ( 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 @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_zdiv__mono2__lemma) ).
thf(1669,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ D ) @ E ) ) @ F ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ F ) @ D ) )
=> ( ( 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 @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1058,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_1107_int__ge__induct) ).
thf(5033,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)],[1058]) ).
thf(701,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_mult__strict__right__mono) ).
thf(3751,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(760,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(3964,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1084,axiom,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_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_465_power__add) ).
thf(5118,plain,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_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)],[1084]) ).
thf(1151,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) @ one_one_int ) ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) @ one_one_int ) )
= one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_Legendre__1mod4) ).
thf(5363,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) @ one_one_int ) ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) @ one_one_int ) )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(522,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_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(3051,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)],[522]) ).
thf(994,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( number_number_of_int @ min ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_zcong__neg__1__impl__ne__1) ).
thf(4796,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( number_number_of_int @ min ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(475,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_64_rel__simps_I17_J) ).
thf(2891,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)],[475]) ).
thf(25,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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_real__mult__le__cancel__iff2) ).
thf(1271,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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
=> ( 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 ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(326,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ zero_zero_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_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 @ zero_zero_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_mult__le__0__iff) ).
thf(2308,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ zero_zero_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_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 @ 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 @ 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 @ zero_zero_int ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(816,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 @ ( times_times_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_semiring__mult__number__of) ).
thf(4236,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 @ ( times_times_nat @ ( number_number_of_nat @ B ) ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(677,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ~ ( hBOOL @ ( member_int @ B @ ( d22set @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1113_d22set__le__swap) ).
thf(3663,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ~ ( hBOOL @ ( member_int @ B @ ( d22set @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(202,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_dvd_Oless__imp__neq) ).
thf(1865,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(489,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_diff__cancel2) ).
thf(2935,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1001,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_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(4822,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)],[1001]) ).
thf(666,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(3619,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(658,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( hAPP_real_real @ ( times_times_real @ C ) @ A )
= ( hAPP_real_real @ ( times_times_real @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_real__mult__left__cancel) ).
thf(3579,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( ( hAPP_real_real @ ( times_times_real @ C ) @ A )
= ( hAPP_real_real @ ( times_times_real @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_real_real @ ( times_times_real @ C ) @ A )
= ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1023,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_semiring__numeral__0__eq__0) ).
thf(4887,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(595,axiom,
! [A: real,B: real] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( minus_minus_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( minus_minus_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 ) ) ) ) ) ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_power2__diff) ).
thf(3355,plain,
! [A: real,B: real] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( minus_minus_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( minus_minus_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 ) ) ) ) ) ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(11,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 @ ( times_times_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_mult__nonneg__nonneg) ).
thf(1224,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 @ ( times_times_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(965,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_274_quartic__square__square) ).
thf(4716,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)],[965]) ).
thf(262,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 ) @ A ) )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_eq__diff__iff) ).
thf(2079,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 ) @ A ) )
=> ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(536,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_927_nat__add__commute) ).
thf(3101,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)],[536]) ).
thf(963,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 ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_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 @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) ).
thf(4704,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 ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_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 @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(550,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_858_pos__add__strict) ).
thf(3155,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)],[550]) ).
thf(650,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_zle__diff1__eq) ).
thf(3551,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( 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 @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(939,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add__numeral__0__right) ).
thf(4620,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(641,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_zcong__def) ).
thf(3515,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(961,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ C ) ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ B ) ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_MultInv__zcong__prop2) ).
thf(4699,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ C ) ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( multInv @ D @ B ) ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(324,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_956_neq0__conv) ).
thf(2299,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)],[324]) ).
thf(167,axiom,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_zcong__refl) ).
thf(1722,plain,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(461,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ one_one_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2839,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(837,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_77_add__nat__number__of) ).
thf(4300,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)],[837]) ).
thf(476,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_362_zero__le__power) ).
thf(2896,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)],[476]) ).
thf(986,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_rel__simps_I46_J) ).
thf(4773,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(5,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_dvd__trans) ).
thf(1209,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(594,axiom,
! [A: real,B: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_real__mult__commute) ).
thf(3352,plain,
! [A: real,B: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1109,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_482_sum__power2__gt__zero__iff) ).
thf(5212,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)],[1109]) ).
thf(1034,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_251_add__Bit1__Bit0) ).
thf(4929,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)],[1034]) ).
thf(1193,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ E ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ F ) ) ) @ G ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ E ) @ G ) ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_xzgcda__linear__aux1) ).
thf(5506,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ E ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ F ) ) ) @ G ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ E ) @ G ) ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(301,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_923_dvd_Ole__less) ).
thf(2214,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(406,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_nat__mult__assoc) ).
thf(2624,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(705,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ? [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 @ C ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ C ) @ B ) )
& ! [D: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ D ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ D ) @ B ) ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_zcong__zless__unique) ).
thf(3764,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ? [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 @ C ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ C ) @ B ) )
& ! [D: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ D ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ D ) @ B ) ) )
=> ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(505,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) )
=> ( ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_zero__less__mult__pos2) ).
thf(2987,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) )
=> ( ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1197,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_18_one__power2) ).
thf(5520,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)],[1197]) ).
thf(312,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_diff__add__inverse2) ).
thf(2257,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(697,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 @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_mult__le__mono1) ).
thf(3732,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 @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(319,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_554_one__less__power) ).
thf(2284,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)],[319]) ).
thf(1189,axiom,
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_t) ).
thf(5491,plain,
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(932,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right) ).
thf(4601,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(624,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_434_le__special_I1_J) ).
thf(3468,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)],[624]) ).
thf(693,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_le__square) ).
thf(3710,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1041,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_456_sum__power2__eq__zero__iff) ).
thf(4958,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)],[1041]) ).
thf(492,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 @ C ) @ 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 @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_zcong__not) ).
thf(2945,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 @ C ) @ 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 @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1077,axiom,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zpower__zpower) ).
thf(5093,plain,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1199,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ A @ B ) ) ) @ ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_mult__sum2sq) ).
thf(5531,plain,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ A @ B ) ) ) @ ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(465,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_dvd__diff) ).
thf(2856,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(452,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_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2802,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)],[452]) ).
thf(635,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_324_power__eq__imp__eq__base) ).
thf(3500,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)],[635]) ).
thf(545,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_325_power__eq__imp__eq__base) ).
thf(3138,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)],[545]) ).
thf(61,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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_mult__less__cancel__left__pos) ).
thf(1376,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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(77,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_mult__strict__left__mono__neg) ).
thf(1439,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(784,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ min ) ) @ A )
= ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_zmod__minus1) ).
thf(4107,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ min ) ) @ A )
= ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1123,axiom,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( A != zero_zero_int )
=> ( ( hAPP_int_int @ ( times_times_int @ B ) @ A )
!= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_no__zero__divisors) ).
thf(5267,plain,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( A != zero_zero_int )
=> ( ( hAPP_int_int @ ( times_times_int @ B ) @ A )
!= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(552,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_217_semiring__add__number__of) ).
thf(3160,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)],[552]) ).
thf(244,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_mult__dvd__mono) ).
thf(2025,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(912,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_arith__simps_I32_J) ).
thf(4541,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(543,axiom,
! [A: nat] :
~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less) ).
thf(3133,plain,
! [A: nat] :
~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(233,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_dvd__0__right) ).
thf(1993,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1142,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_287_semiring__one__add__one__is__two) ).
thf(5335,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)],[1142]) ).
thf(716,axiom,
! [A: real,B: nat,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_real_real @ ( times_times_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_464_power__add) ).
thf(3800,plain,
! [A: real,B: nat,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_real_real @ ( times_times_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)],[716]) ).
thf(829,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(4277,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ zero_zero_real ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(806,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_1001_add__le__mono1) ).
thf(4181,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)],[806]) ).
thf(845,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(4332,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(512,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_zero__neq__one) ).
thf(3006,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(63,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ 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 ) @ B ) ) )
| ( ( 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 @ B ) @ zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_zero__le__mult__iff) ).
thf(1381,plain,
! [A: real,B: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ 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 ) @ B ) ) )
| ( ( 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 @ B ) @ zero_zero_real ) ) ) ) )
& ( ( ( ( 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 ) ) )
| ( ( 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 @ B ) @ zero_zero_real ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(206,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_dvd__refl) ).
thf(1877,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(86,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_mult__right__mono) ).
thf(1471,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(279,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2129,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(679,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 @ ( hAPP_int_int @ ( div_mod_int @ B ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_zmod__le__nonneg__dividend) ).
thf(3668,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 @ ( hAPP_int_int @ ( div_mod_int @ B ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1006,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_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 ) ) ) ) ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__sum) ).
thf(4833,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_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 ) ) ) ) ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(884,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(4462,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(274,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 @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( C = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_zcong__less__eq) ).
thf(2111,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 @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( C = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(655,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_677_linorder__neqE__linordered__idom) ).
thf(3572,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)],[655]) ).
thf(880,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(4452,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(519,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_515_zero__less__power__nat__eq) ).
thf(3034,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)],[519]) ).
thf(1160,axiom,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ min ) @ ( bit1 @ A ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_diff__bin__simps_I6_J) ).
thf(5392,plain,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ min ) @ ( bit1 @ A ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ min ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1136,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_rel__simps_I39_J) ).
thf(5318,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(947,axiom,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_power__mult) ).
thf(4652,plain,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(470,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ zero_zero_int ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_IntPrimes_Ozcong__zero) ).
thf(2874,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ zero_zero_int ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(117,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_real__zero__not__eq__one) ).
thf(1556,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1102,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_semiring__numeral__1__eq__1) ).
thf(5180,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(969,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ one_one_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_zmult__1__right) ).
thf(4726,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(310,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_power__0) ).
thf(2252,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(416,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_power__commutes) ).
thf(2664,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(31,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_818_comm__mult__strict__left__mono) ).
thf(1293,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(389,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_559_less__0__number__of) ).
thf(2553,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)],[389]) ).
thf(549,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_436_le__special_I3_J) ).
thf(3150,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)],[549]) ).
thf(462,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_power__mult) ).
thf(2842,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1144,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_454_zero__less__power2) ).
thf(5340,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)],[1144]) ).
thf(1119,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_438_zero__power2) ).
thf(5254,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)],[1119]) ).
thf(300,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( 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 @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_zmult2__lemma__aux4) ).
thf(2212,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( 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 @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ D ) ) ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(438,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( inv @ B @ A ) ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_inv__less__p__minus__1) ).
thf(2765,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( inv @ B @ A ) ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(860,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_481_sum__power2__gt__zero__iff) ).
thf(4373,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)],[860]) ).
thf(282,axiom,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_zprime__zdvd__power) ).
thf(2139,plain,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(434,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( times_times_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_463_power__add) ).
thf(2752,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( times_times_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)],[434]) ).
thf(587,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( member_int @ A @ ( d22set @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_d22set__g__1) ).
thf(3325,plain,
! [A: int,B: int] :
( ( hBOOL @ ( member_int @ A @ ( d22set @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(270,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_dvd__triv__left) ).
thf(2101,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1163,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_164_less__special_I2_J) ).
thf(5403,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)],[1163]) ).
thf(1090,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(5139,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(352,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_zcong__zadd) ).
thf(2418,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( plus_plus_int @ C ) @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ B ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1009,axiom,
! [A: int,B: int] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_arith__simps_I32_J) ).
thf(4844,plain,
! [A: int,B: int] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(7,axiom,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_dvd__triv__right) ).
thf(1213,plain,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1155,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ C ) @ ( multInv @ D @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ ( multInv @ D @ B ) ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_MultInv__zcong__prop3) ).
thf(5377,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ C ) @ ( multInv @ D @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ ( multInv @ D @ B ) ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(80,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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) )
<=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_sum__squares__gt__zero__iff) ).
thf(1445,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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) )
=> ( ( 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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(105,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 @ A ) @ zero_zero_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 @ zero_zero_real ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_split__mult__neg__le) ).
thf(1528,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 @ A ) @ zero_zero_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 @ zero_zero_real ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(777,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_mult__dvd__mono) ).
thf(4085,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(257,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_zero__le__square) ).
thf(2064,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(337,axiom,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_power__eq__if) ).
thf(2369,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(857,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_74_less__eq__number__of__int__code) ).
thf(4362,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)],[857]) ).
thf(1004,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq) ).
thf(4827,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(1061,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ one_one_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(5042,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ one_one_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_dvd_Ole__less__trans) ).
thf(1726,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(19,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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_real__mult__less__mono2) ).
thf(1250,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 @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(740,axiom,
! [A: int,B: int,C: int] :
( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ C ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_zmod__eq__dvd__iff) ).
thf(3876,plain,
! [A: int,B: int,C: int] :
( ( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ C ) ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(161,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_mult__right__mono) ).
thf(1694,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(504,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(2984,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(227,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( 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 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_zdvd__imp__le) ).
thf(1973,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( 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 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(891,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_62_nat__1__add__1) ).
thf(4481,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)],[891]) ).
thf(631,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_479_not__sum__power2__lt__zero) ).
thf(3490,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)],[631]) ).
thf(119,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ one_one_real ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1562,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ one_one_real ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(238,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_rel__simps_I7_J) ).
thf(2005,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(255,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_569_order__le__neq__implies__less) ).
thf(2054,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)],[255]) ).
thf(187,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_gcd__lcm__complete__lattice__nat_Obot__least) ).
thf(1809,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1028,axiom,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ B ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_zdiff__power3) ).
thf(4901,plain,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ B ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( div_mod_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_mod__mult__distrib2) ).
thf(1203,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( div_mod_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1017,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(4868,plain,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1055,axiom,
! [A: int] :
( ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_power2__eq__square__number__of) ).
thf(5025,plain,
! [A: int] :
( ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(414,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(2652,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(972,axiom,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_s1) ).
thf(4735,plain,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(908,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ one_one_int @ ( number_number_of_int @ min ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_one__not__neg__one__mod__m) ).
thf(4529,plain,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ one_one_int @ ( number_number_of_int @ min ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(27,axiom,
! [A: nat,B: nat,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_dvd__power__le) ).
thf(1277,plain,
! [A: nat,B: nat,C: real,D: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(834,axiom,
! [A: int] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real ) ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0) ).
thf(4292,plain,
! [A: int] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ one_one_real ) @ one_one_real ) ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(232,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) )
=> ( ( A != zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_zdvd__mult__cancel) ).
thf(1990,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) )
=> ( ( A != zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(49,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_435_le__special_I3_J) ).
thf(1340,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)],[49]) ).
thf(854,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 @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_zprime__zdvd__zmult) ).
thf(4355,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 @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1044,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_power3__eq__cube) ).
thf(4986,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1173,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( bit0 @ A ) ) @ B )
= ( bit0 @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_mult__Bit0) ).
thf(5435,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( bit0 @ A ) ) @ B )
= ( bit0 @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(643,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3522,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(513,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_mult__less__cancel__left__neg) ).
thf(3009,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ zero_zero_int ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1030,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_669_realpow__two__sum__zero__iff) ).
thf(4907,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)],[1030]) ).
thf(456,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_999_trans__le__add1) ).
thf(2816,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)],[456]) ).
thf(127,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ one_one_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1583,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ one_one_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(878,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_158_zless__add1__eq) ).
thf(4441,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)],[878]) ).
thf(268,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_495_power__strict__increasing__iff) ).
thf(2096,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)],[268]) ).
thf(36,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_497_power__less__imp__less__exp) ).
thf(1304,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)],[36]) ).
thf(559,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_978_trans__less__add2) ).
thf(3193,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)],[559]) ).
thf(613,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_dvd_Oantisym) ).
thf(3427,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(327,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_dvd_Oless__trans) ).
thf(2318,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(445,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_comm__semiring__class_Odistrib) ).
thf(2784,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(882,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_rel__simps_I40_J) ).
thf(4456,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(563,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_bin__less__0__simps_I2_J) ).
thf(3206,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(399,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_mult__less__mono2) ).
thf(2597,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(924,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_zmod__simps_I3_J) ).
thf(4581,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1149,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_nat__number__of__Pls) ).
thf(5358,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1088,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 ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(5133,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 ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(967,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_numeral__1__eq__1) ).
thf(4722,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(847,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_981_less__add__eq__less) ).
thf(4336,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)],[847]) ).
thf(115,axiom,
! [A: int] :
( ( hAPP_int_int @ ( div_mod_int @ zero_zero_int ) @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_zmod__zero) ).
thf(1551,plain,
! [A: int] :
( ( hAPP_int_int @ ( div_mod_int @ zero_zero_int ) @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1179,axiom,
! [A: int,B: int,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ B ) ) @ C ) )
= ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__number__of__left) ).
thf(5452,plain,
! [A: int,B: int,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ B ) ) @ C ) )
= ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(602,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1187_mod__less) ).
thf(3391,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(223,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1961,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1015,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_power2__eq__square) ).
thf(4864,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1159,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_rel__simps_I49_J) ).
thf(5388,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(284,axiom,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_right__distrib__number__of) ).
thf(2143,plain,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1033,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
<=> ? [D: int] :
( B
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_zcong__iff__lin) ).
thf(4922,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ? [D: int] :
( B
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) ) )
& ( ? [D: int] :
( B
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(910,axiom,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ A ) @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_diff__bin__simps_I1_J) ).
thf(4534,plain,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ A ) @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(541,axiom,
! [A: nat,B: nat,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_dvd__power__le) ).
thf(3129,plain,
! [A: nat,B: nat,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(421,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
<=> ~ ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
| ? [D: nat] :
( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_nat__diff__split__asm) ).
thf(2678,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ~ ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
| ? [D: nat] :
( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) )
& ( ~ ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
| ? [D: nat] :
( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(738,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 @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1137_neg__mod__bound) ).
thf(3872,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 @ B ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(474,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 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_le__diff__conv2) ).
thf(2888,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 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
=> ( 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 @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(460,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_453_zero__less__power2) ).
thf(2831,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)],[460]) ).
thf(949,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_334_power__0__left) ).
thf(4658,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)],[949]) ).
thf(491,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_combine__common__factor) ).
thf(2942,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ D ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(1177,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_zdiff__zmult__distrib2) ).
thf(5446,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(769,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_473_power2__less__imp__less) ).
thf(3988,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)],[769]) ).
thf(392,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 @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_dvd__pos__nat) ).
thf(2567,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 @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(672,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_888_nat__less__cases) ).
thf(3640,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)],[672]) ).
thf(133,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 @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_mult__nonneg__nonneg) ).
thf(1598,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 @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(638,axiom,
! [A: int,B: fun_int_bool,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_incr__mult__lemma) ).
thf(3507,plain,
! [A: int,B: fun_int_bool,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( plus_plus_int @ D ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(856,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_378_power__decreasing) ).
thf(4360,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)],[856]) ).
thf(346,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2397,plain,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ D ) )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(827,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_987_less__imp__le__nat) ).
thf(4272,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)],[827]) ).
thf(67,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_686_real__less__def) ).
thf(1400,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)],[67]) ).
thf(531,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_872_realpow__pos__nth) ).
thf(3082,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)],[531]) ).
thf(953,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_cube__square) ).
thf(4673,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(136,axiom,
! [A: int,B: int,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_zpower__zdvd__prop1) ).
thf(1605,plain,
! [A: int,B: int,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1192,axiom,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ B ) ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) @ one_one_int ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ B ) ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ one_one_int ) ) @ ( number_number_of_int @ B ) ) ) ) @ one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1135_zmod__number__of__Bit1) ).
thf(5499,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ B ) ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) @ one_one_int ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ B ) ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ A ) ) @ one_one_int ) ) @ ( number_number_of_int @ B ) ) ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(1038,axiom,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(4950,plain,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(427,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_85_rel__simps_I15_J) ).
thf(2732,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)],[427]) ).
thf(20,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_mult__less__cancel__right__disj) ).
thf(1252,plain,
! [A: real,B: real,C: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(621,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 @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_power__less__power__Suc) ).
thf(3462,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 @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(904,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(4517,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ one_one_int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(572,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( div_mod_nat @ B ) @ C ) ) )
<=> ( ( ( C = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) )
& ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ C ) )
=> ( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1194_split__mod) ).
thf(3228,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( div_mod_nat @ B ) @ C ) ) )
=> ( ( ( C = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) )
& ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ C ) )
=> ( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ E ) ) ) ) ) ) )
& ( ( ( ( C = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) )
& ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ C ) )
=> ( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( div_mod_nat @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(833,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_rel__simps_I9_J) ).
thf(4287,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(887,axiom,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ pls ) @ ( bit1 @ A ) )
= ( bit1 @ ( hAPP_int_int @ ( minus_minus_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_diff__bin__simps_I4_J) ).
thf(4469,plain,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ pls ) @ ( bit1 @ A ) )
= ( bit1 @ ( hAPP_int_int @ ( minus_minus_int @ min ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(458,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_357_double__eq__0__iff) ).
thf(2821,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)],[458]) ).
thf(525,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 @ dvd_dvd_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_zdvd__antisym__nonneg) ).
thf(3058,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 @ dvd_dvd_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(350,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_516_zero__less__power__nat__eq__number__of) ).
thf(2407,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)],[350]) ).
thf(711,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_366_power__mono) ).
thf(3786,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)],[711]) ).
thf(23,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_dvd__mult2) ).
thf(1267,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(106,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_880_real__le__refl) ).
thf(1531,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(842,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_954_gr__implies__not0) ).
thf(4324,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)],[842]) ).
thf(941,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_rel__simps_I37_J) ).
thf(4630,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(14,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_376_power__less__imp__less__base) ).
thf(1230,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)],[14]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_divides__ge) ).
thf(1484,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(432,axiom,
! [A: int,B: fun_int_bool,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_decr__mult__lemma) ).
thf(2747,plain,
! [A: int,B: fun_int_bool,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(393,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_one__dvd) ).
thf(2569,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(185,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_nat__mult__eq__one) ).
thf(1790,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(203,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 @ A ) @ zero_zero_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 @ zero_zero_nat ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_split__mult__neg__le) ).
thf(1869,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 @ A ) @ zero_zero_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 @ zero_zero_nat ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(21,axiom,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_dvd__refl) ).
thf(1262,plain,
! [A: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(797,axiom,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add__numeral__0) ).
thf(4145,plain,
! [A: real] :
( ( hAPP_real_real @ ( plus_plus_real @ ( number267125858f_real @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(251,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_333_field__power__not__zero) ).
thf(2044,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)],[251]) ).
thf(1066,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_mult__2__right) ).
thf(5062,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(334,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_892_linorder__neqE__nat) ).
thf(2354,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)],[334]) ).
thf(1172,axiom,
~ ! [A: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(5431,plain,
~ ! [A: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(919,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_zero__is__num__zero) ).
thf(4561,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(851,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( ( inv @ B @ A )
!= one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_inv__not__1) ).
thf(4346,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( ( inv @ B @ A )
!= one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(865,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_mult__strict__left__mono) ).
thf(4398,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 @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(266,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_380_power__strict__decreasing) ).
thf(2092,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)],[266]) ).
thf(74,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_488_power__increasing) ).
thf(1432,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)],[74]) ).
thf(289,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_mult__strict__left__mono__neg) ).
thf(2165,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(34,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_mult__pos__neg2) ).
thf(1300,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(688,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_norR__mem__unique__aux) ).
thf(3691,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(626,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_377_power__decreasing) ).
thf(3475,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)],[626]) ).
thf(517,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ one_one_nat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(3026,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ one_one_nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(230,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_988_le__neq__implies__less) ).
thf(1980,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)],[230]) ).
thf(1106,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_252_add__Bit0__Bit1) ).
thf(5203,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)],[1106]) ).
thf(724,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) @ E ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_zcong__zmult__prop2) ).
thf(3828,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1095,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__Pls) ).
thf(5152,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(793,axiom,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_zpower__zdvd__prop2) ).
thf(4132,plain,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(155,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_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_less__bin__lemma) ).
thf(1658,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_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1048,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(5001,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(400,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_less__diff__conv) ).
thf(2599,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(171,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 @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_int__less__induct) ).
thf(1738,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 @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ! [D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( minus_minus_int @ D ) @ one_one_int ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(731,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_155_rel__simps_I32_J) ).
thf(3853,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)],[731]) ).
thf(632,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 @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_diff__le__mono) ).
thf(3493,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 @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(339,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 @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_nat__mult__less__cancel1) ).
thf(2379,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 @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_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 @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(894,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( minus_minus_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 @ ( minus_minus_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_add__diff__add) ).
thf(4488,plain,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( minus_minus_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 @ ( minus_minus_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(99,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( minus_minus_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_dvd__diff) ).
thf(1504,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( minus_minus_real @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(810,axiom,
! [A: nat,B: nat] :
( ( A
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_mult__eq__self__implies__10) ).
thf(4202,plain,
! [A: nat,B: nat] :
( ( A
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(59,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_dvd__mult) ).
thf(1372,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ B ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(141,axiom,
! [A: bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) )
=> ( hBOOL @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_902_dvd_Oless__imp__triv) ).
thf(1617,plain,
! [A: bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) )
=> ( hBOOL @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(420,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_real__mult__assoc) ).
thf(2675,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(308,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_517_nat__power__less__imp__less) ).
thf(2247,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)],[308]) ).
thf(112,axiom,
! [A: nat,B: nat,C: int] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( number_number_of_nat @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( number_number_of_nat @ C ) ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( number_number_of_nat @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_left__distrib__number__of) ).
thf(1543,plain,
! [A: nat,B: nat,C: int] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( number_number_of_nat @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( number_number_of_nat @ C ) ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( number_number_of_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(538,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_893_nat__neq__iff) ).
thf(3107,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)],[538]) ).
thf(211,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ 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 ) @ B ) ) )
| ( ( 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 @ B ) @ zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_zero__le__mult__iff) ).
thf(1898,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ 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 ) @ B ) ) )
| ( ( 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 @ B ) @ zero_zero_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_eq_int @ zero_zero_int ) @ B ) ) )
| ( ( 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 @ B ) @ zero_zero_int ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(196,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_power__0) ).
thf(1849,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(674,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_dvd_Oneq__le__trans) ).
thf(3652,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(390,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_931_nat__add__right__cancel) ).
thf(2558,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)],[390]) ).
thf(762,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_1111_ex__least__nat__le) ).
thf(3970,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)],[762]) ).
thf(1110,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_Pls__def) ).
thf(5223,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(540,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_rel__simps_I13_J) ).
thf(3124,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(386,axiom,
! [A: nat,B: nat,C: nat] :
( ( A
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_dvdI) ).
thf(2543,plain,
! [A: nat,B: nat,C: nat] :
( ( A
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(1116,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_Bit1__Min) ).
thf(5240,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(318,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_148_rel__simps_I12_J) ).
thf(2279,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)],[318]) ).
thf(901,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Bit0__Pls) ).
thf(4510,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(335,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_303_power__increasing__iff) ).
thf(2357,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)],[335]) ).
thf(424,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot) ).
thf(2711,plain,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
=> ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(100,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_882_real__le__trans) ).
thf(1506,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)],[100]) ).
thf(174,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_add__diff__assoc) ).
thf(1749,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1035,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(4932,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(539,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_354_add__0__iff) ).
thf(3117,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)],[539]) ).
thf(494,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_982_add__lessD1) ).
thf(2949,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)],[494]) ).
thf(825,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_diff__diff__right) ).
thf(4267,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(165,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_mult__zero__left) ).
thf(1717,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(642,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_502_power__strict__increasing) ).
thf(3520,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)],[642]) ).
thf(464,axiom,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_eq__number__of) ).
thf(2848,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)],[464]) ).
thf(999,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_285_semiring__one__add__one__is__two) ).
thf(4819,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)],[999]) ).
thf(685,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 @ B ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_power__Suc__less) ).
thf(3684,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 @ B ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(863,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_914_dvd_Oord__le__eq__trans) ).
thf(4392,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(581,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 @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_mult__strict__right__mono) ).
thf(3288,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 @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(946,axiom,
hBOOL @ ( hAPP_int_bool @ zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zprime__2) ).
thf(4651,plain,
hBOOL @ ( hAPP_int_bool @ zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(872,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(4424,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1012,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_zadd__zmult__distrib2) ).
thf(4851,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(457,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 ) @ A ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_Nat_Odiff__diff__eq) ).
thf(2818,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 ) @ A ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(985,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_zdiff__zmult__distrib) ).
thf(4770,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(473,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_953_gr0I) ).
thf(2885,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)],[473]) ).
thf(423,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
& ! [B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_zprime__def) ).
thf(2696,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
& ! [B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
& ! [B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(459,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(2828,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(498,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_63_less__int__code_I16_J) ).
thf(2960,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)],[498]) ).
thf(1141,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_divisors__zero) ).
thf(5332,plain,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(838,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_82_less__eq__int__code_I15_J) ).
thf(4310,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)],[838]) ).
thf(678,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_power__one__right) ).
thf(3665,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(662,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) )
= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_zdvd__iff__zmod__eq__0__number__of) ).
thf(3593,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) )
= zero_zero_int ) )
& ( ( ( hAPP_int_int @ ( div_mod_int @ ( number_number_of_int @ B ) ) @ ( number_number_of_int @ A ) )
= zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(357,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2435,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(944,axiom,
! [A: int,B: int] :
( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_mult__eq__0__iff) ).
thf(4639,plain,
! [A: int,B: int] :
( ( ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) )
& ( ( ( A = zero_zero_int )
| ( B = zero_zero_int ) )
=> ( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(72,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ 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 ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_zero__less__mult__pos) ).
thf(1421,plain,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ 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 ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(605,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 @ A ) @ zero_zero_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 @ zero_zero_int ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_split__mult__neg__le) ).
thf(3400,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 @ A ) @ zero_zero_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 @ zero_zero_int ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(620,axiom,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_Legendre__def) ).
thf(3452,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(363,axiom,
! [A: int,B: int] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
<=> ( ( standardRes @ B @ A )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1190_StandardRes__prop3) ).
thf(2458,plain,
! [A: int,B: int] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( standardRes @ B @ A )
!= zero_zero_int ) )
& ( ( ( standardRes @ B @ A )
!= zero_zero_int )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(82,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 @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_mult__nonpos__nonpos) ).
thf(1459,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 @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(926,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(4587,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1019,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_zdvd__reduce) ).
thf(4873,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(869,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_dvd__mult__left) ).
thf(4419,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(42,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 @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_mult__neg__neg) ).
thf(1321,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 @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(214,axiom,
! [A: real,B: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1913,plain,
! [A: real,B: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ B )
= ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(647,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_154_less__eq__int__code_I14_J) ).
thf(3533,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)],[647]) ).
thf(619,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_48_le__number__of__eq__not__less) ).
thf(3447,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)],[619]) ).
thf(195,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_165_less__special_I2_J) ).
thf(1844,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)],[195]) ).
thf(739,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I2_J) ).
thf(3874,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(775,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_rel__simps_I26_J) ).
thf(4078,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1133,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_power__one__right) ).
thf(5308,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(430,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ 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 @ zero_zero_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_q__pos__lemma) ).
thf(2743,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ 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 @ zero_zero_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(782,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_comm__mult__left__mono) ).
thf(4102,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 @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(483,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_375_power__less__imp__less__base) ).
thf(2919,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)],[483]) ).
thf(1086,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_439_zero__power2) ).
thf(5124,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)],[1086]) ).
thf(124,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_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1575,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)],[124]) ).
thf(524,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_938_nat__le__linear) ).
thf(3056,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)],[524]) ).
thf(411,axiom,
! [A: int,B: int] :
( ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_order__le__neq__implies__less) ).
thf(2643,plain,
! [A: int,B: int] :
( ( 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)],[411]) ).
thf(130,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_323_power__eq__imp__eq__base) ).
thf(1590,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)],[130]) ).
thf(44,axiom,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_power__gt1__lemma) ).
thf(1326,plain,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(290,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_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_838_zero__less__mult__pos) ).
thf(2167,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(343,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) @ B ) ) )
=> ( hBOOL @ ( member_int @ A @ ( wset @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_wset__subset) ).
thf(2389,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) @ B ) ) )
=> ( hBOOL @ ( member_int @ A @ ( wset @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(630,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1035_mult__less__cancel2) ).
thf(3484,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( 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 @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(723,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_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3825,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)],[723]) ).
thf(950,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_440_zero__power2) ).
thf(4666,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)],[950]) ).
thf(101,axiom,
! [A: real,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ zero_zero_real ) )
<=> ( ( ( 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 @ 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 @ zero_zero_real ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_mult__le__0__iff) ).
thf(1508,plain,
! [A: real,B: real] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ zero_zero_real ) )
=> ( ( ( 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 @ 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 @ 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 @ 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 @ zero_zero_real ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(820,axiom,
! [A: real,B: real,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(4250,plain,
! [A: real,B: real,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1170,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_405_odd__nonzero) ).
thf(5426,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)],[1170]) ).
thf(501,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_mult__pos__neg2) ).
thf(2971,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 @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(652,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_rel__simps_I11_J) ).
thf(3561,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(511,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_divides__cases) ).
thf(3003,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1075,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_right__diff__distrib__number__of) ).
thf(5087,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( minus_minus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1002,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_565_pos2) ).
thf(4823,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)],[1002]) ).
thf(351,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_498_power__less__imp__less__exp) ).
thf(2416,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)],[351]) ).
thf(345,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ A )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_power__one) ).
thf(2394,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(151,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) )
<=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_nat__eq__add__iff1) ).
thf(1646,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B )
= C ) )
& ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ B )
= C )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1135,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int ) ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_double__number__of__Bit0) ).
thf(5315,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int ) ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(964,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 ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) ).
thf(4710,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 ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ A ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(398,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_449_power2__eq__imp__eq) ).
thf(2594,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)],[398]) ).
thf(779,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 ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_mult__left__mono__neg) ).
thf(4089,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 ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1157,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( times_times_int @ C ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(5382,plain,
! [A: int,B: int,C: int,D: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) )
= ( hAPP_int_int @ ( times_times_int @ C ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(598,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_nat__1__eq__mult__iff) ).
thf(3369,plain,
! [A: nat,B: nat] :
( ( ( one_one_nat
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( one_one_nat
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(791,axiom,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_realpow__minus__mult) ).
thf(4126,plain,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ one_one_nat ) ) ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(569,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( A
!= ( inv @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_inv__distinct) ).
thf(3220,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) )
=> ( A
!= ( inv @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(455,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_rel__simps_I30_J) ).
thf(2811,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(993,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_168_le__special_I2_J) ).
thf(4791,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)],[993]) ).
thf(146,axiom,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( ( B != zero_zero_nat )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1130_pow__divides__pow__int) ).
thf(1629,plain,
! [A: int,B: nat,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( ( B != zero_zero_nat )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(537,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_diff__mult__distrib2) ).
thf(3104,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1112,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_mult__2) ).
thf(5228,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A )
= ( hAPP_int_int @ ( plus_plus_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(670,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique) ).
thf(3630,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(544,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 @ ( times_times_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_mult__nonneg__nonneg) ).
thf(3136,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 @ ( times_times_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1021,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_245_add__number__of__left) ).
thf(4881,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)],[1021]) ).
thf(1081,axiom,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(5104,plain,
! [A: int] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(287,axiom,
! [A: nat] :
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ A )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_power__one) ).
thf(2152,plain,
! [A: nat] :
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(314,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_312_power__eq__0__iff) ).
thf(2262,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)],[314]) ).
thf(93,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 @ B ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_power__Suc__less) ).
thf(1491,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 @ B ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(945,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( standardRes @ C @ A ) ) @ ( standardRes @ C @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_StandardRes__prop4) ).
thf(4649,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( standardRes @ C @ A ) ) @ ( standardRes @ C @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1099,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_rel__simps_I51_J) ).
thf(5162,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)],[1099]) ).
thf(1164,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 ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_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_7_zadd__power2) ).
thf(5408,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 ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_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)],[1164]) ).
thf(1060,axiom,
( ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ s @ one_one_int ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
thf(5040,plain,
( ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ s @ one_one_int ) )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(38,axiom,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_power__less__power__Suc) ).
thf(1308,plain,
! [A: nat,B: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(646,axiom,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) @ zero_zero_real ) )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_even__power__le__0__imp__0) ).
thf(3529,plain,
! [A: real,B: nat] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) @ zero_zero_real ) )
=> ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(713,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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_nat__mult__le__cancel1) ).
thf(3793,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 @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_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 @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(137,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 @ ( times_times_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_mult__pos__pos) ).
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 ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1070,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( minus_minus_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_diff__bin__simps_I10_J) ).
thf(5072,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( minus_minus_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1092,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ B @ A ) ) @ A ) @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_MultInv__prop2a) ).
thf(5144,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ B @ A ) ) @ A ) @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(781,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_1043_ex__least__nat__less) ).
thf(4098,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)],[781]) ).
thf(482,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 @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_zdvd__not__zless) ).
thf(2917,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 @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1614,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(160,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_zcong__sym) ).
thf(1689,plain,
! [A: int,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(765,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( 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 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_dvd__imp__le) ).
thf(3978,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( 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 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(556,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 @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_neg__mod__sign) ).
thf(3181,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 @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(366,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_divides__add__revr) ).
thf(2475,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(841,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_diff__0__eq__0) ).
thf(4321,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(250,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_929_nat__add__assoc) ).
thf(2041,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)],[250]) ).
thf(804,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_mult__zero__right) ).
thf(4175,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(634,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_le__add__diff__inverse2) ).
thf(3497,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(659,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(3585,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(614,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 @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_mult__right__mono) ).
thf(3430,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 @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(180,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_151_rel__simps_I10_J) ).
thf(1777,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)],[180]) ).
thf(862,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_80_rel__simps_I29_J) ).
thf(4387,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)],[862]) ).
thf(890,axiom,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_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_59_zpower__zadd__distrib) ).
thf(4478,plain,
! [A: int,B: nat,C: nat] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_int_int @ ( times_times_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)],[890]) ).
thf(258,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 @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_nat__dvd__not__less) ).
thf(2066,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 @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(210,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_429_less__special_I1_J) ).
thf(1893,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)],[210]) ).
thf(322,axiom,
! [A: int,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_right__distrib__number__of) ).
thf(2294,plain,
! [A: int,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( hAPP_real_real @ ( plus_plus_real @ B ) @ C ) )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(443,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 @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_Euler_Oaux2) ).
thf(2779,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 @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(242,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_889_less__not__refl3) ).
thf(2019,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)],[242]) ).
thf(487,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_unique__quotient__lemma__neg) ).
thf(2930,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(998,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_zadd__zmult__distrib) ).
thf(4816,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ C ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(772,axiom,
! [A: fun_int_bool,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) )
<=> ( ( ( C = zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ! [D: int,E: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ E ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ E ) @ C ) )
& ( B
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ zero_zero_int ) )
=> ! [D: int,E: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ E ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ zero_zero_int ) )
& ( B
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_split__zmod) ).
thf(3997,plain,
! [A: fun_int_bool,B: int,C: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) )
=> ( ( ( C = zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ! [D: int,E: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ E ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ E ) @ C ) )
& ( B
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ zero_zero_int ) )
=> ! [D: int,E: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ E ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ zero_zero_int ) )
& ( B
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ E ) ) ) ) ) )
& ( ( ( ( C = zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ! [D: int,E: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ E ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ E ) @ C ) )
& ( B
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ zero_zero_int ) )
=> ! [D: int,E: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ E ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ zero_zero_int ) )
& ( B
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ E ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(930,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ B )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(4596,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ B )
= ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ one_one_int ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1546,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(991,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ C ) ) @ C ) ) @ A ) @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ C ) ) @ B ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ D @ C ) ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_aux______4) ).
thf(4787,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ C ) ) @ C ) ) @ A ) @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ C ) ) @ B ) ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( multInv @ D @ C ) ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(88,axiom,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_dvd__triv__left) ).
thf(1480,plain,
! [A: real,B: real] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(771,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_84_less__int__code_I14_J) ).
thf(3992,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)],[771]) ).
thf(212,axiom,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_dvd__triv__right) ).
thf(1908,plain,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1051,axiom,
! [A: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_power__m1__even) ).
thf(5009,plain,
! [A: nat] :
( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(376,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_diff__mult__distrib) ).
thf(2517,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(125,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_555_one__less__power) ).
thf(1578,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)],[125]) ).
thf(888,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) )
= ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_number__of__mult) ).
thf(4472,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) )
= ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(341,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_semiring__numeral__0__eq__0) ).
thf(2385,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(733,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_365_power__mono) ).
thf(3860,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)],[733]) ).
thf(952,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_mult__numeral__1) ).
thf(4670,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(288,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_1062_conj__le__cong) ).
thf(2155,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)],[288]) ).
thf(382,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 @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_mult__neg__neg) ).
thf(2534,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 @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(311,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_zcong__scalar) ).
thf(2255,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(997,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_356_double__eq__0__iff) ).
thf(4809,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)],[997]) ).
thf(735,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 @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(3865,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 @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(822,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( ( standardRes @ C @ A )
= ( standardRes @ C @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_StandardRes__prop2) ).
thf(4254,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( ( ( standardRes @ C @ A )
= ( standardRes @ C @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( ( standardRes @ C @ A )
= ( standardRes @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(1049,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_32_one__add__one__is__two) ).
thf(5004,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)],[1049]) ).
thf(966,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_right__distrib__number__of) ).
thf(4719,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( hAPP_int_int @ ( plus_plus_int @ B ) @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ B ) ) @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(378,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_398_bin__less__0__simps_I4_J) ).
thf(2522,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)],[378]) ).
thf(1171,axiom,
hBOOL @ ( hAPP_int_bool @ ( quadRes @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(5430,plain,
hBOOL @ ( hAPP_int_bool @ ( quadRes @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( B != zero_zero_nat )
=> ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_no__zero__divisors) ).
thf(1593,plain,
! [A: nat,B: nat] :
( ( B != zero_zero_nat )
=> ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(622,axiom,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_zcong__1) ).
thf(3464,plain,
! [A: int,B: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(401,axiom,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_power__one__right) ).
thf(2604,plain,
! [A: real] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(495,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 ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_pos__mod__sign) ).
thf(2951,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 ) @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1072,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_zadd__0__right) ).
thf(5078,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(906,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_30_add__special_I3_J) ).
thf(4523,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)],[906]) ).
thf(1198,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_455_sum__power2__eq__zero__iff) ).
thf(5522,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)],[1198]) ).
thf(590,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
thf(3337,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(1185,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_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(5477,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)],[1185]) ).
thf(18,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_mult__nonpos__nonneg) ).
thf(1248,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ B ) @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(855,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 @ B ) @ A ) )
=> ( ( B
!= ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_Euler_Oaux1) ).
thf(4357,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 @ B ) @ A ) )
=> ( ( B
!= ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(895,axiom,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_s) ).
thf(4491,plain,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(176,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_163_less__special_I4_J) ).
thf(1757,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)],[176]) ).
thf(1162,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ A ) @ B ) )
<=> ? [C: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ C ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_QuadRes__def) ).
thf(5398,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ A ) @ B ) )
=> ? [C: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ C ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ A ) ) )
& ( ? [C: int] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ C ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(858,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_725_dvd__0__left) ).
thf(4367,plain,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat ) @ A ) )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(515,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) )
<=> ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_nat__eq__add__iff2) ).
thf(3015,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) )
=> ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) )
& ( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(76,axiom,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( minus_minus_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 @ ( minus_minus_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( minus_minus_real @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_add__diff__add) ).
thf(1436,plain,
! [A: real,B: real,C: real,D: real] :
( ( hAPP_real_real @ ( minus_minus_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 @ ( minus_minus_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( minus_minus_real @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(451,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_zcong__zmult) ).
thf(2800,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ C ) @ A ) @ ( hAPP_int_int @ ( times_times_int @ D ) @ B ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(56,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_mult__strict__left__mono) ).
thf(1363,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 @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(331,axiom,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zle__refl) ).
thf(2334,plain,
! [A: int] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1026,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_mult__numeral__1__right) ).
thf(4895,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(873,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).
thf(4427,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(628,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_dvd__diffD1) ).
thf(3479,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(349,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_975_not__add__less2) ).
thf(2404,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)],[349]) ).
thf(612,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) ) @ B )
= ( hAPP_nat_nat @ ( div_mod_nat @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_mod__mult__self3) ).
thf(3424,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C ) ) @ B )
= ( hAPP_nat_nat @ ( div_mod_nat @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(727,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_bin__less__0__simps_I1_J) ).
thf(3843,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1137,axiom,
! [A: int,B: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_zero__le__even__power_H) ).
thf(5322,plain,
! [A: int,B: nat] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(1138,axiom,
! [A: int,B: int,C: nat] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ C ) ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_zpower__zmod) ).
thf(5324,plain,
! [A: int,B: int,C: nat] :
( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ C ) ) @ B )
= ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(722,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_nat__diff__add__eq2) ).
thf(3822,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ E ) @ A ) ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ E ) @ D ) ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(548,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_156_rel__simps_I27_J) ).
thf(3145,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)],[548]) ).
thf(408,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2636,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(805,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_1109_mono__nat__linear__lb) ).
thf(4178,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)],[805]) ).
thf(588,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_dvd__trans) ).
thf(3328,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(744,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_426_int__one__le__iff__zero__less) ).
thf(3897,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)],[744]) ).
thf(298,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) @ zero_zero_int ) )
<=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_sum__squares__le__zero__iff) ).
thf(2201,plain,
! [A: int,B: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) @ 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_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(987,axiom,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_power__gt1__lemma) ).
thf(4777,plain,
! [A: nat,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1098,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_zadd__0) ).
thf(5159,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(95,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_676_linorder__neqE__linordered__idom) ).
thf(1495,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)],[95]) ).
thf(800,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_rel__simps_I25_J) ).
thf(4157,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(47,axiom,
! [A: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_not__square__less__zero) ).
thf(1335,plain,
! [A: real] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1053,axiom,
! [A: real,B: real] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_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 ) ) ) ) ) ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_power2__sum) ).
thf(5019,plain,
! [A: real,B: real] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_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 ) ) ) ) ) ) @ ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(776,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_divides__mul__l) ).
thf(4083,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(260,axiom,
! [A: int] :
( ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ A ) )
<=> ? [B: int,C: int] :
( ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ B @ C ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_is__sum2sq__def) ).
thf(2070,plain,
! [A: int] :
( ( ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ A ) )
=> ? [B: int,C: int] :
( ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ B @ C ) )
= A ) )
& ( ? [B: int,C: int] :
( ( twoSqu949963151sum2sq @ ( product_Pair_int_int @ B @ C ) )
= A )
=> ( hBOOL @ ( hAPP_int_bool @ twoSqu820444569sum2sq @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1166,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_wset__mem__inv__mem) ).
thf(5413,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(730,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_38_zless__linear) ).
thf(3850,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)],[730]) ).
thf(425,axiom,
! [A: real,B: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_sum__squares__eq__zero__iff) ).
thf(2714,plain,
! [A: real,B: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) )
= 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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(209,axiom,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ A ) ) @ A ) ) @ B ) @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ A ) ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1074_aux______3) ).
thf(1891,plain,
! [A: int,B: int,C: int,D: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ A ) ) @ A ) ) @ B ) @ ( hAPP_int_int @ ( times_times_int @ ( multInv @ D @ A ) ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(449,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 @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_nat__mult__dvd__cancel1) ).
thf(2795,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 @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(87,axiom,
! [A: real] :
( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_not__real__square__gt__zero) ).
thf(1473,plain,
! [A: real] :
( ( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1083,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_138_number__of__reorient) ).
thf(5110,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)],[1083]) ).
thf(718,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 @ 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 @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_split__mult__pos__le) ).
thf(3805,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 @ 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 @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1175,axiom,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ pls ) @ ( bit0 @ A ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_diff__bin__simps_I3_J) ).
thf(5440,plain,
! [A: int] :
( ( hAPP_int_int @ ( minus_minus_int @ pls ) @ ( bit0 @ A ) )
= ( bit0 @ ( hAPP_int_int @ ( minus_minus_int @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(840,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(4318,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
| ( A = one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_dvd__power) ).
thf(1742,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
| ( A = one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1126,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_times__numeral__code_I5_J) ).
thf(5275,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(53,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_430_less__special_I1_J) ).
thf(1352,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)],[53]) ).
thf(792,axiom,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_divides__exp2) ).
thf(4129,plain,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(763,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_power__dvd__imp__le) ).
thf(3974,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(597,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_477_sum__power2__le__zero__iff) ).
thf(3360,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)],[597]) ).
thf(54,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 @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_real__mult__less__iff1) ).
thf(1357,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 @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_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 @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(648,axiom,
! [A: int,B: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_not__sum__squares__lt__zero) ).
thf(3538,plain,
! [A: int,B: int] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(603,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( member_int @ A @ ( sr @ B ) ) )
=> ( ( standardRes @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1193_StandardRes__SR__prop) ).
thf(3394,plain,
! [A: int,B: int] :
( ( hBOOL @ ( member_int @ A @ ( sr @ B ) ) )
=> ( ( standardRes @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(958,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_444_zero__le__power2) ).
thf(4691,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)],[958]) ).
thf(898,axiom,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add__Pls__right) ).
thf(4501,plain,
! [A: int] :
( ( hAPP_int_int @ ( plus_plus_int @ A ) @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(748,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 @ ( zcong @ A @ B ) @ C ) )
<=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_zcong__zmod__eq) ).
thf(3918,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 @ ( zcong @ A @ B ) @ C ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ A ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) ) )
& ( ( ( hAPP_int_int @ ( div_mod_int @ A ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(813,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
<=> ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_nat__mult__eq__cancel__disj) ).
thf(4221,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
=> ( ( A = zero_zero_nat )
| ( B = C ) ) )
& ( ( ( A = zero_zero_nat )
| ( B = C ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(592,axiom,
! [A: real,B: real] :
( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_real__two__squares__add__zero__iff) ).
thf(3341,plain,
! [A: real,B: real] :
( ( ( ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) )
= 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_real_real @ ( times_times_real @ A ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(278,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 @ ( standardRes @ B @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1192_StandardRes__ubound) ).
thf(2127,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 @ ( standardRes @ B @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1011,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_one__neq__zero) ).
thf(4848,plain,
one_one_int != zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(356,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_71_less__eq__int__code_I13_J) ).
thf(2430,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)],[356]) ).
thf(691,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( C = A )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_dvd_Oord__less__eq__trans) ).
thf(3701,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( C = A )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(477,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_MultInv__prop4) ).
thf(2898,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(109,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_zcong__square) ).
thf(1537,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_int_int @ ( times_times_int @ A ) @ A ) @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( hAPP_int_int @ ( minus_minus_int @ B ) @ one_one_int ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(787,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_445_power2__le__imp__le) ).
thf(4118,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)],[787]) ).
thf(737,axiom,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_real__add__mult__distrib) ).
thf(3869,plain,
! [A: real,B: real,C: real] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_real_real @ ( plus_plus_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( plus_plus_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ C ) ) @ ( hAPP_real_real @ ( times_times_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(720,axiom,
! [A: real,B: real,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_power__mult__distrib) ).
thf(3817,plain,
! [A: real,B: real,C: nat] :
( ( hAPP_nat_real @ ( power_power_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ C )
= ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(97,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_mult__nonneg__nonpos2) ).
thf(1500,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 @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_real_real @ ( times_times_real @ A ) @ B ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(216,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
& ! [D: nat] :
( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_nat__diff__split) ).
thf(1923,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
& ! [D: nat] :
( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
& ! [D: nat] :
( ( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(817,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_400_bin__less__0__simps_I3_J) ).
thf(4239,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)],[817]) ).
thf(373,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_501_power__strict__increasing) ).
thf(2507,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)],[373]) ).
thf(844,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ E ) ) )
=> ( ( 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 @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ E ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_unique__quotient__lemma) ).
thf(4330,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) @ C ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ D ) ) @ E ) ) )
=> ( ( 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 @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ E ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(384,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_dvd_Oless__asym_H) ).
thf(2539,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(702,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_dvd_Oord__eq__less__trans) ).
thf(3753,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(925,axiom,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(4584,plain,
! [A: int,B: int] :
( ( hAPP_int_int @ ( times_times_int @ A ) @ B )
= ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(566,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_1005_add__leE) ).
thf(3212,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)],[566]) ).
thf(468,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_nat__mult__eq__cancel1) ).
thf(2866,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(914,axiom,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( minus_minus_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 ) ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_power2__diff) ).
thf(4547,plain,
! [A: int,B: int] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( minus_minus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( minus_minus_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 ) ) ) ) ) ) @ ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(71,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_384_even__less__0__iff) ).
thf(1416,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)],[71]) ).
thf(615,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 @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_zcong__zless__0) ).
thf(3432,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 @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(871,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_rel__simps_I24_J) ).
thf(4423,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(671,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_496_power__strict__increasing__iff) ).
thf(3637,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)],[671]) ).
thf(508,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_998_nat__add__left__cancel__le) ).
thf(2993,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)],[508]) ).
thf(948,axiom,
! [A: int,B: nat] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ A )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_power__commutes) ).
thf(4655,plain,
! [A: int,B: nat] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ A )
= ( hAPP_int_int @ ( times_times_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(419,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_Nat_Odiff__cancel) ).
thf(2672,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(617,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_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3437,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)],[617]) ).
thf(1096,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_247_add__number__of__eq) ).
thf(5155,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)],[1096]) ).
thf(756,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_1116_less__imp__add__positive) ).
thf(3950,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)],[756]) ).
thf(988,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ one_one_int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_zmult__1) ).
thf(4779,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ one_one_int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(905,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_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(4520,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)],[905]) ).
thf(828,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 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_le__diff__iff) ).
thf(4274,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 ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(328,axiom,
! [A: nat] :
~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot) ).
thf(2321,plain,
! [A: nat] :
~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(219,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_dvd__diff__nat) ).
thf(1944,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(58,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_433_le__special_I1_J) ).
thf(1367,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)],[58]) ).
thf(750,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_diff__add__assoc2) ).
thf(3924,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(471,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 @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1138_pos__mod__bound) ).
thf(2881,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 @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1181,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_212_plus__numeral__code_I9_J) ).
thf(5458,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)],[1181]) ).
thf(917,axiom,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_mult__2__right) ).
thf(4555,plain,
! [A: real] :
( ( hAPP_real_real @ ( times_times_real @ A ) @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_real_real @ ( plus_plus_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(534,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 @ ( div_mod_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(3096,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 @ ( div_mod_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(984,axiom,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ zero_zero_int ) @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(4767,plain,
! [A: int] :
( ( hAPP_int_int @ ( times_times_int @ zero_zero_int ) @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(607,axiom,
! [A: real,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
| ( A = one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_dvd__power) ).
thf(3405,plain,
! [A: real,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
| ( A = one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ dvd_dvd_real @ A ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(84,axiom,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_mult__less__cancel__left__neg) ).
thf(1463,plain,
! [A: real,B: real,C: real] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ zero_zero_real ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_real_real @ ( times_times_real @ C ) @ A ) ) @ ( hAPP_real_real @ ( times_times_real @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(509,axiom,
! [A: real,B: nat,C: nat] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2998,plain,
! [A: real,B: nat,C: nat] :
( ( hAPP_real_real @ ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(120,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_338_power__strict__mono) ).
thf(1565,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)],[120]) ).
thf(975,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_number__of__Pls) ).
thf(4742,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(323,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 @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_mult__nonpos__nonpos) ).
thf(2297,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 @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(358,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= zero_zero_nat )
<=> ? [C: nat] :
( A
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_mod__eq__0__iff) ).
thf(2438,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= zero_zero_nat )
=> ? [C: nat] :
( A
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) )
& ( ? [C: nat] :
( A
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( div_mod_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(304,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_dvd_Oorder__refl) ).
thf(2238,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(586,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_985_nat__less__le) ).
thf(3316,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)],[586]) ).
thf(292,axiom,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) )
=> ( ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_zero__less__mult__pos2) ).
thf(2170,plain,
! [A: int,B: int] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_int_int @ ( times_times_int @ A ) @ B ) ) )
=> ( ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2106,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(264,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 @ dvd_dvd_int @ C ) @ B ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_zmod__zdvd__zmod) ).
thf(2087,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 @ dvd_dvd_int @ C ) @ B ) )
=> ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( div_mod_int @ A ) @ B ) ) @ C )
= ( hAPP_int_int @ ( div_mod_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(753,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_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) )
<=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_sum__squares__gt__zero__iff) ).
thf(3933,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_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) )
=> ( ( 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_int_int @ ( times_times_int @ A ) @ A ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(883,axiom,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_number__of__is__id) ).
thf(4459,plain,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(503,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_dvd_Oless__imp__not__eq2) ).
thf(2980,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(656,axiom,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_wset__g__1) ).
thf(3575,plain,
! [A: int,B: int,C: int] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_int_int @ ( minus_minus_int @ C ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( member_int @ A @ ( wset @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(916,axiom,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_int @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ C ) ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_left__distrib__number__of) ).
thf(4552,plain,
! [A: int,B: int,C: int] :
( ( hAPP_int_int @ ( times_times_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_int @ C ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( times_times_int @ A ) @ ( number_number_of_int @ C ) ) ) @ ( hAPP_int_int @ ( times_times_int @ B ) @ ( number_number_of_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(836,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_semiring__norm_I112_J) ).
thf(4298,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(415,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_nat__mult__eq__1__iff) ).
thf(2655,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(5899,plain,
$false,
inference(cvc4,[status(thm)],[1586,3883,1823,5136,1767,3397,2787,2480,3927,4682,1295,5385,2199,3021,5509,4188,3962,1879,5422,2094,3944,1411,2306,3053,4450,4464,2336,2109,4824,1995,3930,4169,3798,1559,4729,1729,4183,2921,3477,3566,5028,1956,4992,1549,1554,4904,2512,4339,4075,3858,2495,5242,2527,3012,2099,4623,5348,1855,1200,2077,3681,1211,3990,3072,2210,2117,1596,5225,2808,3905,3762,4515,1443,2776,2953,2590,5297,2947,1569,1939,3959,3912,3098,2014,5173,2114,1269,1971,4614,1533,5237,4747,4592,4633,1655,4739,2607,1310,5288,4110,2448,2141,3616,3693,2627,3481,4247,2146,2360,3848,1705,1788,3217,4234,5037,2035,4839,4884,2740,5146,1872,4435,3577,4142,1391,1441,3730,4916,3466,4607,2400,1518,5352,3350,2723,2763,1782,2548,5486,3513,4679,3947,4124,4137,1724,2531,4467,1228,1482,3820,1409,3976,4563,2667,1323,2274,3776,1826,3410,3803,3043,5461,3195,3029,3131,4956,3046,3689,2755,3495,4761,3061,1330,1860,1264,1313,1279,4349,5182,3845,3089,2745,2571,4353,2169,4617,2049,1609,1398,5052,4265,2989,5231,2420,5355,1379,3385,5256,5193,2767,4492,1347,1572,5480,4270,3902,3657,3734,2520,1641,3708,4507,4400,5493,1232,4253,4967,3268,3258,4756,3788,1302,2090,1632,3670,3163,2451,4724,4115,5360,4162,4432,2456,2007,2178,4411,1489,4696,4205,2616,1946,4396,2324,2027,5084,4578,3075,4072,1811,3527,3473,3983,1682,4847,3525,2122,1828,2925,1978,2291,4134,3569,5311,4871,3923,3290,4798,5259,1283,5045,3986,3068,1215,3712,5101,3808,2002,4701,2965,1600,3378,5379,3739,5096,3421,3505,1886,4504,1622,4087,2772,3157,1526,3676,1345,2286,2639,2103,2750,3588,4892,4285,1696,4475,1975,4483,3510,2922,2910,2473,2646,5443,5070,5291,2047,4576,2641,3679,1863,3435,1206,4604,5012,3503,3303,4753,2574,3720,5411,1306,4531,5438,3186,1338,5142,4370,2737,2621,2790,2905,2382,4172,2773,5281,4999,2000,1636,5049,3261,2428,2805,2249,2541,3867,1217,1487,5366,1619,3207,3286,1274,5206,1580,2277,4878,5512,4609,4989,5349,5455,1502,4344,4091,4785,4499,2032,4821,2132,4836,3339,3778,2477,2872,3600,1656,2327,1281,1910,2958,1423,3271,2445,4295,4280,2758,3980,1602,1365,4192,2670,3403,2565,3198,4155,3314,3065,3556,2068,1624,4402,1836,2344,2492,4104,1634,4732,2228,5330,5515,1541,1983,3831,1772,3862,1328,2973,1970,2858,5081,3650,5233,3440,3001,2245,1350,4123,1360,1762,3413,2377,5270,4668,4512,5006,4789,4544,4429,4636,1498,2694,4693,2509,1672,3176,4898,2023,5075,4983,3210,5107,1461,2038,4867,4736,2781,1567,4676,1493,2798,4333,3954,3141,3311,5031,3143,1964,1942,5496,3622,4421,4315,5464,4750,5337,5263,1414,2196,2240,1842,4744,2613,4861,2172,2551,2085,1612,2649,2968,5273,4384,2845,3770,2243,4244,2465,4829,1799,4120,4689,2272,2932,1588,2536,1297,3541,5374,5149,1539,1456,2900,2387,1831,4934,2497,4231,1852,3628,1874,5305,3760,3967,2862,2052,2482,1246,1715,4953,1720,5369,4259,3201,1393,1627,3215,5245,5170,1318,3225,1241,4782,5415,2057,3841,5126,3675,4572,4550,4148,1434,1857,3624,5090,4212,4889,3183,2883,3173,1466,2402,5419,2915,2793,5209,1663,2423,2529,3660,5327,2391,1959,2585,5048,3888,3274,3686,3696,4453,2260,5483,4919,3358,2149,4594,1219,3607,3890,5278,4438,1747,1374,4599,4943,3387,3741,4341,1916,2938,5395,5065,5121,1652,2134,5474,2225,4283,1784,2188,5067,3086,1752,3283,2016,3272,4801,5099,1535,2991,3590,4328,4590,1520,4612,4758,1226,5022,3223,4485,3773,2029,3330,1997,4764,5190,3783,5449,4854,3416,5158,4526,4537,3796,1786,4558,1669,5033,3751,3964,5118,5363,3051,4796,2891,1271,2308,4236,3663,1865,2935,4822,3619,3579,4887,3355,1224,4716,2079,3101,4704,3155,3551,4620,3515,4699,2299,1722,2839,4300,2896,4773,1209,3352,5212,4929,5506,2214,2624,3764,2987,5520,2257,3732,2284,5491,4601,3468,3710,4958,2945,5093,5531,2856,2802,3500,3138,1376,1439,4107,5267,3160,2025,4541,3133,1993,5335,3800,4277,4181,4332,3006,1381,1877,1471,2129,3668,4833,4462,2111,3572,4452,3034,5392,5318,4652,2874,1556,5180,4726,2252,2664,1293,2553,3150,2842,5340,5254,2212,2765,4373,2139,2752,3325,2101,5403,5139,2418,4844,1213,5377,1445,1528,4085,2064,2369,4362,4827,5042,1726,1250,3876,1694,2984,1973,4481,3490,1562,2005,2054,1809,4901,1203,4868,5025,2652,4735,4529,1277,4292,1990,1340,4355,4986,5435,3522,3009,4907,2816,1583,4441,2096,1304,3193,3427,2318,2784,4456,3206,2597,4581,5358,5133,4722,4336,1551,5452,3391,1961,4864,5388,2143,4922,4534,3129,2678,3872,2888,2831,4658,2942,5446,3988,2567,3640,1598,3507,4360,2397,4272,1400,3082,4673,1605,5499,4950,2732,1252,3462,4517,3228,4287,4469,2821,3058,2407,3786,1267,1531,4324,4630,1230,1484,2747,2569,1790,1869,1262,4145,2044,5062,2354,5431,4561,4346,4398,2092,1432,2165,1300,3691,3475,3026,1980,5203,3828,5152,4132,1658,5001,2599,1738,3853,3493,2379,4488,1504,4202,1372,1617,2675,2247,1543,3107,1898,1849,3652,2558,3970,5223,3124,2543,5240,2279,4510,2357,2711,1506,1749,4932,3117,2949,4267,1717,3520,2848,4819,3684,4392,3288,4651,4424,4851,2818,4770,2885,2696,2828,2960,5332,4310,3665,3593,2435,4639,1421,3400,3452,2458,1459,4587,4873,4419,1321,1913,3533,3447,1844,3874,4078,5308,2743,4102,2919,5124,1575,3056,2643,1590,1326,2167,2389,3484,3825,4666,1508,4250,5426,2971,3561,3003,5087,4823,2416,2394,1646,5315,4710,2594,4089,5382,3369,4126,3220,2811,4791,1629,3104,5228,3630,3136,4881,5104,2152,2262,1491,4649,5162,5408,5040,1308,3529,3793,1607,5072,5144,4098,2917,1614,1689,3978,3181,2475,4321,2041,4175,3497,3585,3430,1777,4387,4478,2066,1893,2294,2779,2019,2930,4816,3997,4596,1546,4787,1480,3992,1908,5009,2517,1578,4472,2385,3860,4670,2155,2534,2255,4809,3865,4254,5004,4719,2522,5430,1593,3464,2604,2951,5078,4523,5522,3337,5477,1248,4357,4491,1757,5398,4367,3015,1436,2800,1363,2334,4895,4427,3479,2404,3424,3843,5322,5324,3822,3145,2636,4178,3328,3897,2201,4777,5159,1495,4157,1335,5019,4083,2070,5413,3850,2714,1891,2795,1473,5110,3805,5440,4318,1742,5275,1352,4129,3974,3360,1357,3538,3394,4691,4501,3918,4221,3341,2127,4848,2430,3701,2898,1537,4118,3869,3817,1500,1923,4239,2507,4330,2539,3753,4584,3212,2866,4547,1416,3432,4423,3637,2993,4655,2672,3437,5155,3950,4779,4520,4274,2321,1944,1367,3924,2881,5458,4555,3096,4767,3405,1463,2998,1565,4742,2297,2438,2238,3316,2170,2106,2087,3933,4459,2980,3575,4552,4298,2655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM926_3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 17:44:35 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.90/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.14/1.15 % [INFO] Parsing done (311ms).
% 2.14/1.16 % [INFO] Running in sequential loop mode.
% 2.62/1.36 % [INFO] eprover registered as external prover.
% 2.62/1.36 % [INFO] cvc4 registered as external prover.
% 2.62/1.37 % [INFO] Scanning for conjecture ...
% 3.33/1.55 % [INFO] Found a conjecture and 1204 axioms. Running axiom selection ...
% 4.29/1.77 % [INFO] Axiom selection finished. Selected 1197 axioms (removed 7 axioms).
% 5.55/2.16 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.55/2.19 % [INFO] Type checking passed.
% 5.55/2.19 % [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 ...
% 25.02/7.01 % External prover 'cvc4' found a proof!
% 25.02/7.01 % [INFO] Killing All external provers ...
% 25.02/7.01 % Time passed: 6492ms (effective reasoning time: 5846ms)
% 25.02/7.01 % 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)>
% 25.04/7.02 % Axioms used in derivation (1197): fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_822_mult__strict__left__mono, fact_269_double__number__of__Bit0, fact_865_real__mult__less__mono2, fact_925_dvd_Oless__irrefl, fact_547_nat__number__of__Pls, fact_999_trans__le__add1, fact_946_eq__diff__iff, fact_78_nat__numeral__1__eq__1, fact_327_zdvd__antisym__nonneg, fact_1168_zmult2__lemma__aux4, fact_997_le__iff__add, fact_47_zpower__zpower, fact_505_int__pos__lt__two__imp__zero__or__one, fact_959_zero__less__diff, fact_559_less__0__number__of, fact_325_power__eq__imp__eq__base, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_1039_dvd__imp__le, fact_598_unique__quotient__lemma__neg, fact_613_number__of__diff, fact_846_mult__pos__pos, fact_454_zero__less__power2, fact_88_zle__add1__eq__le, fact_439_zero__power2, fact_770_split__mult__neg__le, fact_740_mult__dvd__mono, fact_118_mem__def, fact_7_zadd__power2, fact_434_le__special_I1_J, fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_528_rel__simps_I13_J, fact_457_power__commutes, fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_742_dvd__mult, fact_753_dvd__add, fact_1178_mod__less__divisor, fact_296_power__less__power__Suc, fact_329_dvd__power__same, fact_214_semiring__mult__number__of, fact_884_diff__0__eq__0, fact_772_split__mult__neg__le, fact_287_semiring__one__add__one__is__two, fact_763_divides__add__revr, fact_1005_add__leE, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_321_power__le__dvd, fact_136_eq__number__of, fact_152_rel__simps_I4_J, fact_766_nat__mult__eq__one, fact_368_zero__less__power, fact_1117_pow__divides__eq__int, fact_162_less__special_I4_J, fact_678_dvd__refl, fact_1145_zcong__zmod, fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_278_mult__2, fact_928_nat__add__left__commute, fact_139_number__of__reorient, fact_248_add__number__of__eq, fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_395_semiring__numeral__0__eq__0, fact_757_one__dvd, fact_564_zcong__trans, fact_702_no__zero__divisors, fact_799_mult__nonneg__nonpos2, fact_74_less__eq__number__of__int__code, fact_754_dvd__add, fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_201_mult__Pls, fact_363_zero__le__power, fact_164_less__special_I2_J, fact_257_mult__numeral__1, fact_733_dvd__mult__left, fact_365_power__mono, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_355_add__0__iff, fact_393_number__of__Pls, fact_135_eq__number__of, fact_283_mult__2__right, fact_478_sum__power2__le__zero__iff, fact_657_zprime__zdvd__zmult__better, fact_207_zmult__1__right, fact_160_power__even__eq, fact_1053_nat__diff__add__eq1, fact_1153_zdiff__zmod__right, fact_1156_zmod__zdvd__zmod, fact_590_zcong__iff__lin, fact_899_dvd_Oless__asym_H, fact_218_semiring__add__number__of, fact_282_semiring__mult__2__right, fact_479_not__sum__power2__lt__zero, fact_686_real__less__def, fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_1172_neq__one__mod__two, fact_441_zero__eq__power2, fact_354_add__0__iff, fact_1095_MultInv__prop2, fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_374_power__less__imp__less__base, fact_313_power__eq__0__iff, fact_930_nat__add__left__cancel, fact_399_bin__less__0__simps_I1_J, fact_50_le__number__of__eq__not__less, fact_220_left__distrib__number__of, fact_995_le__add2, fact_407_power__Suc__less, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_331_dvd__power__same, fact_370_zero__less__power, fact_756_one__dvd, fact_328_zdvd__mult__cancel, fact_514_nat__zero__less__power__iff, fact_1114_d22set__g__1, fact_835_zero__less__mult__pos2, fact_146_zadd__left__commute, fact_842_mult__pos__neg2, fact_384_even__less__0__iff, fact_216_semiring__add__number__of, fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_237_add__numeral__0__right, fact_32_one__add__one__is__two, fact_421_number__of__Bit0, fact_554_one__less__power, fact_1035_mult__less__cancel2, fact_979_add__less__mono1, fact_252_add__Bit0__Bit1, fact_171_crossproduct__eq, fact_862_real__mult__le__cancel__iff1, fact_921_dvd_Oless__le__not__le, fact_746_dvd__mult2, fact_1118_gcd__lcm__complete__lattice__nat_Otop__le, fact_1033_mult__less__mono2, fact_638_zcong__eq__trans, fact_808_mult__le__0__iff, fact_361_zadd__0__right, fact_1129_pow__divides__eq__nat, fact_801_mult__nonneg__nonpos2, fact_1096_wset__mem__inv__mem, fact_850_mult__less__cancel__left__pos, fact_1063_zdvd__mono, fact_1007_le__diff__conv, fact_266_semiring__norm_I110_J, fact_159_power__even__eq, fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_927_nat__add__commute, fact_1047_nat__mult__eq__cancel1, fact_1060_is__sum2sq__def, fact_965_le__0__eq, fact_71_less__eq__int__code_I13_J, fact_662_zcong__zprime__prod__zero, fact_1022_mult__le__mono1, fact_629_zcong__def, fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_797_mult__nonpos__nonneg, fact_974_not__add__less1, fact_953_gr0I, fact_378_power__decreasing, fact_9_power2__sum, fact_367_power__mono, fact_975_not__add__less2, fact_1056_nat__diff__add__eq2, fact_1001_add__le__mono1, fact_932_diff__add__inverse2, fact_765_divides__mul__r, fact_618_zcong__zdiff, fact_165_less__special_I2_J, fact_785_comm__mult__left__mono, fact_357_double__eq__0__iff, fact_1191_StandardRes__prop1, fact_73_less__number__of__int__code, fact_1094_MultInv__prop2a, fact_199_rel__simps_I38_J, fact_463_power__add, fact_225_right__distrib__number__of, fact_853_mult__less__cancel__right__disj, fact_614_diff__bin__simps_I1_J, fact_222_left__distrib__number__of, fact_40_zle__antisym, fact_333_field__power__not__zero, fact_1068_zcong__zless__unique, fact_397_semiring__numeral__0__eq__0, fact_712_zero__neq__one, fact_145_zadd__assoc, fact_977_trans__less__add1, fact_1146_zdvd__zmod__imp__zdvd, fact_567_mult__nat__number__of, fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_739_mult__dvd__mono, fact_372_zdvd__reduce, fact_1195_mod__lemma, fact_531_rel__simps_I6_J, fact_687_divides__antisym, fact_913_dvd__antisym, fact_821_mult__strict__left__mono, fact_1017_add__mult__distrib, fact_887_diffs0__imp__equal, fact_578_zcong__zmult__self, fact_251_add__Bit1__Bit0, fact_869_exp__eq__1, fact_784_mult__right__mono__neg, fact_549_rel__simps_I25_J, fact_684_real__zero__not__eq__one, fact_38_zless__linear, fact_658_Int2_Ozcong__zero, fact_494_power__strict__increasing__iff, fact_845_mult__pos__neg, fact_987_less__imp__le__nat, fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_871_two__realpow__ge__one, fact_243_number__of__mult, fact_294_power__less__power__Suc, fact_37_zless__le, fact_72_rel__simps_I31_J, fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_910_dvd_Oord__eq__less__trans, fact_163_less__special_I4_J, fact_951_diff__mult__distrib, fact_558_dvd__power, fact_761_real__mult__right__cancel, fact_460_power__mult__distrib, fact_339_power__strict__mono, fact_980_add__less__mono, fact_550_rel__simps_I11_J, fact_1018_add__mult__distrib2, fact_396_semiring__numeral__0__eq__0, fact_918_dvd_Oantisym__conv, fact_260_semiring__numeral__1__eq__1, fact_1044_nat__less__add__iff2, fact_1032_nat__diff__split__asm, fact_500_power__strict__increasing, fact_324_power__eq__imp__eq__base, fact_272_power3__eq__cube, fact_782_mult__left__mono__neg, fact_577_zcong__scalar, fact_677_linorder__neqE__linordered__idom, fact_261_semiring__numeral__1__eq__1, fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_878_less__zeroE, fact_443_zero__le__power2, fact_503_s, fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_653_zcong__not__zero, fact_312_power__eq__0__iff, fact_709_mult__zero__left, fact_420_le__nat__number__of, fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_450_power2__eq__imp__eq, fact_641_zcong__square__zless, fact_81_rel__simps_I5_J, fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_988_le__neq__implies__less, fact_376_power__less__imp__less__base, fact_575_zcong__zmult, fact_501_power__strict__increasing, fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_635_diff__bin__simps_I5_J, fact_14_power2__eq__square__number__of, fact_972_mult__cancel1, fact_425_power__one__right, fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_1041_mult__le__cancel1, fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_1104_int__le__induct, fact_636_diff__bin__simps_I6_J, fact_1125_gcd__lcm__complete__lattice__nat_Obot__less, fact_905_dvd_Oless__imp__not__less, fact_967_diff__is__0__eq_H, fact_719_combine__common__factor, fact_1010_add__diff__assoc, fact_601_q__neg__lemma, fact_1187_mod__less, fact_897_dvd_Oless__asym, fact_53_le__number__of, fact_569_order__le__neq__implies__less, fact_13_power2__eq__square__number__of, fact_498_power__less__imp__less__exp, fact_156_rel__simps_I27_J, fact_856_not__square__less__zero, fact_249_number__of__add, fact_789_mult__left__mono, fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_356_double__eq__0__iff, fact_481_sum__power2__gt__zero__iff, fact_75_zadd__strict__right__mono, fact_1120_gcd__lcm__complete__lattice__nat_Oless__top, fact_403_pos__zmult__pos, fact_143_zmult__commute, fact_669_realpow__two__sum__zero__iff, fact_539_eq__number__of__Pls__Min, fact_1090_MultInv__zcong__prop2, fact_544_power__0, fact_597_zdiv__mono2__neg__lemma, fact_1080_inv__less__p__minus__1, fact_748_dvd__triv__right, fact_1184_StandardRes__def, fact_255_number__of__Bit1, fact_338_power__strict__mono, fact_861_real__mult__less__iff1, fact_1093_Int2_Oaux____1, fact_147_zadd__commute, fact_828_mult__neg__neg, fact_616_zdiff__zmult__distrib2, fact_509_self__quotient__aux2, fact_689_real__mult__commute, fact_857_pos__add__strict, fact_944_diff__le__mono, fact_39_zle__trans, fact_998_nat__add__left__cancel__le, fact_537_rel__simps_I23_J, fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_1052_nat__le__add__iff1, fact_840_mult__pos__neg2, fact_508_zprime__def, fact_771_split__mult__neg__le, fact_904_dvd_Oless__imp__not__eq, fact_989_less__or__eq__imp__le, fact_1162_neg__mod__conj, fact_524_rel__simps_I42_J, fact_1151_zmod__self, fact_970_mult__0__right, fact_149_less__int__code_I15_J, fact_760_dvd__diff, fact_1011_le__diff__conv2, fact_656_zcong__zero__equiv__div, fact_1012_le__add__diff__inverse2, fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_1110_d22set__eq__wset, fact_362_zero__le__power, fact_685_less__eq__real__def, fact_35_zle__refl, fact_1003_add__leD2, fact_939_eq__imp__le, fact_172_crossproduct__eq, fact_532_rel__simps_I8_J, fact_743_dvd__mult, fact_51_less__number__of, fact_1142_zmod__eq__dvd__iff, fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_562_zcong__sym, fact_1136_zdvd__iff__zmod__eq__0__number__of, fact_690_real__mult__1, fact_244_number__of__mult, fact_1097_wset__inv__mem__mem, fact_0_tpos, fact_825_mult__strict__right__mono, fact_1059_number__of1, fact_1155_zmod__minus1__right, fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_360_zadd__0, fact_67_rel__simps_I2_J, fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_488_power__increasing, fact_1152_zmod__zero, fact_326_zdvd__not__zless, fact_580_power__m1__even, fact_277_semiring__mult__2, fact_55_zadd__zless__mono, fact_671_convex__bound__lt, fact_711_mult__zero__left, fact_311_power__eq__0__iff, fact_876_le0, fact_639_mult__sum2sq, fact_414_sum__squares__le__zero__iff, fact_358_Pls__def, fact_1049_nat__mult__dvd__cancel__disj, fact_722_comm__semiring__class_Odistrib, fact_495_power__strict__increasing__iff, fact_223_right__distrib__number__of, fact_486_one__le__power, fact_545_power__0, fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, fact_382_power__strict__decreasing, fact_591_power__0__left__number__of, fact_48_le__number__of__eq__not__less, fact_935_Nat_Odiff__cancel, fact_82_less__eq__int__code_I15_J, fact_813_zero__le__square, fact_651_zdiff__power3, fact_1083_MultInv__zcong__prop1, fact_392_semiring__norm_I112_J, fact_1105_int__less__induct, fact_239_mult__number__of__left, fact_1188_mod__less__eq__dividend, fact_625_diff__bin__simps_I10_J, fact_1135_zmod__number__of__Bit1, fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_1170_zmult2__lemma__aux2, fact_489_power__increasing, fact_931_nat__add__right__cancel, fact_151_rel__simps_I10_J, fact_885_minus__nat_Odiff__0, fact_235_add__numeral__0, fact_773_split__mult__pos__le, fact_497_power__less__imp__less__exp, fact_962_Nat_Oadd__0__right, fact_650_zdiff__power2, fact_960_add__eq__self__zero, fact_584_power__eq__0__iff__number__of, fact_33_one__add__one__is__two, fact_471_power__mult, fact_1175_zmod__eq__0D, fact_259_mult__numeral__1__right, fact_741_dvd__mult, fact_649_power2__diff, fact_1002_add__le__mono, fact_473_power2__less__imp__less, fact_623_left__diff__distrib__number__of, fact_1025_nat__mult__eq__1__iff, fact_723_comm__semiring__class_Odistrib, fact_615_diff__bin__simps_I7_J, fact_612_number__of__diff, fact_792_mult__right__mono, fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_69_rel__simps_I14_J, fact_205_add__Bit0__Bit0, fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest, fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_573_IntPrimes_Ozcong__zero, fact_777_mult__mono, fact_644_zcong__zmult__prop1, fact_827_mult__neg__neg, fact_1031_nat__diff__split, fact_262_semiring__numeral__1__eq__1, fact_802_mult__nonneg__nonpos, fact_161_power__even__eq, fact_844_mult__pos__neg, fact_1004_add__leD1, fact_90_is__mult__sum2sq, fact_1070_Wilson__Russ, fact_633_zle__diff1__eq, fact_340_power__strict__mono, fact_654_zdvd__bounds, fact_933_diff__add__inverse, fact_270_double__number__of__Bit0, fact_1106_d22set__induct__old, fact_170_crossproduct__eq, fact_1115_d22set__mem, fact_240_mult__number__of__left, fact_592_power__0__left__number__of, fact_405_odd__nonzero, fact_660_neg__one__power, fact_926_dvd__diff__nat, fact_868_divides__rev, fact_1055_nat__le__add__iff2, fact_510_self__quotient__aux1, fact_1081_MultInv__prop1, fact_916_dvd_Ole__neq__trans, fact_805_mult__nonneg__nonneg, fact_1103_wset__mem, fact_879_diff__commute, fact_153_rel__simps_I22_J, fact_198_rel__simps_I44_J, fact_1082_inv__not__0, fact_676_linorder__neqE__linordered__idom, fact_727_add__diff__add, fact_1150_zmod__simps_I3_J, fact_964_diff__add__0, fact_859_divides__ge, fact_288_p0, fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_732_dvd__mult__left, fact_593_power__0__left__number__of, fact_383_even__less__0__iff, fact_949_nat__mult__assoc, fact_595_zcong__zless__0, fact_318_dvd__power__le, fact_795_mult__nonpos__nonpos, fact_675_real__le__eq__diff, fact_954_gr__implies__not0, fact_800_mult__nonneg__nonpos2, fact_919_dvd_Oeq__refl, fact_852_mult__less__cancel__left__disj, fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_1180_mod__geq, fact_314_le__imp__power__dvd, fact_566_nat__number__of__mult__left, fact_520_Bit1__Min, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_1008_le__add__diff, fact_738_mult__dvd__mono, fact_375_power__less__imp__less__base, fact_377_power__decreasing, fact_1147_zdvd__zmod, fact_535_rel__simps_I26_J, fact_679_dvd__refl, fact_1167_zmult2__lemma__aux3, fact_298_power__gt1__lemma, fact_265_semiring__norm_I110_J, fact_866_real__two__squares__add__zero__iff, fact_872_realpow__pos__nth, fact_1086_MultInv__prop3, fact_459_power__commutes, fact_1101_wset__g__1, fact_433_le__special_I1_J, fact_692_realpow__minus__mult, fact_428_odd__less__0, fact_491_power__inject__exp, fact_890_less__not__refl2, fact_337_zdvd__imp__le, fact_1020_mult__le__mono, fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_992_dvd__reduce, fact_563_zcong__refl, fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_472_power2__less__imp__less, fact_258_mult__numeral__1__right, fact_254_number__of__Bit1, fact_667_divides__cases, fact_466_power__one, fact_700_divisors__zero, fact_390_zprime__zdvd__power, fact_583_power__eq__0__iff__number__of, fact_422_number__of__Bit0, fact_599_zdiv__mono2__lemma, fact_507_even__power__le__0__imp__0, fact_938_nat__le__linear, fact_1169_zmult2__lemma__aux1, fact_600_unique__quotient__lemma, fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot, fact_1098_wset__mem__mem, fact_963_plus__nat_Oadd__0, fact_981_less__add__eq__less, fact_1158_pos__mod__sign, fact_208_zmult__1, fact_194_rel__simps_I46_J, fact_976_nat__add__left__cancel__less, fact_708_mult__zero__right, fact_408_power__Suc__less, fact_548_semiring__norm_I113_J, fact_492_power__inject__exp, fact_1171_divmod__int__rel__mod__eq, fact_1181_mod__if, fact_982_add__lessD1, fact_1131_divides__le, fact_668_QuadRes__def, fact_724_dvd__0__left, fact_843_mult__pos__neg, fact_465_power__add, fact_907_dvd_Oless__not__sym, fact_731_dvd__mult__right, fact_984_less__diff__conv, fact_922_dvd_Oless__le, fact_387_add__scale__eq__noteq, fact_640_zcong__square, fact_256_mult__numeral__1, fact_474_power2__less__imp__less, fact_1042_mult__le__cancel2, fact_1078_inv__not__p__minus__1, fact_1179_mod__eq__0__iff, fact_836_zero__less__mult__pos2, fact_943_diff__le__mono2, fact_68_less__int__code_I13_J, fact_59_zpower__zadd__distrib, fact_648_power2__diff, fact_70_rel__simps_I19_J, fact_955_less__nat__zero__code, fact_810_zero__le__mult__iff, fact_440_zero__power2, fact_404_zmult__zless__mono2, fact_1092_Int2_Oaux____2, fact_718_combine__common__factor, fact_221_left__distrib__number__of, fact_3_t__l__p, fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_285_semiring__one__add__one__is__two, fact_89_zprime__2, fact_85_rel__simps_I15_J, fact_892_linorder__neqE__nat, fact_553_one__less__power, 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fact_814_mult__strict__left__mono__neg, fact_831_mult__neg__pos, fact_504_Euler_Oaux____1, fact_776_mult__mono, fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_1072_inv__inv, fact_451_power2__less__0, fact_330_dvd__power__same, fact_157_rel__simps_I21_J, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_1064_number__of2, fact_280_semiring__mult__2__right, fact_65_less__eq__int__code_I16_J, fact_929_nat__add__assoc, fact_150_rel__simps_I16_J, fact_394_number__of__Pls, fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_796_mult__nonpos__nonneg, fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_617_zdiff__zmult__distrib, fact_413_sum__squares__le__zero__iff, fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_914_dvd_Oord__le__eq__trans, fact_11_power2__sum, fact_993_dvd__diffD1, fact_581_power__m1__even, fact_485_one__le__power, fact_1174_pos__zmod__mult__2, fact_506_even__power__le__0__imp__0, fact_1027_nat__1__eq__mult__iff, fact_619_zdvd__zdiffD, fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_86_zless__imp__add1__zle, fact_683_dvd__trans, fact_834_zero__less__mult__pos2, fact_527_not__real__square__gt__zero, fact_561_eq__0__number__of, fact_1109_mono__nat__linear__lb, fact_1193_StandardRes__SR__prop, fact_1183_le__mod__geq, fact_483_zero__le__even__power_H, fact_475_sum__power2__ge__zero, help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U, fact_181_crossproduct__noteq, fact_60_nat__mult__2, fact_1197_StandardRes__prop2, fact_652_zcong__less__eq, fact_1069_norR__mem__unique__aux, fact_322_power__le__dvd, fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J, fact_627_less__bin__lemma, fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_477_sum__power2__le__zero__iff, fact_431_less__special_I3_J, fact_297_power__gt1__lemma, fact_755_dvd__add, fact_1029_nat__dvd__not__less, fact_693_realpow__minus__mult, fact_195_rel__simps_I39_J, fact_1057_nat__eq__add__iff2, fact_696_power__eq__if, fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_1173_zmod__minus1, fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_279_mult__2, fact_883_real__le__antisym, fact_819_comm__mult__strict__left__mono, fact_411_sum__squares__ge__zero, fact_499_power__less__imp__less__exp, fact_720_combine__common__factor, fact_217_semiring__add__number__of, fact_729_dvd__mult__right, fact_540_power__dvd__imp__le, fact_54_le__number__of, fact_1091_MultInv__zcong__prop3, fact_1189_StandardRes__eq__zcong, fact_546_power__0, fact_204_add__Pls, fact_140_rel__simps_I51_J, fact_1185_mod__mult__distrib, fact_381_power__strict__decreasing, fact_815_mult__strict__left__mono__neg, fact_1149_zmod__zmult1__eq, fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_6_qf1pt, fact_824_mult__strict__right__mono, fact_794_mult__nonpos__nonpos, fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_268_mult__Bit1, fact_968_diff__is__0__eq, fact_826_mult__strict__right__mono, fact_389_add__scale__eq__noteq, fact_628_xzgcda__linear__aux1, fact_482_sum__power2__gt__zero__iff, fact_246_add__number__of__left, fact_985_nat__less__le, fact_983_add__diff__inverse, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_966_less__eq__nat_Osimps_I1_J, fact_364_zero__le__power, fact_250_number__of__add, fact_423_power__one__right, fact_704_mult__eq__0__iff, fact_991_diff__less__mono, fact_1038_mult__eq__self__implies__10, fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_788_mult__left__mono, fact_780_mult__mono_H, fact_490_power__increasing, fact_1159_pos__mod__conj, fact_695_mult__eq__if, fact_728_add__diff__add, fact_36_zle__linear, fact_28_add__special_I2_J, fact_1192_StandardRes__ubound, fact_1108_int__gr__induct, fact_519_rel__simps_I43_J, fact_737_dvdI, fact_816_mult__strict__right__mono__neg, fact_717_one__neq__zero, fact_518_rel__simps_I47_J, fact_923_dvd_Ole__less, fact_1034_mult__less__mono1, fact_210_zadd__zmult__distrib, fact_749_dvd__triv__right, fact_940_le__trans, fact_680_dvd__refl, fact_902_dvd_Oless__imp__triv, fact_169_le__special_I2_J, fact_768_nat__power__eq__0__iff, fact_701_no__zero__divisors, fact_775_mult__mono, fact_493_power__inject__exp, fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_817_mult__strict__right__mono__neg, fact_202_mult__Bit0, fact_521_rel__simps_I37_J, fact_1030_add__gr__0, fact_335_power__0__left, fact_8_zadd__power3, fact_1019_nat__dvd__1__iff__1, fact_316_le__imp__power__dvd, fact_643_zcong__id, fact_1111_ex__least__nat__le, fact_1113_d22set__le__swap, fact_402_int__0__less__1, fact_417_not__sum__squares__lt__zero, fact_1132_mult__left__cancel, fact_300_power__le__imp__le__exp, fact_366_power__mono, fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_758_one__dvd, fact_958_diff__less, fact_973_mult__cancel2, fact_1071_zfact_Osimps, fact_247_add__number__of__eq, fact_242_arith__simps_I32_J, fact_267_one__is__num__one, fact_502_power__strict__increasing, fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_315_le__imp__power__dvd, fact_16_one__power2, fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_369_zero__less__power, fact_299_power__gt1__lemma, fact_1045_nat__mult__eq__cancel__disj, fact_551_pos__zmult__eq__1__iff__lemma, fact_1077_inv__not__1, fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_1046_left__add__mult__distrib, fact_1066_incr__mult__lemma, fact_895_diff__less__mono2, fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_1190_StandardRes__prop3, fact_769_divides__exp, fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_213_semiring__mult__number__of, fact_76_zadd__left__mono, fact_576_zcong__scalar2, fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_292_real__sum__squared__expand, fact_1036_mult__less__cancel1, fact_631_add__number__of__diff1, fact_1100_wset__less, fact_848_mult__pos__pos, fact_698_divisors__zero, fact_241_arith__simps_I32_J, fact_523_rel__simps_I45_J, fact_1099_wset__subset
% 25.04/7.02 % No. of inferences in proof: 2398
% 25.04/7.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6492 ms resp. 5846 ms w/o parsing
% 26.17/7.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.17/7.42 % [INFO] Killing All external provers ...
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