TSTP Solution File: NUM926+2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM926+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 11:43:26 EDT 2023
% Result : Theorem 17.30s 4.57s
% Output : Refutation 18.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 765
% Syntax : Number of formulae : 1484 ( 666 unt; 48 typ; 0 def)
% Number of atoms : 3394 (1292 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 14611 ( 271 ~; 88 |; 395 &;12382 @)
% ( 161 <=>;1314 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 14 con; 0-3 aty)
% Number of variables : 2747 ( 0 ^;2723 !; 24 ?;2747 :)
% Comments :
%------------------------------------------------------------------------------
thf(plus_plus_int_type,type,
plus_plus_int: $i > $i > $i ).
thf(power_power_int_type,type,
power_power_int: $i > $i > $i ).
thf(number_number_of_nat_type,type,
number_number_of_nat: $i > $i ).
thf(bit0_type,type,
bit0: $i > $i ).
thf(bit1_type,type,
bit1: $i > $i ).
thf(pls_type,type,
pls: $i ).
thf(times_times_int_type,type,
times_times_int: $i > $i > $i ).
thf(number_number_of_int_type,type,
number_number_of_int: $i > $i ).
thf(m_type,type,
m: $i ).
thf(one_one_int_type,type,
one_one_int: $i ).
thf(dvd_dvd_real_type,type,
dvd_dvd_real: $i > $i > $o ).
thf(power_power_real_type,type,
power_power_real: $i > $i > $i ).
thf(is_int_type,type,
is_int: $i > $o ).
thf(number267125858f_real_type,type,
number267125858f_real: $i > $i ).
thf(times_times_nat_type,type,
times_times_nat: $i > $i > $i ).
thf(one_one_nat_type,type,
one_one_nat: $i ).
thf(one_one_real_type,type,
one_one_real: $i ).
thf(times_times_real_type,type,
times_times_real: $i > $i > $i ).
thf(zero_zero_real_type,type,
zero_zero_real: $i ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: $i > $i > $o ).
thf(zero_zero_nat_type,type,
zero_zero_nat: $i ).
thf(power_power_nat_type,type,
power_power_nat: $i > $i > $i ).
thf(ord_less_nat_type,type,
ord_less_nat: $i > $i > $o ).
thf(ord_less_real_type,type,
ord_less_real: $i > $i > $o ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: $i > $i > $o ).
thf(zcong_type,type,
zcong: $i > $i > $i > $o ).
thf(plus_plus_real_type,type,
plus_plus_real: $i > $i > $i ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: $i > $i > $o ).
thf(min_type,type,
min: $i ).
thf(plus_plus_nat_type,type,
plus_plus_nat: $i > $i > $i ).
thf(dvd_dvd_nat_type,type,
dvd_dvd_nat: $i > $i > $o ).
thf(ord_less_int_type,type,
ord_less_int: $i > $i > $o ).
thf(zprime_type,type,
zprime: $i > $o ).
thf(zero_zero_int_type,type,
zero_zero_int: $i ).
thf(dvd_dvd_int_type,type,
dvd_dvd_int: $i > $i > $o ).
thf(minus_minus_int_type,type,
minus_minus_int: $i > $i > $i ).
thf(minus_minus_nat_type,type,
minus_minus_nat: $i > $i > $i ).
thf(twoSqu140629262sum2sq_type,type,
twoSqu140629262sum2sq: $i > $i ).
thf(minus_minus_real_type,type,
minus_minus_real: $i > $i > $i ).
thf(t_type,type,
t: $i ).
thf(s1_type,type,
s1: $i ).
thf(s_type,type,
s: $i ).
thf(legendre_type,type,
legendre: $i > $i > $i ).
thf(undefined_int_type,type,
undefined_int: $i > $i ).
thf(int_type,type,
int: $i ).
thf(quadRes_type,type,
quadRes: $i > $i > $o ).
thf(twoSqu142715416sum2sq_type,type,
twoSqu142715416sum2sq: $i > $o ).
thf(product_Pair_int_int_type,type,
product_Pair_int_int: $i > $i > $i ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_power__less__power__Suc) ).
thf(1036,plain,
! [A: $i,B: $i] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(246,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_rel__simps_I11_J) ).
thf(1586,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ min )
=> ( ord_less_eq_int @ A @ min ) )
& ( ( ord_less_eq_int @ A @ min )
=> ( ord_less_int @ ( bit0 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(332,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( power_power_int @ A @ one_one_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1879,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( power_power_int @ A @ one_one_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(85,axiom,
~ ( ord_less_int @ min @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_rel__simps_I7_J) ).
thf(1024,plain,
~ ( ord_less_int @ min @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_zadd__zmult__distrib) ).
thf(2295,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_semiring__mult__number__of) ).
thf(1633,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(387,axiom,
! [A: $i,B: $i] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_not__sum__power2__lt__zero) ).
thf(2072,plain,
! [A: $i,B: $i] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_order__le__neq__implies__less) ).
thf(1559,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(288,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(1729,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_power__even__eq) ).
thf(2412,plain,
! [A: $i,B: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(494,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_nat__number__of__Pls) ).
thf(2463,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( times_times_int @ A @ B ) )
=> ( ( dvd_dvd_int @ C @ A )
| ( dvd_dvd_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_zprime__zdvd__zmult__better) ).
thf(2595,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( times_times_int @ A @ B ) )
=> ( ( dvd_dvd_int @ C @ A )
| ( dvd_dvd_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(514,axiom,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_semiring__mult__2) ).
thf(2544,plain,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1179,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( number_number_of_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_number__of__diff) ).
thf(1818,plain,
! [A: $i,B: $i] :
( ( number_number_of_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
<=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_power__strict__increasing__iff) ).
thf(1369,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_nat @ A @ B ) )
& ( ( ord_less_nat @ A @ B )
=> ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_divides__exp2) ).
thf(1190,plain,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_semiring__add__number__of) ).
thf(2131,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ C @ B ) ) )
<=> ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_crossproduct__eq) ).
thf(1454,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ C @ B ) ) )
=> ( ( A = C )
| ( B = D ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_real__mult__commute) ).
thf(962,plain,
! [A: $i,B: $i] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_476_sum__power2__le__zero__iff) ).
thf(1982,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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 ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_int )
=> ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_even__power__le__0__imp__0) ).
thf(2427,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ ( 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)],[485]) ).
thf(498,axiom,
! [A: $i] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__special_I2_J) ).
thf(2480,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) )
=> ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less_eq_int @ ( bit1 @ pls ) @ A )
=> ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(448,axiom,
ord_less_eq_int @ one_one_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(2280,plain,
ord_less_eq_int @ one_one_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(234,axiom,
is_int @ ( undefined_int @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Int__Oint) ).
thf(1554,plain,
is_int @ ( undefined_int @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1110,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(440,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(2250,plain,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(470,axiom,
! [A: $i] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
<=> ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_le__special_I4_J) ).
thf(2363,plain,
! [A: $i] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
=> ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less_eq_int @ A @ ( bit1 @ pls ) )
=> ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ E @ A )
=> ( ord_less_eq_int @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_unique__quotient__lemma) ).
thf(2210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ E @ A )
=> ( ord_less_eq_int @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_zero__less__power) ).
thf(1068,plain,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(596,axiom,
! [A: $i] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_power3__eq__cube) ).
thf(2808,plain,
! [A: $i] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_454_sum__power2__eq__zero__iff) ).
thf(2395,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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 ) )
=> ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(696,axiom,
! [A: $i] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_semiring__mult__2) ).
thf(3153,plain,
! [A: $i] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_power__less__imp__less__exp) ).
thf(2953,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_real @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_dvd__power__le) ).
thf(1073,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_real @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3108,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(41,axiom,
! [A: $i] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(873,plain,
! [A: $i] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(247,axiom,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(1591,plain,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ one_one_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ one_one_int @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_one__less__power) ).
thf(2380,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ one_one_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ one_one_int @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C )
=> ( ( zcong @ B @ zero_zero_int @ C )
| ( zcong @ A @ zero_zero_int @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_zcong__zprime__prod__zero) ).
thf(1971,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C )
=> ( ( zcong @ B @ zero_zero_int @ C )
| ( zcong @ A @ zero_zero_int @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(202,axiom,
is_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).
thf(1437,plain,
is_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2976,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(15,axiom,
! [A: $i] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(762,plain,
! [A: $i] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_nat__mult__eq__one) ).
thf(730,plain,
! [A: $i,B: $i] :
( ( ( ( times_times_nat @ A @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( ( times_times_nat @ A @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_rel__simps_I32_J) ).
thf(1882,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(555,axiom,
! [A: $i] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_mult__2__right) ).
thf(2671,plain,
! [A: $i] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_rel__simps_I51_J) ).
thf(2014,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( bit1 @ A )
= ( bit1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit1 @ A )
= ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(2837,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(116,axiom,
! [A: $i] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1142,plain,
! [A: $i] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1173,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1486,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(661,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_one__add__one__is__two) ).
thf(3017,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) )
<=> ( dvd_dvd_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_zdvd__reduce) ).
thf(3049,plain,
! [A: $i,B: $i,C: $i] :
( ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) )
=> ( dvd_dvd_int @ A @ B ) )
& ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(657,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(3004,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(691,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( number_number_of_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_number__of__is__id) ).
thf(3135,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( number_number_of_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ C @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_zprime__power__zdvd__cancel__left) ).
thf(2918,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ C @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(668,axiom,
! [A: $i] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_number__of__Bit0) ).
thf(3044,plain,
! [A: $i] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( plus_plus_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)],[668]) ).
thf(459,axiom,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_diff__bin__simps_I10_J) ).
thf(2316,plain,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd_int @ D @ E )
=> ( ( dvd_dvd_int @ D @ ( plus_plus_int @ B @ C ) )
<=> ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_zdvd__period) ).
thf(2933,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd_int @ D @ E )
=> ( ( ( dvd_dvd_int @ D @ ( plus_plus_int @ B @ C ) )
=> ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) )
& ( ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) )
=> ( dvd_dvd_int @ D @ ( plus_plus_int @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ C )
=> ( ( ord_less_eq_int @ B @ A )
| ( ord_less_eq_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_Euler_Oaux2) ).
thf(1233,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ C )
=> ( ( ord_less_eq_int @ B @ A )
| ( ord_less_eq_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(542,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zprime__2) ).
thf(2627,plain,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_real ) )
=> ( dvd_dvd_real @ A @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_dvd__power) ).
thf(913,plain,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_real ) )
=> ( dvd_dvd_real @ A @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(60,axiom,
! [A: $i] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_power__0) ).
thf(945,plain,
! [A: $i] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(93,axiom,
! [A: $i] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_real__le__refl) ).
thf(1063,plain,
! [A: $i] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(525,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2575,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_zcong__zdiff) ).
thf(1078,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_power__inject__exp) ).
thf(1788,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(199,axiom,
! [A: $i] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1426,plain,
! [A: $i] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(712,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_475_sum__power2__le__zero__iff) ).
thf(3217,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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 ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(487,axiom,
! [A: $i] :
( ( ord_less_eq_int @ one_one_int @ A )
<=> ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_int__one__le__iff__zero__less) ).
thf(2434,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_int @ zero_zero_int @ A ) )
& ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ one_one_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_field__power__not__zero) ).
thf(2712,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_field__power__not__zero) ).
thf(1196,plain,
! [A: $i,B: $i] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(317,axiom,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_power__0__left__number__of) ).
thf(1835,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_power2__eq__imp__eq) ).
thf(2972,plain,
! [A: $i,B: $i] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2763,plain,
! [A: $i,B: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_divides__mul__l) ).
thf(1576,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ B )
=> ( ( zcong @ A @ B @ C )
<=> ? [D: $i] :
( ( is_int @ D )
& ( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_zcong__iff__lin) ).
thf(2020,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ B )
=> ( ( ( zcong @ A @ B @ C )
=> ? [D: $i] :
( ( is_int @ D )
& ( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) )
& ( ? [D: $i] :
( ( is_int @ D )
& ( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) )
=> ( zcong @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( A != zero_zero_int )
=> ( dvd_dvd_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_zdvd__mult__cancel) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( A != zero_zero_int )
=> ( dvd_dvd_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_divides__mul__r) ).
thf(1386,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_power2__le__imp__le) ).
thf(1724,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(416,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_rel__simps_I17_J) ).
thf(2173,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(506,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_Bit1__Min) ).
thf(2516,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(227,axiom,
! [A: $i] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_power__one__right) ).
thf(1529,plain,
! [A: $i] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(340,axiom,
! [A: $i] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_less__0__number__of) ).
thf(1904,plain,
! [A: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
=> ( ord_less_int @ pls @ A ) )
& ( ( ord_less_int @ pls @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_semiring__add__number__of) ).
thf(2869,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(334,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_semiring__numeral__0__eq__0) ).
thf(1887,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ B @ C ) @ E )
<=> ( zcong @ A @ ( times_times_int @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_zcong__zmult__prop2) ).
thf(2957,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( ( zcong @ A @ ( times_times_int @ B @ C ) @ E )
=> ( zcong @ A @ ( times_times_int @ B @ D ) @ E ) )
& ( ( zcong @ A @ ( times_times_int @ B @ D ) @ E )
=> ( zcong @ A @ ( times_times_int @ B @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zless__imp__add1__zle) ).
thf(1746,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_zcong__zadd) ).
thf(3103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(535,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2603,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(598,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_zero__eq__power2) ).
thf(2814,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(719,plain,
~ ? [A: $i,B: $i] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_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(464,axiom,
is_int @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OPls) ).
thf(2339,plain,
is_int @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_zdiff__zmult__distrib) ).
thf(2755,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_zdiff__zmult__distrib2) ).
thf(3061,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1264,plain,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_zero__le__power) ).
thf(3148,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1313,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_power__less__imp__less__exp) ).
thf(934,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__int__code_I16_J) ).
thf(2126,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ one_one_int @ B )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_one__le__power) ).
thf(2745,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ one_one_int @ B )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zle__antisym) ).
thf(1409,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_eq__number__of) ).
thf(724,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2698,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(269,axiom,
is_int @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_m) ).
thf(1660,plain,
is_int @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( number_number_of_int @ ( times_times_int @ A @ B ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_number__of__mult) ).
thf(1760,plain,
! [A: $i,B: $i] :
( ( number_number_of_int @ ( times_times_int @ A @ B ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zadd__strict__right__mono) ).
thf(3131,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(679,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_semiring__numeral__0__eq__0) ).
thf(3089,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ( quadRes @ A @ B )
<=> ? [C: $i] :
( ( is_int @ C )
& ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_QuadRes__def) ).
thf(2488,plain,
! [A: $i,B: $i] :
( ( ( quadRes @ A @ B )
=> ? [C: $i] :
( ( is_int @ C )
& ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ) )
& ( ? [C: $i] :
( ( is_int @ C )
& ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) )
=> ( quadRes @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ A @ one_one_real )
=> ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_power__decreasing) ).
thf(1545,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ A @ one_one_real )
=> ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zle__add1__eq__le) ).
thf(1800,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(336,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_eq__number__of__Pls__Min) ).
thf(1892,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(611,axiom,
! [A: $i,B: $i] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_zero__le__even__power_H) ).
thf(2857,plain,
! [A: $i,B: $i] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(118,axiom,
! [A: $i] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
<=> ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_even__less__0__iff) ).
thf(1147,plain,
! [A: $i] :
( ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
=> ( ord_less_real @ A @ zero_zero_real ) )
& ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(212,axiom,
is_int @ min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OMin) ).
thf(1479,plain,
is_int @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zless__linear) ).
thf(770,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_sum__squares__eq__zero__iff) ).
thf(1398,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(544,axiom,
! [A: $i] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_mult__numeral__1__right) ).
thf(2635,plain,
! [A: $i] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(263,axiom,
! [A: $i] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Bit1__def) ).
thf(1641,plain,
! [A: $i] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(148,axiom,
ord_less_int @ min @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_bin__less__0__simps_I2_J) ).
thf(1232,plain,
ord_less_int @ min @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(320,axiom,
! [A: $i] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_one__not__neg__one__mod__m) ).
thf(1847,plain,
! [A: $i] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) @ zero_zero_int )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ F )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_zdiv__mono2__neg__lemma) ).
thf(2829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) @ zero_zero_int )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ F )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_453_sum__power2__eq__zero__iff) ).
thf(2403,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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 ) )
=> ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(224,axiom,
! [A: $i] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1514,plain,
! [A: $i] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1247,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_zcong__zmult__prop3) ).
thf(2552,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( number_number_of_int @ A )
= B )
<=> ( B
= ( number_number_of_int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_number__of__reorient) ).
thf(2301,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( ( 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)],[454]) ).
thf(310,axiom,
! [A: $i] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_diff__bin__simps_I5_J) ).
thf(1815,plain,
! [A: $i] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
<=> ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_le__number__of__eq__not__less) ).
thf(2852,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
=> ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
=> ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(3231,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(492,axiom,
~ ! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ A ) ) ),
file('/export/starexec/sandbox/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(2456,plain,
~ ! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_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)],[492]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_int @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_dvd__power__le) ).
thf(2178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_int @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int @ B )
<=> ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_inv__not__p__minus__1__aux) ).
thf(2324,plain,
! [A: $i,B: $i] :
( ( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int @ B )
=> ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) )
& ( ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B )
=> ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(396,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( min
= ( bit1 @ A ) )
<=> ( min = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_rel__simps_I43_J) ).
thf(2105,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( min
= ( bit1 @ A ) )
=> ( min = A ) )
& ( ( min = A )
=> ( min
= ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_zadd__left__commute) ).
thf(2782,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
<=> ( ( B = zero_zero_nat )
| ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_nat__mult__dvd__cancel__disj_H) ).
thf(1040,plain,
! [A: $i,B: $i,C: $i] :
( ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
=> ( ( B = zero_zero_nat )
| ( dvd_dvd_nat @ A @ C ) ) )
& ( ( ( B = zero_zero_nat )
| ( dvd_dvd_nat @ A @ C ) )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(442,axiom,
! [A: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int )
<=> ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_le__special_I4_J) ).
thf(2259,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int )
=> ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less_eq_int @ A @ ( bit1 @ pls ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( power_power_int @ A @ B )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_power__eq__0__iff) ).
thf(3163,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( ( power_power_int @ A @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) )
=> ( ( power_power_int @ A @ B )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1418,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( dvd_dvd_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_zpower__zdvd__prop2) ).
thf(1960,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( dvd_dvd_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ B )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1581,plain,
! [A: $i,B: $i] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ B )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_power__gt1__lemma) ).
thf(1489,plain,
! [A: $i,B: $i] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(638,axiom,
! [A: $i] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_power__m1__even) ).
thf(2950,plain,
! [A: $i] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(435,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_numeral__1__eq__1) ).
thf(2237,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(618,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(2880,plain,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(30,axiom,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_real__mult__1) ).
thf(834,plain,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(346,axiom,
! [A: $i] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_rel__simps_I25_J) ).
thf(1928,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
=> ( ord_less_int @ min @ A ) )
& ( ( ord_less_int @ min @ A )
=> ( ord_less_eq_int @ min @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1377,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(956,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ A @ one_one_int )
=> ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_power__decreasing) ).
thf(1622,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ A @ one_one_int )
=> ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(226,axiom,
! [A: $i,B: $i] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_not__sum__squares__lt__zero) ).
thf(1526,plain,
! [A: $i,B: $i] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_dvd__power__same) ).
thf(998,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(713,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_power2__eq__imp__eq) ).
thf(3226,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_power__Suc__less) ).
thf(2965,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_diff__bin__simps_I9_J) ).
thf(3211,plain,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_power__add) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ A )
= ( times_times_real @ A @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_power__commutes) ).
thf(981,plain,
! [A: $i,B: $i] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ A )
= ( times_times_real @ A @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ D @ C )
=> ~ ( dvd_dvd_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_divides__div__not) ).
thf(766,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ D @ C )
=> ~ ( dvd_dvd_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_Int2_Oaux1) ).
thf(3189,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(449,axiom,
! [A: $i] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_less__special_I3_J) ).
thf(2281,plain,
! [A: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1345,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(594,axiom,
! [A: $i] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right) ).
thf(2799,plain,
! [A: $i] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(450,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( bit1 @ A )
= min )
<=> ( A = min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_rel__simps_I47_J) ).
thf(2286,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( bit1 @ A )
= min )
=> ( A = min ) )
& ( ( A = min )
=> ( ( bit1 @ A )
= min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(395,axiom,
( ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ s @ one_one_int ) )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
thf(2103,plain,
( ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ s @ one_one_int ) )
= ( times_times_int @ ( plus_plus_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)],[395]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__number__of) ).
thf(2750,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(279,axiom,
! [A: $i] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1696,plain,
! [A: $i] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_divides__cases) ).
thf(2884,plain,
! [A: $i,B: $i] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(363,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_numeral__1__eq__1) ).
thf(1975,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(238,axiom,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1564,plain,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(682,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3097,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(714,axiom,
! [A: $i] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_power2__ge__self) ).
thf(3229,plain,
! [A: $i] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(1438,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1199,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(702,axiom,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_mult__numeral__1) ).
thf(3186,plain,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_zdvd__imp__le) ).
thf(1338,plain,
! [A: $i,B: $i] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_le__imp__power__dvd) ).
thf(1311,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__int__code_I14_J) ).
thf(2232,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(671,axiom,
! [A: $i] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_zero__le__power2) ).
thf(3054,plain,
! [A: $i] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(390,axiom,
! [A: $i] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_add__numeral__0) ).
thf(2083,plain,
! [A: $i] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_659_realpow__two__sum__zero__iff) ).
thf(2496,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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 ) )
=> ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( A
= ( plus_plus_int @ A @ B ) )
<=> ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_add__0__iff) ).
thf(2621,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( A
= ( plus_plus_int @ A @ B ) )
=> ( B = zero_zero_int ) )
& ( ( B = zero_zero_int )
=> ( A
= ( plus_plus_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_semiring__mult__number__of) ).
thf(2790,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(552,axiom,
! [A: $i] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_power3__eq__cube) ).
thf(2660,plain,
! [A: $i] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_power2__less__imp__less) ).
thf(1868,plain,
! [A: $i,B: $i] :
( ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J) ).
thf(2382,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(370,axiom,
! [A: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_rel__simps_I27_J) ).
thf(2000,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
=> ( ord_less_eq_int @ A @ pls ) )
& ( ( ord_less_eq_int @ A @ pls )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(262,axiom,
! [A: $i] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
<=> ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_less__special_I4_J) ).
thf(1636,plain,
! [A: $i] :
( ( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
=> ( ord_less_int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less_int @ A @ ( bit1 @ pls ) )
=> ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_power__eq__0__iff) ).
thf(798,plain,
! [A: $i,B: $i] :
( ( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) )
=> ( ( power_power_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ ( power_power_real @ A @ B ) @ C )
= ( power_power_real @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1163,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ ( power_power_real @ A @ B ) @ C )
= ( power_power_real @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(2264,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_real__mult__assoc) ).
thf(894,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_zmult__zless__mono2) ).
thf(2601,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(576,axiom,
! [A: $i] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_number__of__Bit1) ).
thf(2733,plain,
! [A: $i] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_real @ C @ ( times_times_real @ E @ A ) )
!= ( plus_plus_real @ D @ ( times_times_real @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_add__scale__eq__noteq) ).
thf(952,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_real @ C @ ( times_times_real @ E @ A ) )
!= ( plus_plus_real @ D @ ( times_times_real @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( minus_minus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_diff__square) ).
thf(2277,plain,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( minus_minus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_power__add) ).
thf(1570,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(407,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_semiring__norm_I112_J) ).
thf(2147,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(272,axiom,
! [A: $i] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_power2__less__0) ).
thf(1666,plain,
! [A: $i] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_mult__Bit1) ).
thf(2969,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(676,axiom,
! [A: $i] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A != zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_zero__less__power2) ).
thf(3069,plain,
! [A: $i] :
( ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( A != zero_zero_real ) )
& ( ( A != zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(536,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_semiring__norm_I113_J) ).
thf(2606,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_sum__power2__gt__zero__iff) ).
thf(2528,plain,
! [A: $i,B: $i] :
( ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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 ) )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_power2__less__imp__less) ).
thf(3207,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_real__mult__order) ).
thf(1021,plain,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
<=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_real__mult__less__iff1) ).
thf(778,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
=> ( ord_less_real @ A @ B ) )
& ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(663,axiom,
! [A: $i] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_power2__less__0) ).
thf(3022,plain,
! [A: $i] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1502,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_int ) )
=> ( dvd_dvd_int @ A @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_dvd__power) ).
thf(1824,plain,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_int ) )
=> ( dvd_dvd_int @ A @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_add__number__of__left) ).
thf(1619,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_sum__squares__eq__zero__iff) ).
thf(2445,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) )
& ( ( ( A = zero_zero_int )
& ( B = zero_zero_int ) )
=> ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(584,axiom,
! [A: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_rel__simps_I28_J) ).
thf(2758,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
=> ( ord_less_eq_int @ A @ min ) )
& ( ( ord_less_eq_int @ A @ min )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(1602,plain,
! [A: $i,B: $i] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
<=> ( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_zless__add1__eq) ).
thf(2628,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
=> ( ( ord_less_int @ A @ B )
| ( A = B ) ) )
& ( ( ( ord_less_int @ A @ B )
| ( A = B ) )
=> ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(344,axiom,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_mult__2) ).
thf(1920,plain,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(497,axiom,
! [A: $i] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_nat__mult__2) ).
thf(2477,plain,
! [A: $i] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__eq__number__of__int__code) ).
thf(2872,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_zmult__assoc) ).
thf(2200,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_power__le__imp__le__exp) ).
thf(1159,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( zcong @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_zcong__refl) ).
thf(757,plain,
! [A: $i,B: $i] : ( zcong @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_power__less__power__Suc) ).
thf(1407,plain,
! [A: $i,B: $i] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1281,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
<=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_power__increasing__iff) ).
thf(1573,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) )
& ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(80,axiom,
! [A: $i] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1012,plain,
! [A: $i] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(360,axiom,
! [A: $i] :
( ( times_times_int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_mult__Pls) ).
thf(1968,plain,
! [A: $i] :
( ( times_times_int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ A @ B )
<=> ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(879,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) )
& ( ( ( ord_less_eq_int @ A @ B )
& ( A != B ) )
=> ( ord_less_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(553,axiom,
! [A: $i] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__special_I3_J) ).
thf(2663,plain,
! [A: $i] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
=> ( ord_less_eq_int @ A @ pls ) )
& ( ( ord_less_eq_int @ A @ pls )
=> ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_realpow__pos__nth) ).
thf(1555,plain,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(463,axiom,
? [A: $i] :
( ( is_int @ A )
& ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306__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(2332,plain,
? [A: $i] :
( ( is_int @ A )
& ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ B @ ( plus_plus_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)],[463]) ).
thf(601,axiom,
! [A: $i] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_power__one) ).
thf(2826,plain,
! [A: $i] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_self__quotient__aux2) ).
thf(2820,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(385,axiom,
! [A: $i,B: $i] : ( zcong @ A @ B @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_zcong__1) ).
thf(2068,plain,
! [A: $i,B: $i] : ( zcong @ A @ B @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(259,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A = zero_zero_int )
| ( A = one_one_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_int__pos__lt__two__imp__zero__or__one) ).
thf(1624,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( 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)],[259]) ).
thf(515,axiom,
! [A: $i] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_diff__bin__simps_I4_J) ).
thf(2547,plain,
! [A: $i] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(457,axiom,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).
thf(2313,plain,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( dvd_dvd_int @ A @ B )
=> ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_zdvd__antisym__nonneg) ).
thf(1128,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( dvd_dvd_int @ A @ B )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_number__of__mult) ).
thf(2100,plain,
! [A: $i,B: $i] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_power__increasing) ).
thf(948,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( plus_plus_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) )
!= ( plus_plus_real @ ( times_times_real @ C @ B ) @ ( times_times_real @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_crossproduct__noteq) ).
thf(1328,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C != D )
& ( A != B ) )
=> ( ( plus_plus_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) )
!= ( plus_plus_real @ ( times_times_real @ C @ B ) @ ( times_times_real @ D @ A ) ) ) )
& ( ( ( plus_plus_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) )
!= ( plus_plus_real @ ( times_times_real @ C @ B ) @ ( times_times_real @ D @ A ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( A
= ( plus_plus_real @ A @ B ) )
<=> ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_add__0__iff) ).
thf(1096,plain,
! [A: $i,B: $i] :
( ( ( A
= ( plus_plus_real @ A @ B ) )
=> ( B = zero_zero_real ) )
& ( ( B = zero_zero_real )
=> ( A
= ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_zcong__scalar) ).
thf(2724,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ C @ B ) @ E )
<=> ( zcong @ A @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_zcong__zmult__prop1) ).
thf(3237,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( ( zcong @ A @ ( times_times_int @ C @ B ) @ E )
=> ( zcong @ A @ ( times_times_int @ D @ B ) @ E ) )
& ( ( zcong @ A @ ( times_times_int @ D @ B ) @ E )
=> ( zcong @ A @ ( times_times_int @ C @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_power__mult__distrib) ).
thf(1350,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(348,axiom,
ord_less_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_rel__simps_I6_J) ).
thf(1936,plain,
ord_less_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__number__of__eq) ).
thf(3105,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(248,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( zprime @ A )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_prime__g__5) ).
thf(1592,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( zprime @ A )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(7,axiom,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(742,plain,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(410,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).
thf(2157,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(606,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ pls )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add__Pls__right) ).
thf(2840,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ pls )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) )
<=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_sum__squares__gt__zero__iff) ).
thf(1270,plain,
! [A: $i,B: $i] :
( ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) )
=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) )
& ( ( ( A != zero_zero_real )
| ( B != zero_zero_real ) )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1851,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ord_less_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_power__strict__decreasing) ).
thf(1259,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ord_less_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(653,axiom,
! [A: $i] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_rel__simps_I22_J) ).
thf(2990,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq_int @ pls @ A ) )
& ( ( ord_less_eq_int @ pls @ A )
=> ( ord_less_eq_int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(305,axiom,
! [A: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__special_I3_J) ).
thf(1794,plain,
! [A: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(558,axiom,
! [A: $i] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_rel__simps_I9_J) ).
thf(2685,plain,
! [A: $i] :
( ( ( ord_less_int @ min @ ( bit1 @ A ) )
=> ( ord_less_int @ min @ A ) )
& ( ( ord_less_int @ min @ A )
=> ( ord_less_int @ min @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(567,axiom,
! [A: $i] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_double__number__of__Bit0) ).
thf(2709,plain,
! [A: $i] :
( ( times_times_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)],[567]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1227,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(331,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(1878,plain,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(573,axiom,
! [A: $i] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_mult__2) ).
thf(2726,plain,
! [A: $i] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( power_power_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_zpower__zdvd__prop1) ).
thf(2638,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( power_power_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( zcong @ A @ B @ zero_zero_int )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_IntPrimes_Ozcong__zero) ).
thf(1118,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( zcong @ A @ B @ zero_zero_int )
=> ( A = B ) )
& ( ( A = B )
=> ( zcong @ A @ B @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
<=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_power__strict__increasing__iff) ).
thf(3001,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_nat @ A @ B ) )
& ( ( ord_less_nat @ A @ B )
=> ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_dvd__power__le) ).
thf(989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(700,axiom,
! [A: $i] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_rel__simps_I4_J) ).
thf(3176,plain,
! [A: $i] :
( ( ( ord_less_int @ pls @ ( bit0 @ A ) )
=> ( ord_less_int @ pls @ A ) )
& ( ( ord_less_int @ pls @ A )
=> ( ord_less_int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(191,axiom,
is_int @ s1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s1____) ).
thf(1397,plain,
is_int @ s1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(239,axiom,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1567,plain,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_divides__ge) ).
thf(1493,plain,
! [A: $i,B: $i] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_power__mult) ).
thf(1082,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_order__le__neq__implies__less) ).
thf(1361,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
<=> ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_real__mult__le__cancel__iff2) ).
thf(1182,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ B ) )
& ( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3094,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ B @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_power__Suc__less) ).
thf(1584,plain,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ B @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(309,axiom,
! [A: $i] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_rel__simps_I8_J) ).
thf(1810,plain,
! [A: $i] :
( ( ( ord_less_int @ min @ ( bit0 @ A ) )
=> ( ord_less_int @ min @ A ) )
& ( ( ord_less_int @ min @ A )
=> ( ord_less_int @ min @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(704,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_rel__simps_I44_J) ).
thf(3194,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_power__eq__imp__eq__base) ).
thf(1207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(649,axiom,
! [A: $i,B: $i] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_arith__simps_I32_J) ).
thf(2978,plain,
! [A: $i,B: $i] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_nat__number__of__mult__left) ).
thf(3141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_plus__numeral__code_I9_J) ).
thf(2877,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_pos__zmult__eq__1__iff__lemma) ).
thf(1964,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( 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)],[359]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_zero__less__power) ).
thf(1942,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_power__strict__mono) ).
thf(753,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2561,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_not__real__square__gt__zero) ).
thf(901,plain,
! [A: $i] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(482,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_zadd__0__right) ).
thf(2419,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
<=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_power__increasing__iff) ).
thf(1075,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) )
& ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(381,axiom,
! [A: $i,B: $i] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_zero__le__even__power_H) ).
thf(2053,plain,
! [A: $i,B: $i] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(422,axiom,
is_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
thf(2196,plain,
is_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_times__numeral__code_I5_J) ).
thf(1842,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
<=> ( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_le__nat__number__of) ).
thf(3032,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
=> ( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ pls ) ) )
& ( ( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ pls ) )
=> ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( times_times_real @ ( number267125858f_real @ B ) @ C ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_mult__number__of__left) ).
thf(1937,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( times_times_real @ ( number267125858f_real @ B ) @ C ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(335,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_zmult__1__right) ).
thf(1889,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(264,axiom,
! [A: $i] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_number__of__Bit0) ).
thf(1644,plain,
! [A: $i] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_real__add__left__mono) ).
thf(837,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1451,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_power__dvd__imp__le) ).
thf(1382,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( ( B = zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= ( plus_plus_nat @ A @ ( times_times_nat @ ( minus_minus_nat @ B @ one_one_nat ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_mult__eq__if) ).
thf(1131,plain,
! [A: $i,B: $i] :
( ( ( B = zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= ( plus_plus_nat @ A @ ( times_times_nat @ ( minus_minus_nat @ B @ one_one_nat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( legendre @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Residues_OLegendre) ).
thf(1552,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( legendre @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(353,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_bin__less__0__simps_I4_J) ).
thf(1947,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
=> ( ord_less_int @ A @ zero_zero_int ) )
& ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(283,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(1715,plain,
ord_less_eq_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_power__strict__increasing) ).
thf(3064,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(445,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_mult__numeral__1) ).
thf(2272,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_crossproduct__noteq) ).
thf(1297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C != D )
& ( A != B ) )
=> ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) )
& ( ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_less__eq__int__code_I15_J) ).
thf(3126,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( ( number_number_of_nat @ A )
= B )
<=> ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_number__of__reorient) ).
thf(2387,plain,
! [A: $i,B: $i] :
( ( ( ( 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)],[477]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_zadd__left__mono) ).
thf(1831,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(92,axiom,
! [A: $i] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_power__one) ).
thf(1060,plain,
! [A: $i] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(527,axiom,
! [A: $i,B: $i] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__sum) ).
thf(2581,plain,
! [A: $i,B: $i] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(2465,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_order__le__neq__implies__less) ).
thf(984,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ one_one_real @ B )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_one__le__power) ).
thf(911,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ one_one_real @ B )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_zprime__power__zdvd__cancel__right) ).
thf(2505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ( power_power_int @ A @ B )
= ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_power__eq__imp__eq__base) ).
thf(1429,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ( power_power_int @ A @ B )
= ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(613,axiom,
( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(2862,plain,
( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_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)],[613]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( times_times_int @ B @ A )
= one_one_int )
<=> ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_pos__zmult__eq__1__iff) ).
thf(2766,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( ( times_times_int @ B @ A )
= one_one_int )
=> ( ( B = one_one_int )
& ( A = one_one_int ) ) )
& ( ( ( B = one_one_int )
& ( A = one_one_int ) )
=> ( ( times_times_int @ B @ A )
= one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ B @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_Euler_Oaux1) ).
thf(1599,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ B @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(260,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
<=> ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_double__eq__0__iff) ).
thf(1627,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( ( plus_plus_int @ A @ A )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of_int @ min ) @ B )
=> ~ ( zcong @ A @ one_one_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_zcong__neg__1__impl__ne__1) ).
thf(2370,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of_int @ min ) @ B )
=> ~ ( zcong @ A @ one_one_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(324,axiom,
~ ( ord_less_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_rel__simps_I3_J) ).
thf(1857,plain,
~ ( ord_less_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(300,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Bit0__Pls) ).
thf(1779,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(278,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(1695,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(3173,plain,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(16,axiom,
ord_less_eq_int @ min @ min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_rel__simps_I24_J) ).
thf(765,plain,
ord_less_eq_int @ min @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(471,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_one__add__one__is__two) ).
thf(2368,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( plus_plus_real @ A @ ( times_times_real @ B @ A ) )
= ( times_times_real @ ( plus_plus_real @ B @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1187,plain,
! [A: $i,B: $i] :
( ( plus_plus_real @ A @ ( times_times_real @ B @ A ) )
= ( times_times_real @ ( plus_plus_real @ B @ one_one_real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_real )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_even__power__le__0__imp__0) ).
thf(2617,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( 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)],[540]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ord_less_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_power__strict__decreasing) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ord_less_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_left__distrib__number__of) ).
thf(773,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_real__le__antisym) ).
thf(888,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(590,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_pos__zmult__pos) ).
thf(2788,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(168,axiom,
! [A: $i] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_double__eq__0__iff) ).
thf(1318,plain,
! [A: $i] :
( ( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( ( plus_plus_real @ A @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_power__strict__increasing) ).
thf(1202,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_mult__nat__number__of) ).
thf(2203,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(592,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_zadd__0) ).
thf(2793,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ one_one_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_self__quotient__aux1) ).
thf(1663,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ one_one_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_power__eq__0__iff) ).
thf(1026,plain,
! [A: $i,B: $i] :
( ( ( ( power_power_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) )
=> ( ( power_power_real @ A @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_diff__bin__simps_I7_J) ).
thf(1895,plain,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(548,axiom,
! [A: $i] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_le__imp__0__less) ).
thf(2645,plain,
! [A: $i] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(420,axiom,
! [A: $i] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_even__less__0__iff) ).
thf(2189,plain,
! [A: $i] :
( ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
=> ( ord_less_int @ A @ zero_zero_int ) )
& ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(654,axiom,
! [A: $i] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_odd__nonzero) ).
thf(2995,plain,
! [A: $i] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(451,axiom,
! [A: $i] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_semiring__mult__2) ).
thf(2292,plain,
! [A: $i] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_power__add) ).
thf(1483,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ ( power_power_int @ B @ C ) @ one_one_int @ D )
=> ( zcong @ ( power_power_int @ B @ ( times_times_nat @ C @ A ) ) @ one_one_int @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_zcong__zpower__zmult) ).
thf(2941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ ( power_power_int @ B @ C ) @ one_one_int @ D )
=> ( zcong @ ( power_power_int @ B @ ( times_times_nat @ C @ A ) ) @ one_one_int @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_zero__less__power) ).
thf(856,plain,
! [A: $i,B: $i] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(8,axiom,
! [A: $i] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(745,plain,
! [A: $i] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(687,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( 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/sandbox/benchmark/theBenchmark.p',fact_547_zmult__eq__1__iff) ).
thf(3111,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( 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 ) ) ) )
=> ( ( times_times_int @ A @ B )
= one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( zcong @ A @ one_one_int @ B )
| ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_zcong__square) ).
thf(2524,plain,
! [A: $i,B: $i] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( zcong @ A @ one_one_int @ B )
| ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rel__simps_I31_J) ).
thf(2121,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(2144,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(633,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_semiring__norm_I112_J) ).
thf(2936,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(574,axiom,
! [A: $i,B: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_sum__squares__ge__zero) ).
thf(2729,plain,
! [A: $i,B: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ C @ ( times_times_real @ ( times_times_real @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(965,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ C @ ( times_times_real @ ( times_times_real @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
<=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_power__strict__increasing__iff) ).
thf(750,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) )
& ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_power2__le__imp__le) ).
thf(2556,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
<=> ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_less__bin__lemma) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) )
& ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(446,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rel__simps_I2_J) ).
thf(2275,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( is_int @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Power_Opower__class_Opower_000tc__Int__Oint) ).
thf(2033,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( is_int @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( twoSqu142715416sum2sq @ B )
=> ( ( twoSqu142715416sum2sq @ A )
=> ( twoSqu142715416sum2sq @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq) ).
thf(2149,plain,
! [A: $i,B: $i] :
( ( twoSqu142715416sum2sq @ B )
=> ( ( twoSqu142715416sum2sq @ A )
=> ( twoSqu142715416sum2sq @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(143,axiom,
! [A: $i] : ( is_int @ ( twoSqu140629262sum2sq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_TwoSquares__Mirabelle__ccrtsbwhjp_Osum2sq) ).
thf(1219,plain,
! [A: $i] : ( is_int @ ( twoSqu140629262sum2sq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
<=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_nat__power__eq__0__iff) ).
thf(824,plain,
! [A: $i,B: $i] :
( ( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) )
& ( ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( power_power_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(376,axiom,
! [A: $i] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_rel__simps_I21_J) ).
thf(2028,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
=> ( ord_less_eq_int @ pls @ A ) )
& ( ( ord_less_eq_int @ pls @ A )
=> ( ord_less_eq_int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(249,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_nat__1__add__1) ).
thf(1595,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2894,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ C @ A @ B )
=> ( C = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_zcong__zless__imp__eq) ).
thf(1374,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ C @ A @ B )
=> ( C = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(120,axiom,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1154,plain,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_int @ ( power_power_int @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_power__le__dvd) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_int @ ( power_power_int @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(431,axiom,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_pos2) ).
thf(2225,plain,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(3240,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ ( times_times_int @ B @ A ) )
= ( times_times_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2849,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ ( times_times_int @ B @ A ) )
= ( times_times_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(678,axiom,
! [A: $i] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_diff__bin__simps_I6_J) ).
thf(3086,plain,
! [A: $i] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ~ ( zcong @ B @ zero_zero_int @ C )
& ~ ( zcong @ A @ zero_zero_int @ C ) )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_zcong__zprime__prod__zero__contra) ).
thf(1652,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ~ ( zcong @ B @ zero_zero_int @ C )
& ~ ( zcong @ A @ zero_zero_int @ C ) )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(556,axiom,
! [A: $i] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_rel__simps_I45_J) ).
thf(2674,plain,
! [A: $i] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(188,axiom,
is_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_t____) ).
thf(1388,plain,
is_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(229,axiom,
is_int @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s____) ).
thf(1535,plain,
is_int @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_power__less__imp__less__base) ).
thf(1124,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(561,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_int__0__neq__1) ).
thf(2695,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(404,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_rel__simps_I16_J) ).
thf(2134,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(716,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_add__numeral__0__right) ).
thf(3234,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(380,axiom,
! [A: $i] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_odd__less__0) ).
thf(2048,plain,
! [A: $i] :
( ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
=> ( ord_less_int @ A @ zero_zero_int ) )
& ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(612,axiom,
! [A: $i] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2859,plain,
! [A: $i] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(634,axiom,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Bit0__def) ).
thf(2938,plain,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(302,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(1784,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_le__number__of) ).
thf(1389,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(419,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I19_J) ).
thf(2188,plain,
ord_less_eq_int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(650,axiom,
! [A: $i] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_power3__eq__cube) ).
thf(2981,plain,
! [A: $i] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1139,plain,
! [A: $i,B: $i] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ B ) ) )
<=> ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_zero__less__power__nat__eq__number__of) ).
thf(1669,plain,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ B ) ) )
=> ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) )
& ( ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(936,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(578,axiom,
! [A: $i] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__special_I2_J) ).
thf(2738,plain,
! [A: $i] :
( ( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
=> ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less_eq_int @ ( bit1 @ pls ) @ A )
=> ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
<=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_power__increasing__iff) ).
thf(1997,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) )
& ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(489,axiom,
! [A: $i] :
( ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= one_one_int )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( number_number_of_int @ min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_neg__one__power) ).
thf(2442,plain,
! [A: $i] :
( ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= one_one_int )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( number_number_of_int @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add1__zle__eq) ).
thf(2055,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(484,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_bin__less__0__simps_I1_J) ).
thf(2425,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
<=> ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_real__mult__le__cancel__iff1) ).
thf(1224,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
=> ( ord_less_eq_real @ A @ B ) )
& ( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2308,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( 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/sandbox/benchmark/theBenchmark.p',fact_578_power__eq__0__iff__number__of) ).
thf(3077,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( ( 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 ) )
=> ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_zspecial__product) ).
thf(3091,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(208,axiom,
! [A: $i] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_power__0) ).
thf(1464,plain,
! [A: $i] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(460,axiom,
! [A: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_rel__simps_I30_J) ).
thf(2319,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
=> ( ord_less_eq_int @ A @ min ) )
& ( ( ord_less_eq_int @ A @ min )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_le__number__of__eq__not__less) ).
thf(1356,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
=> ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) ) )
& ( ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
=> ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_eq__number__of) ).
thf(2510,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( 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)],[505]) ).
thf(456,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_semiring__one__add__one__is__two) ).
thf(2311,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2521,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(428,axiom,
! [A: $i] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_rel__simps_I26_J) ).
thf(2214,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
=> ( ord_less_eq_int @ min @ A ) )
& ( ( ord_less_eq_int @ min @ A )
=> ( ord_less_eq_int @ min @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_sum__squares__le__zero__iff) ).
thf(2774,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int )
=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) )
& ( ( ( A = zero_zero_int )
& ( B = zero_zero_int ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(626,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_rel__simps_I12_J) ).
thf(2906,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ pls )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(347,axiom,
! [A: $i] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_mult__2__right) ).
thf(1933,plain,
! [A: $i] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(640,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint) ).
thf(2955,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(399,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( power_power_int @ A @ one_one_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_power__one__right) ).
thf(2116,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( power_power_int @ A @ one_one_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(571,axiom,
! [A: $i] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power2__eq__square__number__of) ).
thf(2721,plain,
! [A: $i] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_power__less__imp__less__base) ).
thf(2119,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(409,axiom,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: $i,B: $i] :
( ( is_int @ A )
& ( is_int @ B )
& ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ),
file('/export/starexec/sandbox/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(2151,plain,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: $i,B: $i] :
( ( is_int @ A )
& ( is_int @ B )
& ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(547,axiom,
! [A: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__special_I2_J) ).
thf(2642,plain,
! [A: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_add__Bit1__Bit0) ).
thf(2229,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(481,axiom,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_rel__simps_I46_J) ).
thf(2415,plain,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(652,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_semiring__mult__number__of) ).
thf(2987,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_power__inject__exp) ).
thf(784,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(483,axiom,
! [A: $i] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_power2__eq__square) ).
thf(2422,plain,
! [A: $i] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(298,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_rel__simps_I37_J) ).
thf(1771,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(636,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(2943,plain,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(637,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
<=> ( ord_less_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_rel__simps_I13_J) ).
thf(2945,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ min )
=> ( ord_less_int @ A @ min ) )
& ( ( ord_less_int @ A @ min )
=> ( ord_less_int @ ( bit1 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(595,axiom,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307__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(2802,plain,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(3138,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(675,axiom,
! [A: $i] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(3066,plain,
! [A: $i] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(624,axiom,
! [A: $i] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_eq__0__number__of) ).
thf(2896,plain,
! [A: $i] :
( ( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
=> ( ord_less_eq_int @ A @ pls ) )
& ( ( ord_less_eq_int @ A @ pls )
=> ( zero_zero_nat
= ( number_number_of_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( times_times_int @ ( number_number_of_int @ B ) @ C ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mult__number__of__left) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( times_times_int @ ( number_number_of_int @ B ) @ C ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_power__Suc__less) ).
thf(1307,plain,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(418,axiom,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_power__0__left) ).
thf(2180,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(27,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( zprime @ A )
<=> ( ( ord_less_int @ one_one_int @ A )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_zprime__def) ).
thf(811,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( zprime @ A )
=> ( ( ord_less_int @ one_one_int @ A )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ) )
& ( ( ( ord_less_int @ one_one_int @ A )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) )
=> ( zprime @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_real @ ( power_power_real @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_power__le__dvd) ).
thf(1080,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_real @ ( power_power_real @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(665,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_rel__simps_I10_J) ).
thf(3027,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ pls )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(397,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_zero__power2) ).
thf(2111,plain,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(368,axiom,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(1993,plain,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(444,axiom,
! [A: $i] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_le__special_I1_J) ).
thf(2267,plain,
! [A: $i] :
( ( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
=> ( ord_less_eq_int @ pls @ A ) )
& ( ( ord_less_eq_int @ pls @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(341,axiom,
! [A: $i] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1909,plain,
! [A: $i] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(34,axiom,
! [A: $i] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(848,plain,
! [A: $i] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(169,axiom,
! [A: $i] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1325,plain,
! [A: $i] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(493,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_number__of__Pls) ).
thf(2461,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_zadd__zmult__distrib2) ).
thf(2911,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_mult__Bit0) ).
thf(2578,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(690,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_power__less__power__Suc) ).
thf(3133,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_nat__power__less__imp__less) ).
thf(858,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(458,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_t) ).
thf(2314,plain,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_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)],[458]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
<=> ( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ pls @ B ) )
& ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_less__nat__number__of) ).
thf(2343,plain,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
=> ( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ pls @ B ) )
& ( ord_less_int @ A @ B ) ) )
& ( ( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ pls @ B ) )
& ( ord_less_int @ A @ B ) )
=> ( ord_less_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(289,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_rel__simps_I38_J) ).
thf(1731,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_left__distrib__number__of) ).
thf(2785,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_power2__le__imp__le) ).
thf(2593,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(658,axiom,
! [A: $i] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_zero__eq__power2) ).
thf(3006,plain,
! [A: $i] :
( ( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(513,axiom,
( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(2542,plain,
( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(549,axiom,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_rel__simps_I39_J) ).
thf(2647,plain,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(354,axiom,
! [A: $i] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_le__special_I1_J) ).
thf(1952,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
=> ( ord_less_eq_int @ pls @ A ) )
& ( ( ord_less_eq_int @ pls @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_power2__sum) ).
thf(3150,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(462,axiom,
! [A: $i] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_diff__bin__simps_I3_J) ).
thf(2329,plain,
! [A: $i] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_zcong__trans) ).
thf(1171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_right__distrib__number__of) ).
thf(2075,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(488,axiom,
! [A: $i] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_double__number__of__Bit0) ).
thf(2439,plain,
! [A: $i] :
( ( times_times_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)],[488]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ A @ ( times_times_real @ B @ ( times_times_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ A @ ( times_times_real @ B @ ( times_times_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_power__mult__distrib) ).
thf(1699,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ A )
= ( times_times_nat @ A @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_power__commutes) ).
thf(1213,plain,
! [A: $i,B: $i] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ A )
= ( times_times_nat @ A @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_zcong__zpower) ).
thf(2550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( C != D )
& ( A != B ) )
<=> ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_crossproduct__noteq) ).
thf(2086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( ( C != D )
& ( A != B ) )
=> ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) )
& ( ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(405,axiom,
! [A: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rel__simps_I29_J) ).
thf(2139,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_power__mult) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(128,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_real__zero__not__eq__one) ).
thf(1176,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1113,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(211,axiom,
! [A: $i] : ( zcong @ A @ zero_zero_int @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_zcong__id) ).
thf(1477,plain,
! [A: $i] : ( zcong @ A @ zero_zero_int @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ B )
= ( times_times_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1496,plain,
! [A: $i,B: $i] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ B )
= ( times_times_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(851,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_dvd__power__same) ).
thf(2999,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ one_one_real @ A )
=> ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_power__strict__increasing) ).
thf(1562,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ one_one_real @ A )
=> ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(427,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_semiring__numeral__0__eq__0) ).
thf(2212,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ ( times_times_nat @ B @ A ) )
= ( times_times_nat @ ( plus_plus_nat @ B @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(959,plain,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ ( times_times_nat @ B @ A ) )
= ( times_times_nat @ ( plus_plus_nat @ B @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_number__of__add) ).
thf(2244,plain,
! [A: $i,B: $i] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
<=> ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_crossproduct__eq) ).
thf(1000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( A = C )
| ( B = D ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(287,axiom,
! [A: $i] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1726,plain,
! [A: $i] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
<=> ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_real__le__eq__diff) ).
thf(1364,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) )
& ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real )
=> ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_power__mono) ).
thf(2967,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_sum__squares__le__zero__iff) ).
thf(1250,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(277,axiom,
zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_s1) ).
thf(1694,plain,
zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(560,axiom,
! [A: $i,B: $i] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_sum__power2__ge__zero) ).
thf(2693,plain,
! [A: $i,B: $i] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(651,axiom,
! [A: $i] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_power2__eq__square) ).
thf(2984,plain,
! [A: $i] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) )
=> ( ( dvd_dvd_int @ B @ C )
| ( dvd_dvd_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_zprime__zdvd__zmult) ).
thf(1973,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) )
=> ( ( dvd_dvd_int @ B @ C )
| ( dvd_dvd_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(308,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_bin__less__0__simps_I3_J) ).
thf(1805,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
=> ( ord_less_int @ A @ zero_zero_int ) )
& ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_dvd__power__same) ).
thf(722,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(436,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OBit1) ).
thf(2239,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_rel__simps_I49_J) ).
thf(2914,plain,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(329,axiom,
! [A: $i] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_semiring__mult__2__right) ).
thf(1873,plain,
! [A: $i] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( A
= ( plus_plus_nat @ A @ B ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_add__0__iff) ).
thf(1467,plain,
! [A: $i,B: $i] :
( ( ( A
= ( plus_plus_nat @ A @ B ) )
=> ( B = zero_zero_nat ) )
& ( ( B = zero_zero_nat )
=> ( A
= ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(707,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_p0) ).
thf(3206,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_power__even__eq) ).
thf(1990,plain,
! [A: $i,B: $i] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_nat @ C @ ( times_times_nat @ E @ A ) )
!= ( plus_plus_nat @ D @ ( times_times_nat @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_add__scale__eq__noteq) ).
thf(968,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_nat @ C @ ( times_times_nat @ E @ A ) )
!= ( plus_plus_nat @ D @ ( times_times_nat @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1049,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(393,axiom,
! [A: $i] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_rel__simps_I42_J) ).
thf(2096,plain,
! [A: $i] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_zcong__scalar2) ).
thf(1758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ A @ B @ C )
<=> ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_zcong__def) ).
thf(1166,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ A @ B @ C )
=> ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) )
& ( ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) )
=> ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_real__mult__right__cancel) ).
thf(939,plain,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_real )
=> ( ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( zcong @ A @ zero_zero_int @ B )
<=> ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_zcong__eq__zdvd__prop) ).
thf(1340,plain,
! [A: $i,B: $i] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( dvd_dvd_int @ B @ A ) )
& ( ( dvd_dvd_int @ B @ A )
=> ( zcong @ A @ zero_zero_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_zero__le__power) ).
thf(1145,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__number__of__int__code) ).
thf(2564,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(608,axiom,
( ~ ( quadRes @ ( plus_plus_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 ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
!= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(2846,plain,
( ~ ( quadRes @ ( plus_plus_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 ) @ ( plus_plus_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)],[608]) ).
thf(82,axiom,
! [A: $i] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1018,plain,
! [A: $i] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(533,axiom,
( ( ord_less_eq_int @ zero_zero_int @ s )
& ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_s0p) ).
thf(2597,plain,
( ( ord_less_eq_int @ zero_zero_int @ s )
& ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(356,axiom,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_zero__power2) ).
thf(1958,plain,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(319,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_semiring__norm_I110_J) ).
thf(1845,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_zdiff__power2) ).
thf(2298,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_add__Bit0__Bit0) ).
thf(2715,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1070,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__int__code_I13_J) ).
thf(2375,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_add__Bit0__Bit1) ).
thf(2060,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ B @ C ) ) @ D ) @ ( times_times_int @ ( minus_minus_int @ E @ ( times_times_int @ B @ F ) ) @ G ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ E @ G ) ) @ ( times_times_int @ B @ ( plus_plus_int @ ( times_times_int @ C @ D ) @ ( times_times_int @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_xzgcda__linear__aux1) ).
thf(3214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ B @ C ) ) @ D ) @ ( times_times_int @ ( minus_minus_int @ E @ ( times_times_int @ B @ F ) ) @ G ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ E @ G ) ) @ ( times_times_int @ B @ ( plus_plus_int @ ( times_times_int @ C @ D ) @ ( times_times_int @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(253,axiom,
! [A: $i] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rel__simps_I5_J) ).
thf(1605,plain,
! [A: $i] :
( ( ( ord_less_int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq_int @ pls @ A ) )
& ( ( ord_less_eq_int @ pls @ A )
=> ( ord_less_int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(265,axiom,
! [A: $i] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
<=> ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_less__special_I4_J) ).
thf(1647,plain,
! [A: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
=> ( ord_less_int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less_int @ A @ ( bit1 @ pls ) )
=> ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_zprime__zdvd__power) ).
thf(3209,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( times_times_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1267,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( times_times_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_power__mono) ).
thf(1230,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(619,axiom,
! [A: $i] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_two__realpow__ge__one) ).
thf(2882,plain,
! [A: $i] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_divides__exp) ).
thf(993,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( zcong @ A @ zero_zero_int @ B )
<=> ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_zcong__zero__equiv__div) ).
thf(1547,plain,
! [A: $i,B: $i] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( dvd_dvd_int @ B @ A ) )
& ( ( dvd_dvd_int @ B @ A )
=> ( zcong @ A @ zero_zero_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_power__gt1__lemma) ).
thf(776,plain,
! [A: $i,B: $i] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_Legendre__def) ).
thf(1748,plain,
! [A: $i,B: $i] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(6,axiom,
! [A: $i] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_power__one) ).
thf(739,plain,
! [A: $i] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(557,axiom,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_power__0__left__number__of) ).
thf(2678,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_arith__simps_I32_J) ).
thf(2518,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(523,axiom,
! [A: $i,B: $i] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_not__sum__squares__lt__zero) ).
thf(2569,plain,
! [A: $i,B: $i] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( ( ord_less_int @ B @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__nat__number__of) ).
thf(2920,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ B @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(563,axiom,
ord_less_eq_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_rel__simps_I23_J) ).
thf(2700,plain,
ord_less_eq_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
| ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_zdvd__bounds) ).
thf(1038,plain,
! [A: $i,B: $i] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
| ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_zdiff__power3) ).
thf(1785,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ A @ B )
<=> ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_real__less__def) ).
thf(1235,plain,
! [A: $i,B: $i] :
( ( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) )
& ( ( ( ord_less_eq_real @ A @ B )
& ( A != B ) )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_zmult__commute) ).
thf(1763,plain,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_power__eq__if) ).
thf(1085,plain,
! [A: $i,B: $i] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( ( 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/sandbox/benchmark/theBenchmark.p',fact_576_power__eq__0__iff__number__of) ).
thf(2468,plain,
! [A: $i,B: $i] :
( ( ( ( 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 ) )
=> ( ( power_power_real @ A @ ( number_number_of_nat @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(551,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ B @ one_one_int ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_zcong__square__zless) ).
thf(2656,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ B @ one_one_int ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_semiring__add__number__of) ).
thf(3019,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( number_number_of_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_right__distrib__number__of) ).
thf(2747,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( number_number_of_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(220,axiom,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1499,plain,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_less__eq__int__code_I14_J) ).
thf(1716,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(430,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_s) ).
thf(2224,plain,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_nat ) )
=> ( dvd_dvd_nat @ A @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_dvd__power) ).
thf(1432,plain,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_nat ) )
=> ( dvd_dvd_nat @ A @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(413,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_semiring__norm_I110_J) ).
thf(2165,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(429,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J) ).
thf(2219,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint) ).
thf(1980,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_power2__eq__imp__eq) ).
thf(2701,plain,
! [A: $i,B: $i] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(625,axiom,
! [A: $i,B: $i] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_not__sum__power2__lt__zero) ).
thf(2903,plain,
! [A: $i,B: $i] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(808,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(439,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ A @ pls )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_diff__bin__simps_I1_J) ).
thf(2247,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ A @ pls )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(296,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_zmult__1) ).
thf(1766,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_nat__zero__less__power__iff) ).
thf(1536,plain,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) ) )
& ( ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(84,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(1023,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_sum__power2__gt__zero__iff) ).
thf(1702,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( 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 ) )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( number267125858f_real @ A )
= B )
<=> ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_number__of__reorient) ).
thf(1052,plain,
! [A: $i,B: $i] :
( ( ( ( number267125858f_real @ A )
= B )
=> ( B
= ( number267125858f_real @ A ) ) )
& ( ( B
= ( number267125858f_real @ A ) )
=> ( ( number267125858f_real @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1797,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(697,axiom,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_power__0__left__number__of) ).
thf(3156,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(42,axiom,
! [A: $i] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(876,plain,
! [A: $i] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(528,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2584,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ B )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1898,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ B )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(321,axiom,
! [A: $i] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_zero__le__power2) ).
thf(1849,plain,
! [A: $i] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ A @ B ) ) @ ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_mult__sum2sq) ).
thf(2558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ A @ B ) ) @ ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu140629262sum2sq @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(398,axiom,
! [A: $i] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2113,plain,
! [A: $i] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_real__add__mult__distrib) ).
thf(1221,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_divides__antisym) ).
thf(1284,plain,
! [A: $i,B: $i] :
( ( ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(647,axiom,
quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(2975,plain,
quadRes @ ( plus_plus_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)],[647]) ).
thf(176,axiom,
! [A: $i] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1353,plain,
! [A: $i] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_rel__simps_I48_J) ).
thf(2357,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( bit0 @ A )
= ( bit0 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit0 @ A )
= ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_number__of__add) ).
thf(2843,plain,
! [A: $i,B: $i] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_zdvd__not__zless) ).
thf(1372,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_power__strict__decreasing) ).
thf(2892,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_one__less__power) ).
thf(991,plain,
! [A: $i,B: $i] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_Euler_Oaux____1) ).
thf(1617,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_power__gt1__lemma) ).
thf(1940,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power_power_real @ A @ B )
= ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_power__eq__imp__eq__base) ).
thf(845,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power_power_real @ A @ B )
= ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_zadd__commute) ).
thf(2045,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_right__distrib__number__of) ).
thf(931,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_rel__simps_I14_J) ).
thf(2960,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_zcong__zmult__self) ).
thf(2194,plain,
! [A: $i,B: $i,C: $i] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_real__two__squares__add__zero__iff) ).
thf(1517,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_power__le__imp__le__exp) ).
thf(1126,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(579,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_semiring__one__add__one__is__two) ).
thf(2743,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_real__mult__less__mono2) ).
thf(1010,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(326,axiom,
! [A: $i,B: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_sum__power2__ge__zero) ).
thf(1866,plain,
! [A: $i,B: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ A @ B @ C )
<=> ( zcong @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_zcong__sym) ).
thf(1421,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ A @ B @ C )
=> ( zcong @ B @ A @ C ) )
& ( ( zcong @ B @ A @ C )
=> ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(373,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_int__0__less__1) ).
thf(2013,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(343,axiom,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__power2) ).
thf(1918,plain,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_real__le__linear) ).
thf(1316,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_power__less__imp__less__base) ).
thf(1157,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_zle__diff1__eq) ).
thf(2078,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ C ) ) @ ( times_times_nat @ B @ ( number_number_of_nat @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_left__distrib__number__of) ).
thf(1654,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ C ) ) @ ( times_times_nat @ B @ ( number_number_of_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_zcong__eq__trans) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(538,axiom,
! [A: $i] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__special_I2_J) ).
thf(2611,plain,
! [A: $i] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(759,plain,
! [A: $i,B: $i] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(301,axiom,
! [A: $i] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__special_I3_J) ).
thf(1781,plain,
! [A: $i] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1216,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_Int2_Ozcong__zero) ).
thf(891,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(672,axiom,
! [A: $i] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_less__special_I1_J) ).
thf(3056,plain,
! [A: $i] :
( ( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
=> ( ord_less_int @ pls @ A ) )
& ( ( ord_less_int @ pls @ A )
=> ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_zadd__assoc) ).
thf(2226,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ one_one_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ one_one_real @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_one__less__power) ).
thf(1108,plain,
! [A: $i,B: $i] :
( ( ord_less_real @ one_one_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ one_one_real @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_le__number__of) ).
thf(3039,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ E @ zero_zero_int )
=> ( ( ord_less_int @ A @ E )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_unique__quotient__lemma__neg) ).
thf(2591,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ E @ zero_zero_int )
=> ( ( ord_less_int @ A @ E )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(566,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_semiring__one__add__one__is__two) ).
thf(2707,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(1721,plain,
! [A: $i,B: $i] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(414,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_rel__simps_I40_J) ).
thf(2167,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_power__decreasing) ).
thf(748,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(441,axiom,
( ( t = one_one_int )
=> ? [A: $i,B: $i] :
( ( is_int @ A )
& ( is_int @ B )
& ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ),
file('/export/starexec/sandbox/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(2251,plain,
( ( t = one_one_int )
=> ? [A: $i,B: $i] :
( ( is_int @ A )
& ( is_int @ B )
& ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(518,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_one__is__num__one) ).
thf(2554,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_power__inject__exp) ).
thf(1508,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(600,axiom,
! [A: $i] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2823,plain,
! [A: $i] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_power__even__eq) ).
thf(2811,plain,
! [A: $i,B: $i] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(323,axiom,
! [A: $i] :
( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_Legendre__1mod4) ).
thf(1854,plain,
! [A: $i] :
( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_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)],[323]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1244,plain,
! [A: $i,B: $i] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(781,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(510,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_zero__is__num__zero) ).
thf(2526,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ ( times_times_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(995,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ ( times_times_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_power__mult) ).
thf(2608,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ A ) @ ( power_power_int @ ( number_number_of_int @ min ) @ B ) @ C )
=> ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( power_power_int @ ( number_number_of_int @ min ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_neg__one__power__eq__mod__m) ).
thf(2431,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ A ) @ ( power_power_int @ ( number_number_of_int @ min ) @ B ) @ C )
=> ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( power_power_int @ ( number_number_of_int @ min ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ B @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_zcong__not__zero) ).
thf(1491,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ B @ zero_zero_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(276,axiom,
! [A: $i] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_less__special_I2_J) ).
thf(1689,plain,
! [A: $i] :
( ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
=> ( ord_less_int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less_int @ ( bit1 @ pls ) @ A )
=> ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(701,axiom,
! [A: $i] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__special_I2_J) ).
thf(3181,plain,
! [A: $i] :
( ( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
=> ( ord_less_int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less_int @ ( bit1 @ pls ) @ A )
=> ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(593,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2796,plain,
! [A: $i,B: $i] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1294,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(204,axiom,
! [A: $i,B: $i] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_sum__squares__ge__zero) ).
thf(1440,plain,
! [A: $i,B: $i] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_divides__rev) ).
thf(1193,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2162,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(392,axiom,
twoSqu142715416sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(2095,plain,
twoSqu142715416sum2sq @ ( times_times_int @ ( plus_plus_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)],[392]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_power__mono) ).
thf(1161,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_zcong__not) ).
thf(899,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(270,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_zero__power2) ).
thf(1661,plain,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( ( 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/sandbox/benchmark/theBenchmark.p',fact_577_power__eq__0__iff__number__of) ).
thf(2036,plain,
! [A: $i,B: $i] :
( ( ( ( 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 ) )
=> ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_power__less__imp__less__exp) ).
thf(1309,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_q__pos__lemma) ).
thf(2494,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
<=> ( ( B = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_zero__less__power__nat__eq) ).
thf(1442,plain,
! [A: $i,B: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
=> ( ( B = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) )
& ( ( ( B = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_real__le__trans) ).
thf(1116,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ ( number267125858f_real @ B ) @ C ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_add__number__of__left) ).
thf(2930,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ ( number267125858f_real @ B ) @ C ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint) ).
thf(1348,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(1774,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) )
& ( ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) )
<=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_sum__squares__gt__zero__iff) ).
thf(1678,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) )
=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) )
& ( ( ( A != zero_zero_int )
| ( B != zero_zero_int ) )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(683,axiom,
! [A: $i] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_quartic__square__square) ).
thf(3100,plain,
! [A: $i] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zle__trans) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_power__increasing) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(24,axiom,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_power__0__left) ).
thf(790,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(706,axiom,
! [A: $i] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_power__0) ).
thf(3203,plain,
! [A: $i] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_zcong__zless__0) ).
thf(1578,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(355,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(1957,plain,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_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)],[355]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_zero__le__power) ).
thf(950,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_rel__simps_I50_J) ).
thf(2587,plain,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(577,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_Pls__def) ).
thf(2736,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(36,axiom,
! [A: $i] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zle__refl) ).
thf(854,plain,
! [A: $i] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_rel__simps_I15_J) ).
thf(2008,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_power__0__left) ).
thf(865,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1480,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_q__neg__lemma) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(325,axiom,
! [A: $i] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_eq__number__of__0) ).
thf(1859,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ord_less_eq_int @ A @ pls ) )
& ( ( ord_less_eq_int @ A @ pls )
=> ( ( number_number_of_nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( power_power_nat @ A @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_exp__eq__1) ).
thf(918,plain,
! [A: $i,B: $i] :
( ( ( ( power_power_nat @ A @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = one_one_nat )
| ( B = zero_zero_nat ) )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(268,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_add__numeral__0) ).
thf(1657,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__number__of__eq) ).
thf(2704,plain,
! [A: $i,B: $i] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_power__increasing) ).
thf(897,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(282,axiom,
! [A: $i] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_less__special_I1_J) ).
thf(1710,plain,
! [A: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
=> ( ord_less_int @ pls @ A ) )
& ( ( ord_less_int @ pls @ A )
=> ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ C @ B @ A )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ B @ A )
=> ( C = B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_zcong__less__eq) ).
thf(1065,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ C @ B @ A )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ B @ A )
=> ( C = B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(550,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rel__simps_I33_J) ).
thf(2651,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_le__imp__power__dvd) ).
thf(2070,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(524,axiom,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_four__x__squared) ).
thf(2572,plain,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_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)],[524]) ).
thf(465,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_mult__numeral__1__right) ).
thf(2340,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(554,axiom,
! [A: $i] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of) ).
thf(2668,plain,
! [A: $i] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_less__int__code_I15_J) ).
thf(2063,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(254,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ pls @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_add__Pls) ).
thf(1610,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ pls @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_le__imp__power__dvd) ).
thf(886,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(55,axiom,
! [A: $i] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(928,plain,
! [A: $i] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_zdvd__zdiffD) ).
thf(1152,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(345,axiom,
! [A: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__special_I3_J) ).
thf(1923,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
=> ( ord_less_eq_int @ A @ pls ) )
& ( ( ord_less_eq_int @ A @ pls )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(512,axiom,
! [A: $i] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_power2__eq__square) ).
thf(2539,plain,
! [A: $i] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(222,axiom,
! [A: $i] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_power__one__right) ).
thf(1505,plain,
! [A: $i] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(473,axiom,
! [A: $i] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_semiring__mult__2__right) ).
thf(2372,plain,
! [A: $i] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1093,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ E ) )
=> ( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_int @ C @ ( times_times_int @ E @ A ) )
!= ( plus_plus_int @ D @ ( times_times_int @ E @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq) ).
thf(2353,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ E ) )
=> ( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_int @ C @ ( times_times_int @ E @ A ) )
!= ( plus_plus_int @ D @ ( times_times_int @ E @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_real__mult__left__cancel) ).
thf(839,plain,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_real )
=> ( ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(437,axiom,
! [A: $i] :
( ( power_power_real @ ( number267125858f_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_power2__eq__square__number__of) ).
thf(2241,plain,
! [A: $i] :
( ( power_power_real @ ( number267125858f_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_nat @ ( power_power_nat @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_power__le__dvd) ).
thf(987,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( dvd_dvd_nat @ ( power_power_nat @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_zcong__zmult) ).
thf(2731,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zadd__zless__mono) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_zpower__zadd__distrib) ).
thf(1977,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_power__le__imp__le__exp) ).
thf(3025,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1261,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1532,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__number__of) ).
thf(860,plain,
! [A: $i,B: $i] :
( ( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_divides__add__revr) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) )
=> ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_real__sum__squared__expand) ).
thf(2485,plain,
! [A: $i,B: $i] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_power__strict__mono) ).
thf(822,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ F @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_zdiv__mono2__lemma) ).
thf(2507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ F @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(250,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OBit0) ).
thf(1597,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_less__eq__int__code_I13_J) ).
thf(2864,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(659,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_number__of__Pls) ).
thf(3013,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(546,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_semiring__numeral__1__eq__1) ).
thf(2640,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(352,axiom,
! [A: $i] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__mult__2__right) ).
thf(1944,plain,
! [A: $i] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).
thf(1962,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
<=> ( ( A = C )
| ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_crossproduct__eq) ).
thf(1737,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
=> ( ( A = C )
| ( B = D ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(621,axiom,
! [A: $i] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_less__special_I3_J) ).
thf(2887,plain,
! [A: $i] :
( ( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(559,axiom,
! [A: $i] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_add__numeral__0__right) ).
thf(2690,plain,
! [A: $i] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(603,axiom,
! [A: $i,B: $i] :
( ( ord_less_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_power2__less__imp__less) ).
thf(2832,plain,
! [A: $i,B: $i] :
( ( ord_less_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ one_one_nat @ B )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_one__le__power) ).
thf(1416,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ one_one_nat @ B )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(491,axiom,
! [A: $i] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_number__of__Bit1) ).
thf(2453,plain,
! [A: $i] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( plus_plus_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)],[491]) ).
thf(669,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_semiring__numeral__1__eq__1) ).
thf(3047,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(342,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_zero__less__power2) ).
thf(1912,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( A != zero_zero_int ) )
& ( ( A != zero_zero_int )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(297,axiom,
~ ( ord_less_eq_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_rel__simps_I20_J) ).
thf(1769,plain,
~ ( ord_less_eq_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_power__strict__mono) ).
thf(755,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_zcong__shift) ).
thf(2351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(415,axiom,
! [A: $i] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_power__m1__even) ).
thf(2170,plain,
! [A: $i] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(604,axiom,
! [A: $i] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_cube__square) ).
thf(2834,plain,
! [A: $i] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(705,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ A )
= ( times_times_int @ A @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_power__commutes) ).
thf(3200,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ A )
= ( times_times_int @ A @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_power__mult__distrib) ).
thf(1204,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zpower__zpower) ).
thf(1870,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_real @ A @ B )
<=> ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_less__eq__real__def) ).
thf(972,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ A @ B )
| ( A = B ) ) )
& ( ( ( ord_less_real @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(3392,plain,
$false,
inference(cvc4,[status(thm)],[1036,1586,1879,1024,2295,1633,2072,1559,1729,2412,2463,2595,2544,1179,1818,1369,1190,2131,1454,962,1982,2427,2480,2280,1554,1110,1686,2250,2363,2210,1068,2808,2395,3153,2953,1073,3108,873,1591,2380,1971,1437,2976,762,730,1882,2671,2014,2837,1142,1173,1486,3017,3049,3004,3135,2918,3044,2316,2933,1233,2627,913,945,1063,2575,1078,1788,1426,3217,2434,2712,1196,1835,2972,2763,1576,2020,1613,1386,1724,2173,2516,1529,1904,2869,1887,2957,1746,3103,2603,2814,719,2339,2755,3061,1264,3148,1313,934,2126,2745,1409,724,2698,1660,1760,3131,3089,2488,1545,1800,1892,2857,1147,1479,770,1398,2635,1641,1232,1847,2829,2403,1514,1247,2552,2301,1815,2852,3231,2456,2178,2324,2105,2782,1040,2259,3163,1418,1960,1581,1489,2950,2237,2880,834,1928,1377,956,1622,1394,1526,998,3226,2965,3211,2718,981,766,3189,2281,1345,2799,2286,2103,2750,1696,2884,1975,1564,3097,3229,1438,1199,3186,1338,1311,2232,3054,2083,2496,2621,2790,2660,1868,2382,2000,1636,798,1163,2264,894,2601,2733,952,2277,1570,2147,1666,2969,3069,2606,2528,3207,1021,778,3022,1502,1824,1619,2445,2758,1602,2628,1920,2477,2872,2200,1159,1210,757,1407,1281,1573,1012,1968,879,2663,1555,2332,2826,2820,2068,1624,2547,2313,1128,2100,948,1328,1096,2724,3237,1350,1936,3105,1592,742,2157,2840,1270,1851,1259,2990,1794,2685,2709,1227,1878,2726,2638,1118,3001,989,3176,1397,1567,1493,1082,1361,1182,3094,1584,1810,3194,1207,2978,3141,2877,1964,1942,753,2561,901,2419,1075,2053,2196,1842,3032,1937,1889,1644,837,1451,1382,1131,1552,1947,1715,3064,2272,1297,3126,2387,1831,1060,2581,2465,984,911,2505,1429,2862,2766,1599,1627,2370,1857,1779,1695,3173,765,2368,1187,2617,1185,773,888,2788,1318,1202,2203,2793,1663,1026,1895,2645,2189,2995,2292,1483,2941,856,745,3111,2524,2121,2144,2936,2729,965,750,2556,1103,2275,2033,2149,1219,824,2028,1595,2894,1374,1154,1833,2225,3240,2849,3086,1652,2674,1388,1535,1124,2695,2134,3234,2048,2859,2938,1784,1389,2188,2981,1139,1669,936,2738,1997,2442,2055,2425,1224,2308,3077,3091,1464,2319,1356,2510,2311,2521,2214,2774,2906,1933,2955,2116,2721,2119,2151,2642,2229,2415,2987,784,2422,1771,2943,2945,2802,3138,3066,2896,2197,1307,2180,811,1080,3027,2111,1993,2267,1909,848,1325,2461,2911,2578,3133,858,2314,2343,1821,1731,2785,2593,3006,2542,2647,1952,3150,2329,1171,2075,2439,1474,1699,1213,2550,2086,2139,1015,1176,1113,1477,1496,851,2999,1562,2212,959,2244,1000,1726,1364,2967,1250,1694,2693,2984,1973,1805,2005,722,2239,2914,1873,1467,3206,1990,968,1049,2614,2096,1758,1166,939,1340,1145,2564,2846,1018,2597,1958,1845,2298,2715,1070,2375,2060,3214,1605,1647,3209,1267,1230,2882,993,1547,776,1748,739,2678,2518,2569,2920,2700,1038,1785,1235,1763,1901,1085,2468,2656,3019,2747,1499,1716,2224,1432,2165,2219,1980,2701,2903,808,2247,1766,1536,1023,1702,1052,1797,3156,876,2584,1898,1849,2558,2113,1221,1284,2975,1353,2357,2843,1372,2892,991,1617,1940,845,2045,931,2960,2194,1517,1126,2743,1010,1866,1421,2013,1918,1316,1157,2078,1654,1412,2611,759,1781,1216,891,3056,2226,1108,3039,2591,2707,1721,2167,748,2251,2554,1508,2823,2811,1854,1244,781,2526,995,2608,2431,1491,1689,3181,2796,1294,1440,1193,2162,2095,1161,899,1661,2036,1309,2494,1442,1116,2930,1348,1774,1678,3100,1380,1876,790,3203,1578,1957,950,2587,2736,854,2008,865,1480,3015,1859,918,1657,2704,897,1710,1065,2651,2070,2572,2340,2668,2063,1610,886,928,1152,908,1923,2539,1505,2372,1093,2353,839,2241,987,2159,2731,1829,1977,3025,1261,1532,860,1384,2485,822,2507,1597,2864,3013,2640,1944,1962,1737,2887,2690,2832,1416,2453,3047,1912,1769,755,2351,2170,2834,3200,1204,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM926+2 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 16:40:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.69/1.07 % [INFO] Parsing done (226ms).
% 1.69/1.08 % [INFO] Running in sequential loop mode.
% 2.26/1.27 % [INFO] eprover registered as external prover.
% 2.26/1.27 % [INFO] cvc4 registered as external prover.
% 2.26/1.28 % [INFO] Scanning for conjecture ...
% 2.62/1.40 % [INFO] Found a conjecture and 716 axioms. Running axiom selection ...
% 3.13/1.52 % [INFO] Axiom selection finished. Selected 716 axioms (removed 0 axioms).
% 3.84/1.72 % [INFO] Problem is first-order (TPTP FOF).
% 3.84/1.74 % [INFO] Type checking passed.
% 3.84/1.74 % [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 ...
% 17.30/4.55 % External prover 'cvc4' found a proof!
% 17.30/4.55 % [INFO] Killing All external provers ...
% 17.30/4.56 % Time passed: 4029ms (effective reasoning time: 3468ms)
% 17.30/4.56 % 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)>
% 17.30/4.57 % Axioms used in derivation (716): gsy_c_Int_OBit0, fact_78_nat__numeral__1__eq__1, fact_507__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_310_power__eq__0__iff, fact_88_zle__add1__eq__le, fact_490_power__inject__exp, fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_449_power2__less__0, fact_440_zero__eq__power2, fact_7_zadd__power2, fact_204_Bit0__def, fact_279_semiring__mult__2__right, fact_457_power__commutes, fact_329_dvd__power__same, fact_557_zcong__sym, fact_47_zpower__zpower, fact_645_divides__exp2, fact_276_mult__2, fact_563_order__le__neq__implies__less, fact_154_rel__simps_I27_J, fact_153_rel__simps_I32_J, fact_369_zcong__zpower__zmult, fact_255_mult__numeral__1, fact_368_zero__less__power, fact_543_semiring__norm_I113_J, fact_580_zcong__iff__lin, fact_327_dvd__power__same, fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_352_add__0__iff, fact_283_semiring__one__add__one__is__two, fact_428_less__special_I1_J, fact_542_nat__number__of__Pls, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_483_one__le__power, fact_198_Bit0__Pls, fact_679_q__pos__lemma, fact_489_power__inject__exp, fact_653_zcong__zmult__prop3, fact_669_real__mult__left__cancel, fact_321_power__eq__imp__eq__base, fact_144_zadd__left__commute, fact_395_semiring__numeral__0__eq__0, fact_562_mult__nat__number__of, fact_74_less__eq__number__of__int__code, fact_655_zcong__zprime__prod__zero__contra, 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_218_left__distrib__number__of, fact_301_power__increasing__iff, fact_365_power__mono, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_498_power__strict__increasing, fact_681_unique__quotient__lemma, fact_360_zero__le__power, fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_432_le__special_I1_J, fact_514_rel__simps_I43_J, fact_374_power__less__imp__less__base, fact_564_order__le__neq__implies__less, fact_199_mult__Pls, fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_404_power__Suc__less, fact_641_nat__mult__dvd__cancel__disj_H, fact_607_diff__bin__simps_I4_J, fact_627_diff__square, fact_571_zcong__scalar, fact_208_zadd__zmult__distrib, fact_50_le__number__of__eq__not__less, fact_371_zdvd__period, fact_220_left__distrib__number__of, fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_145_zadd__commute, fact_598_number__of__diff, fact_419_number__of__Bit0, fact_246_add__number__of__eq, fact_203_add__Bit0__Bit0, fact_688_real__le__trans, fact_157_power__even__eq, fact_478_not__sum__power2__lt__zero, fact_216_semiring__add__number__of, fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_32_one__add__one__is__two, fact_594_diff__bin__simps_I7_J, fact_532_rel__simps_I23_J, fact_146_rel__simps_I12_J, fact_600_diff__bin__simps_I10_J, fact_622_divides__cases, fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_376_power__decreasing, fact_468_power__mult, fact_614_zspecial__product, fact_551_dvd__power, fact_159_power__even__eq, fact_677_real__two__squares__add__zero__iff, fact_233_add__numeral__0, fact_521_rel__simps_I24_J, fact_455_power__commutes, fact_499_power__strict__increasing, fact_502_Euler_Oaux____1, fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_316_dvd__power__le, fact_73_less__number__of__int__code, fact_586_zprime__zdvd__zmult, fact_210_plus__numeral__code_I9_J, fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_444_power2__le__imp__le, fact_274_semiring__mult__2, fact_9_power2__sum, fact_546_pos__zmult__eq__1__iff__lemma, fact_269_power3__eq__cube, fact_515_Bit1__Min, fact_71_less__eq__int__code_I13_J, fact_373_power__less__imp__less__base, fact_169_crossproduct__eq, fact_463_power__add, fact_626_power__eq__if, fact_628_divides__add__revr, fact_553_dvd__power, fact_265_one__is__num__one, fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_272_quartic__square__square, fact_680_q__neg__lemma, fact_625_mult__eq__if, fact_516_rel__simps_I37_J, fact_256_mult__numeral__1__right, fact_504_even__power__le__0__imp__0, fact_661_real__zero__not__eq__one, fact_525_rel__simps_I3_J, fact_378_power__strict__decreasing, fact_284_semiring__one__add__one__is__two, fact_386_add__scale__eq__noteq, fact_381_even__less__0__iff, fact_451_zero__less__power2, fact_492_power__strict__increasing__iff, fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_431_le__special_I1_J, fact_268_double__number__of__Bit0, fact_40_zle__antisym, fact_403_odd__nonzero, fact_605_Euler_Oaux1, fact_666_real__mult__commute, fact_139_rel__simps_I48_J, fact_38_zless__linear, fact_382_even__less__0__iff, fact_494_power__strict__increasing__iff, fact_162_less__special_I2_J, fact_442_zero__le__power2, fact_355_double__eq__0__iff, fact_482_zero__le__even__power_H, fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_518_rel__simps_I45_J, fact_460_power__mult__distrib, fact_500_power__strict__increasing, fact_305_s0p, fact_548_one__less__power, fact_567_IntPrimes_Ozcong__zero, fact_72_rel__simps_I31_J, fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_576_power__eq__0__iff__number__of, fact_685_self__quotient__aux2, fact_418_le__nat__number__of, fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_294_power__less__power__Suc, fact_544_rel__simps_I25_J, fact_364_power__mono, fact_37_zless__le, fact_415_not__sum__squares__lt__zero, fact_260_semiring__numeral__1__eq__1, fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_240_arith__simps_I32_J, fact_441_zero__le__power2, fact_410_sum__squares__ge__zero, fact_520_rel__simps_I7_J, fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_527_rel__simps_I8_J, fact_161_less__special_I4_J, fact_636_zcong__shift, fact_251_Bit1__def, fact_583_power__0__left__number__of, fact_167_le__special_I2_J, fact_290_real__sum__squared__expand, fact_201_add__Pls__right, fact_148_rel__simps_I16_J, fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_433_le__special_I3_J, fact_168_crossproduct__eq, fact_81_rel__simps_I5_J, fact_652_zpower__zdvd__prop1, fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_14_power2__eq__square__number__of, fact_577_power__eq__0__iff__number__of, fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_391_number__of__Pls, fact_322_power__eq__imp__eq__base, fact_293_power__less__power__Suc, fact_75_zadd__strict__right__mono, fact_13_power2__eq__square__number__of, fact_338_power__strict__mono, fact_434_le__special_I3_J, fact_151_rel__simps_I22_J, fact_39_zle__trans, fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_393_semiring__numeral__0__eq__0, fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_134_eq__number__of, fact_657_zpower__zdvd__prop2, fact_53_le__number__of, fact_446_power2__eq__imp__eq, gsy_c_Residues_OLegendre, fact_259_semiring__numeral__1__eq__1, fact_505_even__power__le__0__imp__0, fact_519_rel__simps_I42_J, fact_601_diff__bin__simps_I3_J, fact_362_zero__le__power, fact_426_odd__less__0, fact_35_zle__refl, fact_566_Euler_Oaux2, fact_356_Pls__def, fact_295_power__gt1__lemma, fact_242_number__of__mult, fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_0_tpos, gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint, fact_673_real__mult__order, fact_554_less__0__number__of, fact_51_less__number__of, fact_422_power__one__right, fact_267_double__number__of__Bit0, fact_319_power__le__dvd, fact_372_power__less__imp__less__base, fact_439_zero__eq__power2, fact_351_add__0__iff, fact_138_rel__simps_I51_J, fact_572_zcong__zmult__self, fact_160_less__special_I4_J, fact_582_power__0__left__number__of, fact_311_power__eq__0__iff, fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_637_nat__power__eq__0__iff, fact_67_rel__simps_I2_J, fact_325_zdvd__antisym__nonneg, fact_223_right__distrib__number__of, gsy_c_TwoSquares__Mirabelle__ccrtsbwhjp_Osum2sq, fact_82_less__eq__int__code_I15_J, fact_55_zadd__zless__mono, fact_584_zcong__zless__imp__eq, fact_647_zcong__zero__equiv__div, fact_667_real__mult__assoc, fact_488_power__increasing, fact_48_le__number__of__eq__not__less, fact_573_zcong__zadd, fact_221_right__distrib__number__of, fact_620_zcong__neg__1__impl__ne__1, fact_212_semiring__mult__number__of, fact_559_zcong__trans, fact_602_less__bin__lemma, fact_497_power__less__imp__less__exp, fact_556_eq__0__number__of, fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_192_rel__simps_I46_J, fact_585_zcong__zless__0, fact_33_one__add__one__is__two, fact_326_zdvd__mult__cancel, fact_264_semiring__norm_I110_J, fact_69_rel__simps_I14_J, fact_193_rel__simps_I39_J, fact_529_rel__simps_I30_J, fact_273_semiring__mult__2, fact_450_power2__less__0, fact_405_power__Suc__less, fact_603_xzgcda__linear__aux1, fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_512_nat__power__less__imp__less, fact_599_diff__bin__simps_I9_J, gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint, fact_135_number__of__reorient, fact_170_crossproduct__eq, fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_676_real__mult__less__iff1, fact_194_rel__simps_I50_J, fact_413_less__nat__number__of, fact_407_zprime__power__zdvd__cancel__left, fact_90_is__mult__sum2sq, fact_412_sum__squares__le__zero__iff, fact_683_unique__quotient__lemma__neg, fact_624_zcong__eq__trans, fact_452_zero__less__power2, fact_475_sum__power2__le__zero__iff, fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_687_real__le__antisym, fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, fact_656_zcong__zprime__prod__zero, fact_389_semiring__norm_I112_J, fact_336_power__strict__mono, fact_672_real__mult__less__mono2, fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_595_zdiff__zmult__distrib, fact_318_power__le__dvd, fact_618_Legendre__1mod4, gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint, fact_277_mult__2, fact_552_dvd__power, fact_314_le__imp__power__dvd, fact_288_prime__g__5, fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_593_diff__bin__simps_I1_J, fact_671_real__add__mult__distrib, fact_470_power2__less__imp__less, gsy_v_t____, fact_560_pos2, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_243_add__number__of__left, fact_377_power__decreasing, fact_244_add__number__of__left, fact_302_power__increasing__iff, fact_535_power__dvd__imp__le, gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint, fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_596_zdiff__zmult__distrib2, gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint, fact_491_power__inject__exp, fact_612_zcong__square, fact_250_add__Bit0__Bit1, fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_472_power2__less__imp__less, fact_392_number__of__Pls, fact_545_rel__simps_I11_J, fact_196_rel__simps_I44_J, fact_177_crossproduct__noteq, fact_214_semiring__add__number__of, fact_501_s, fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_266_mult__Bit1, fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_465_power__one, fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_528_bin__less__0__simps_I2_J, fact_239_arith__simps_I32_J, fact_539_power__0, fact_298_power__le__imp__le__exp, fact_421_power__one__right, fact_456_power__commutes, fact_638_divides__exp, fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_466_power__one, fact_570_zcong__scalar2, fact_420_number__of__Bit0, fact_471_power2__less__imp__less, fact_59_zpower__zadd__distrib, fact_394_semiring__numeral__0__eq__0, fact_70_rel__simps_I19_J, fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_640_divides__ge, gsy_c_Int_OBit1, fact_379_power__strict__decreasing, fact_513_rel__simps_I47_J, fact_387_add__scale__eq__noteq, fact_697_realpow__pos__nth, fact_409_sum__squares__ge__zero, fact_68_less__int__code_I13_J, fact_3_t__l__p, fact_296_power__gt1__lemma, fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_285_semiring__one__add__one__is__two, fact_643_zcong__less__eq, fact_89_zprime__2, fact_85_rel__simps_I15_J, fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_668_real__add__left__mono, fact_581_power__0__left__number__of, fact_561_nat__number__of__mult__left, fact_84_less__int__code_I14_J, fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_481_zero__le__even__power_H, fact_611_mult__sum2sq, fact_397_bin__less__0__simps_I1_J, fact_523_rel__simps_I13_J, fact_658_QuadRes__def, 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_, fact_427_less__special_I1_J, fact_324_zdvd__not__zless, fact_136_number__of__reorient, fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, gsy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint, fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_503_int__pos__lt__two__imp__zero__or__one, fact_306__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, fact_80_rel__simps_I29_J, fact_238_mult__number__of__left, fact_254_mult__numeral__1, fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_63_less__int__code_I16_J, fact_258_semiring__numeral__1__eq__1, fact_406_power__Suc__less, fact_23_power2__eq__square, fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_663_real__less__def, fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_408_zprime__power__zdvd__cancel__right, fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_690_real__le__refl, fact_29_add__special_I2_J, fact_353_add__0__iff, fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_252_number__of__Bit1, fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_235_add__numeral__0__right, fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096, fact_149_rel__simps_I10_J, fact_568_zcong__1, fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_31_add__special_I3_J, fact_383_sum__squares__eq__zero__iff, fact_12_power2__eq__square__number__of, fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_10_power2__sum, fact_165_le__special_I4_J, fact_467_power__mult, fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_79_Numeral1__eq1__nat, fact_569_zcong__zmult, fact_547_zmult__eq__1__iff, fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_179_crossproduct__noteq, fact_257_mult__numeral__1__right, fact_459_power__mult__distrib, fact_77_add__nat__number__of, fact_15_cube__square, fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_660_self__quotient__aux1, fact_202_add__Pls, fact_299_power__le__imp__le__exp, fact_613_zcong__square__zless, fact_308_s1, fact_445_power2__le__imp__le, fact_649_exp__eq__1, fact_526_rel__simps_I6_J, fact_291_four__x__squared, fact_639_zcong__zpower, fact_363_power__mono, fact_354_double__eq__0__iff, fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_511_zero__less__power__nat__eq__number__of, fact_524_rel__simps_I9_J, fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_200_mult__Bit0, fact_651_Int2_Ozcong__zero, gsy_v_s____, fact_633_Int2_Oaux1, fact_262_numeral__1__eq__1, fact_654_divides__div__not, fact_247_number__of__add, fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_140_zmult__assoc, fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_574_power__m1__even, fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_332_power__0__left, fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_682_zdiv__mono2__lemma, fact_469_power__mult, fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_330_field__power__not__zero, fact_333_power__0__left, fact_437_zero__power2, fact_307__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_, fact_271_power3__eq__cube, fact_390_semiring__norm_I112_J, fact_642_zcong__not__zero, fact_388_zprime__zdvd__power, fact_664_less__eq__real__def, fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_209_zadd__zmult__distrib2, fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_222_right__distrib__number__of, fact_396_bin__less__0__simps_I4_J, fact_436_zero__power2, fact_317_dvd__power__le, fact_443_power2__le__imp__le, fact_133_eq__number__of, fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_541_power__0, fact_411_sum__squares__le__zero__iff, fact_534_eq__number__of__Pls__Min, fact_509_nat__zero__less__power__iff, fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_22_power2__eq__square, fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_617_neg__one__power, fact_309_power__eq__0__iff, 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, fact_662_real__le__eq__diff, fact_141_zmult__commute, fact_616_zdiff__power3, fact_52_less__number__of, fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_24_power2__eq__square, fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_610_inv__not__p__minus__1__aux, fact_17_one__power2, fact_477_not__sum__power2__lt__zero, fact_448_power2__eq__imp__eq, fact_646_divides__rev, fact_142_number__of__is__id, fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_416_sum__squares__gt__zero__iff, fact_150_rel__simps_I4_J, fact_621_Legendre__def, fact_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_313_le__imp__power__dvd, fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_650_zprime__zdvd__zmult__better, fact_234_add__numeral__0, fact_424_int__one__le__iff__zero__less, fact_263_semiring__norm_I110_J, fact_632_nat__mult__eq__one, fact_384_sum__squares__eq__zero__iff, fact_484_one__le__power, fact_435_le__imp__0__less, fact_331_field__power__not__zero, fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_4_p, fact_634_zcong__zmult__prop2, fact_414_not__sum__squares__lt__zero, fact_678_two__realpow__ge__one, fact_549_one__less__power, fact_163_less__special_I2_J, fact_495_power__less__imp__less__exp, fact_533_rel__simps_I28_J, fact_248_number__of__add, fact_462_power__add, fact_644_zdvd__bounds, fact_241_number__of__mult, fact_30_add__special_I3_J, fact_278_semiring__mult__2__right, fact_282_mult__2__right, fact_461_power__add, gsy_c_Power_Opower__class_Opower_000tc__Int__Oint, fact_476_sum__power2__le__zero__iff, fact_487_power__increasing, fact_143_zadd__assoc, fact_579_zcong__not, fact_540_power__0, fact_631_zcong__id, fact_447_power2__eq__imp__eq, fact_510_zero__less__power__nat__eq, fact_615_zdiff__power2, fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_49_le__number__of__eq__not__less, fact_357_int__0__neq__1, fact_253_number__of__Bit1, fact_18_one__power2, fact_400_int__0__less__1, fact_609_diff__bin__simps_I5_J, fact_366_zero__less__power, fact_648_zcong__eq__zdvd__prop, fact_399_zero__is__num__zero, fact_152_less__eq__int__code_I14_J, fact_312_le__imp__power__dvd, fact_207_times__numeral__code_I5_J, fact_323_power__eq__imp__eq__base, fact_425_pos__zmult__eq__1__iff, fact_281_mult__2__right, fact_61_nat__mult__2__right, fact_530_rel__simps_I26_J, fact_137_number__of__reorient, fact_237_mult__number__of__left, fact_464_power__one, fact_398_bin__less__0__simps_I3_J, fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_555_eq__number__of__0, fact_380_power__strict__decreasing, fact_630_divides__mul__r, fact_320_power__le__dvd, fact_458_power__mult__distrib, fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_429_less__special_I3_J, fact_506_zprime__def, fact_87_add1__zle__eq, fact_166_le__special_I2_J, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_66_rel__simps_I34_J, fact_205_zmult__1__right, fact_64_rel__simps_I17_J, fact_675_real__mult__le__cancel__iff1, fact_334_power__0__left, fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_493_power__strict__increasing__iff, fact_629_divides__mul__l, fact_606_zle__diff1__eq, fact_623_divides__antisym, fact_659_realpow__two__sum__zero__iff, fact_158_power__even__eq, fact_5_t, fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096, fact_315_dvd__power__le, fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_689_real__le__linear, fact_438_zero__power2, fact_335_zdvd__imp__le, fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_275_semiring__mult__2, fact_62_nat__1__add__1, fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_83_rel__simps_I33_J, fact_195_rel__simps_I49_J, fact_361_zero__le__power, fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_480_sum__power2__gt__zero__iff, fact_147_less__int__code_I15_J, fact_11_power2__sum, fact_367_zero__less__power, fact_575_power__m1__even, fact_303_power__increasing__iff, fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_249_add__Bit1__Bit0, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_608_diff__bin__simps_I6_J, fact_280_semiring__mult__2__right, fact_65_less__eq__int__code_I16_J, fact_358_zadd__0, fact_619_one__not__neg__one__mod__m, fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_485_one__le__power, fact_517_rel__simps_I40_J, fact_86_zless__imp__add1__zle, fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096, fact_261_numeral__1__eq__1, fact_479_sum__power2__gt__zero__iff, fact_337_power__strict__mono, fact_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_297_power__gt1__lemma, fact_402_zmult__zless__mono2, fact_178_crossproduct__noteq, fact_245_add__number__of__eq, fact_156_zless__add1__eq, gsy_c_Int_OPls, fact_270_power3__eq__cube, fact_60_nat__mult__2, fact_375_power__decreasing, fact_370_zdvd__reduce, fact_292_power__less__power__Suc, fact_670_real__mult__right__cancel, fact_219_left__distrib__number__of, fact_473_sum__power2__ge__zero, fact_54_le__number__of, fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_6_qf1pt, fact_665_real__mult__1, fact_592_zcong__zdiff, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_423_power__one__right, fact_328_dvd__power__same, fact_286_p0, gsy_c_Int_OMin, fact_597_zdvd__zdiffD, fact_453_sum__power2__eq__zero__iff, fact_674_real__mult__le__cancel__iff2, fact_522_not__real__square__gt__zero, fact_36_zle__linear, gsy_v_m, fact_28_add__special_I2_J, fact_531_rel__simps_I20_J, fact_417_sum__squares__gt__zero__iff, fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_8_zadd__power3, fact_604_zcong__def, fact_565_order__le__neq__implies__less, fact_211_semiring__mult__number__of, fact_385_add__scale__eq__noteq, fact_300_power__le__imp__le__exp, fact_359_zadd__0__right, fact_578_power__eq__0__iff__number__of, fact_236_add__numeral__0__right, fact_217_power2__ge__self, gsy_c_HOL_Oundefined_000tc__Int__Oint, fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_215_semiring__add__number__of, fact_454_sum__power2__eq__zero__iff, fact_550_one__less__power, fact_164_le__special_I4_J, fact_635_zcong__zmult__prop1, fact_206_zmult__1, fact_430_less__special_I3_J, fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, gsy_v_s1____, fact_474_sum__power2__ge__zero, fact_16_one__power2, fact_155_rel__simps_I21_J, fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_558_zcong__refl, fact_589_neg__one__power__eq__mod__m, fact_496_power__less__imp__less__exp, fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_213_semiring__mult__number__of, fact_76_zadd__left__mono, fact_684_zdiv__mono2__neg__lemma, fact_486_power__increasing, fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_401_pos__zmult__pos, fact_197_rel__simps_I38_J
% 17.30/4.57 % No. of inferences in proof: 1436
% 17.30/4.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4029 ms resp. 3468 ms w/o parsing
% 18.29/4.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.29/4.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------