TSTP Solution File: NUM926_2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% 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 : n022.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 16.70s 4.56s
% Output : Refutation 18.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 748
% Syntax : Number of formulae : 1449 ( 686 unt; 49 typ; 0 def)
% Number of atoms : 3107 (1292 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 14043 ( 271 ~; 88 |; 307 &;12065 @)
% ( 161 <=>;1151 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 13 con; 0-3 aty)
% Number of variables : 2719 ( 0 ^;2695 !; 24 ?;2719 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(minus_minus_int_type,type,
minus_minus_int: int > int > int ).
thf(minus_minus_nat_type,type,
minus_minus_nat: nat > nat > nat ).
thf(minus_minus_real_type,type,
minus_minus_real: real > real > real ).
thf(one_one_int_type,type,
one_one_int: int ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(one_one_real_type,type,
one_one_real: real ).
thf(plus_plus_int_type,type,
plus_plus_int: int > int > int ).
thf(plus_plus_nat_type,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_real_type,type,
plus_plus_real: real > real > real ).
thf(times_times_int_type,type,
times_times_int: int > int > int ).
thf(times_times_nat_type,type,
times_times_nat: nat > nat > nat ).
thf(times_times_real_type,type,
times_times_real: real > real > real ).
thf(zero_zero_int_type,type,
zero_zero_int: int ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(zero_zero_real_type,type,
zero_zero_real: real ).
thf(zcong_type,type,
zcong: int > int > int > $o ).
thf(zprime_type,type,
zprime: int > $o ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(min_type,type,
min: int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_int_type,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
thf(number267125858f_real_type,type,
number267125858f_real: int > real ).
thf(ord_less_int_type,type,
ord_less_int: int > int > $o ).
thf(ord_less_nat_type,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_real_type,type,
ord_less_real: real > real > $o ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: real > real > $o ).
thf(power_power_int_type,type,
power_power_int: int > nat > int ).
thf(power_power_nat_type,type,
power_power_nat: nat > nat > nat ).
thf(power_power_real_type,type,
power_power_real: real > nat > real ).
thf(product_Pair_int_int_type,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(legendre_type,type,
legendre: int > int > int ).
thf(quadRes_type,type,
quadRes: int > int > $o ).
thf(dvd_dvd_int_type,type,
dvd_dvd_int: int > int > $o ).
thf(dvd_dvd_nat_type,type,
dvd_dvd_nat: nat > nat > $o ).
thf(dvd_dvd_real_type,type,
dvd_dvd_real: real > real > $o ).
thf(twoSqu512355103sum2sq_type,type,
twoSqu512355103sum2sq: int > $o ).
thf(twoSqu2107342101sum2sq_type,type,
twoSqu2107342101sum2sq: product_prod_int_int > int ).
thf(m_type,type,
m: int ).
thf(s1_type,type,
s1: int ).
thf(s_type,type,
s: int ).
thf(t_type,type,
t: int ).
thf(57,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(892,plain,
! [A: real,B: real,C: real] :
( ( 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)],[57]) ).
thf(484,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_le__special_I3_J) ).
thf(2452,plain,
! [A: int] :
( ( ( 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)],[484]) ).
thf(394,axiom,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_zero__le__power2) ).
thf(2094,plain,
! [A: int] : ( 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)],[394]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1024,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(565,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_11_power2__sum) ).
thf(2744,plain,
! [A: int,B: int] :
( ( 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)],[565]) ).
thf(402,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_zadd__0) ).
thf(2131,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(389,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_rel__simps_I30_J) ).
thf(2072,plain,
! [A: int] :
( ( ( 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)],[389]) ).
thf(510,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
<=> ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_less__special_I4_J) ).
thf(2544,plain,
! [A: int] :
( ( ( 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)],[510]) ).
thf(421,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_rel__simps_I46_J) ).
thf(2199,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(641,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_rel__simps_I50_J) ).
thf(3021,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(602,axiom,
! [A: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_eq__0__number__of) ).
thf(2876,plain,
! [A: int] :
( ( ( 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)],[602]) ).
thf(42,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zle__refl) ).
thf(846,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(613,axiom,
! [A: nat,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_497_power__less__imp__less__exp) ).
thf(2921,plain,
! [A: nat,B: nat,C: int] :
( ( 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)],[613]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1031,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(487,axiom,
! [A: int,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_374_power__less__imp__less__base) ).
thf(2463,plain,
! [A: int,B: nat,C: int] :
( ( 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)],[487]) ).
thf(334,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1899,plain,
! [A: int,B: int,C: int] :
( ( 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)],[334]) ).
thf(174,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_real__mult__assoc) ).
thf(1315,plain,
! [A: real,B: real,C: real] :
( ( 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)],[174]) ).
thf(496,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__int__code_I13_J) ).
thf(2499,plain,
! [A: int,B: int] :
( ( ( 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)],[496]) ).
thf(491,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rel__simps_I12_J) ).
thf(2480,plain,
! [A: int] :
( ( ( 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)],[491]) ).
thf(115,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_566_Euler_Oaux2) ).
thf(1083,plain,
! [A: int,B: int,C: int] :
( ( 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)],[115]) ).
thf(309,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_212_semiring__mult__number__of) ).
thf(1818,plain,
! [A: int,B: int] :
( ( 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)],[309]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ B )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_one__le__power) ).
thf(1295,plain,
! [A: nat,B: nat] :
( ( 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)],[169]) ).
thf(270,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_even__less__0__iff) ).
thf(1686,plain,
! [A: int] :
( ( ( 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)],[270]) ).
thf(434,axiom,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_diff__bin__simps_I1_J) ).
thf(2250,plain,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(390,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_less__eq__number__of__int__code) ).
thf(2077,plain,
! [A: int,B: int] :
( ( ( 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)],[390]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_divides__ge) ).
thf(977,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(138,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1158,plain,
! [A: real,B: real,C: real] :
( ( 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)],[138]) ).
thf(424,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(2210,plain,
! [A: int,B: int] :
( ( ( 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)],[424]) ).
thf(534,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( times_times_int @ B @ A ) )
= ( times_times_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2644,plain,
! [A: int,B: int] :
( ( 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)],[534]) ).
thf(196,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1401,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(346,axiom,
! [A: int,B: 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 )
<=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_sum__power2__le__zero__iff) ).
thf(1939,plain,
! [A: int,B: 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 )
=> ( ( 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)],[346]) ).
thf(284,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_semiring__norm_I110_J) ).
thf(1728,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(396,axiom,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
<=> ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_number__of__reorient) ).
thf(2099,plain,
! [A: int,B: nat] :
( ( ( ( number_number_of_nat @ A )
= B )
=> ( B
= ( number_number_of_nat @ A ) ) )
& ( ( B
= ( number_number_of_nat @ A ) )
=> ( ( number_number_of_nat @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(399,axiom,
! [A: nat,B: int] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_power__eq__0__iff__number__of) ).
thf(2114,plain,
! [A: nat,B: int] :
( ( ( ( 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)],[399]) ).
thf(207,axiom,
! [A: real,B: real,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_459_power__mult__distrib) ).
thf(1437,plain,
! [A: real,B: real,C: nat] :
( ( 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)],[207]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_654_divides__div__not) ).
thf(730,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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)],[11]) ).
thf(330,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rel__simps_I16_J) ).
thf(1882,plain,
! [A: int,B: int] :
( ( ( 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)],[330]) ).
thf(429,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_diff__bin__simps_I7_J) ).
thf(2231,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(109,axiom,
! [A: nat,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_zero__le__power) ).
thf(1068,plain,
! [A: nat,B: real] :
( ( 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)],[109]) ).
thf(467,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_rel__simps_I25_J) ).
thf(2395,plain,
! [A: int] :
( ( ( 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)],[467]) ).
thf(610,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_le__special_I2_J) ).
thf(2908,plain,
! [A: int] :
( ( ( 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)],[610]) ).
thf(209,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ ( power_power_real @ A @ B ) @ C )
= ( power_power_real @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1443,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[209]) ).
thf(573,axiom,
ord_less_eq_int @ one_one_int @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(2776,plain,
ord_less_eq_int @ one_one_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(504,axiom,
! [A: int,B: int,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2527,plain,
! [A: int,B: int,C: int,D: int] :
( ( 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)],[504]) ).
thf(679,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(3153,plain,
ord_less_eq_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(545,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_425_pos__zmult__eq__1__iff) ).
thf(2676,plain,
! [A: int,B: int] :
( ( 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)],[545]) ).
thf(371,axiom,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__numeral__0__right) ).
thf(2014,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(355,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_620_zcong__neg__1__impl__ne__1) ).
thf(1971,plain,
! [A: int,B: int] :
( ( 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)],[355]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_293_power__less__power__Suc) ).
thf(1533,plain,
! [A: nat,B: nat] :
( ( 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)],[232]) ).
thf(113,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_zdvd__zdiffD) ).
thf(1078,plain,
! [A: int,B: int,C: int] :
( ( 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)],[113]) ).
thf(172,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1310,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[172]) ).
thf(637,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_number__of__add) ).
thf(3004,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(612,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2918,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(648,axiom,
! [A: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_575_power__m1__even) ).
thf(3044,plain,
! [A: nat] :
( ( 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)],[648]) ).
thf(554,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_zcong__zpower) ).
thf(2712,plain,
! [A: nat,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(154,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_power__0) ).
thf(1233,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(32,axiom,
! [A: int,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_221_right__distrib__number__of) ).
thf(814,plain,
! [A: int,B: real,C: real] :
( ( 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)],[32]) ).
thf(361,axiom,
! [A: int,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(1988,plain,
! [A: int,B: nat] :
( ( 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)],[361]) ).
thf(609,axiom,
! [A: int] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_eq__number__of__0) ).
thf(2901,plain,
! [A: int] :
( ( ( ( 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)],[609]) ).
thf(380,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_220_left__distrib__number__of) ).
thf(2042,plain,
! [A: int,B: int,C: int] :
( ( 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)],[380]) ).
thf(525,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_diff__bin__simps_I4_J) ).
thf(2607,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(547,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_power2__eq__square) ).
thf(2686,plain,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(325,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1867,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(416,axiom,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_le__special_I2_J) ).
thf(2184,plain,
! [A: int] :
( ( ( 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)],[416]) ).
thf(140,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_le__number__of__eq__not__less) ).
thf(1164,plain,
! [A: int,B: int] :
( ( ( 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)],[140]) ).
thf(365,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_zcong__scalar2) ).
thf(1999,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(107,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_le__imp__power__dvd) ).
thf(1063,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[107]) ).
thf(593,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_zmult__1__right) ).
thf(2844,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_458_power__mult__distrib) ).
thf(930,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[71]) ).
thf(461,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rel__simps_I33_J) ).
thf(2360,plain,
! [A: int,B: int] :
( ( ( 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)],[461]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_divides__exp) ).
thf(898,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[59]) ).
thf(316,axiom,
! [A: int,B: int,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1835,plain,
! [A: int,B: int,C: int,D: int] :
( ( 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)],[316]) ).
thf(478,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_413_less__nat__number__of) ).
thf(2432,plain,
! [A: int,B: int] :
( ( ( 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)],[478]) ).
thf(241,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add1__zle__eq) ).
thf(1576,plain,
! [A: int,B: int] :
( ( ( 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)],[241]) ).
thf(5,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
<=> ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_real__le__eq__diff) ).
thf(709,plain,
! [A: real,B: real] :
( ( ( 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)],[5]) ).
thf(369,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_zmult__assoc) ).
thf(2010,plain,
! [A: int,B: int,C: int] :
( ( 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)],[369]) ).
thf(391,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_683_unique__quotient__lemma__neg) ).
thf(2082,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[391]) ).
thf(282,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_471_power2__less__imp__less) ).
thf(1724,plain,
! [A: nat,B: nat] :
( ( 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)],[282]) ).
thf(501,axiom,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_two__realpow__ge__one) ).
thf(2516,plain,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(469,axiom,
! [A: real,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_290_real__sum__squared__expand) ).
thf(2405,plain,
! [A: real,B: real] :
( ( 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)],[469]) ).
thf(600,axiom,
! [A: int,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_int ) )
=> ( dvd_dvd_int @ A @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_dvd__power) ).
thf(2869,plain,
! [A: int,B: nat] :
( ( ( 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)],[600]) ).
thf(331,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_less__special_I3_J) ).
thf(1887,plain,
! [A: int] :
( ( ( 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)],[331]) ).
thf(373,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_rel__simps_I15_J) ).
thf(2020,plain,
! [A: int,B: int] :
( ( ( 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)],[373]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_535_power__dvd__imp__le) ).
thf(841,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[40]) ).
thf(54,axiom,
! [A: real,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_498_power__strict__increasing) ).
thf(885,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[54]) ).
thf(103,axiom,
! [A: nat,B: real] :
( ( ord_less_eq_real @ one_one_real @ B )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_one__le__power) ).
thf(1046,plain,
! [A: nat,B: real] :
( ( 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)],[103]) ).
thf(604,axiom,
! [A: nat,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_294_power__less__power__Suc) ).
thf(2886,plain,
! [A: nat,B: int] :
( ( 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)],[604]) ).
thf(183,axiom,
! [A: real,B: real,C: real,D: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1359,plain,
! [A: real,B: real,C: real,D: real] :
( ( 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)],[183]) ).
thf(468,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
<=> ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_le__special_I4_J) ).
thf(2400,plain,
! [A: int] :
( ( ( 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)],[468]) ).
thf(388,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rel__simps_I22_J) ).
thf(2067,plain,
! [A: int] :
( ( ( 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)],[388]) ).
thf(353,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_402_zmult__zless__mono2) ).
thf(1967,plain,
! [A: int,B: int,C: int] :
( ( 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)],[353]) ).
thf(336,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_zero__less__power2) ).
thf(1904,plain,
! [A: int] :
( ( ( 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)],[336]) ).
thf(274,axiom,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1703,plain,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(538,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_655_zcong__zprime__prod__zero__contra) ).
thf(2654,plain,
! [A: int,B: int,C: int] :
( ( 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)],[538]) ).
thf(198,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_302_power__increasing__iff) ).
thf(1409,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[198]) ).
thf(276,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1709,plain,
! [A: int,B: int,C: int] :
( ( 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)],[276]) ).
thf(378,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(2039,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(568,axiom,
! [A: int] :
( ( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_581_power__0__left__number__of) ).
thf(2755,plain,
! [A: int] :
( ( ( ( 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)],[568]) ).
thf(39,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(838,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_divides__antisym) ).
thf(802,plain,
! [A: nat,B: nat] :
( ( ( ( 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)],[30]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_499_power__strict__increasing) ).
thf(1313,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[173]) ).
thf(660,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__special_I3_J) ).
thf(3089,plain,
! [A: int] :
( ( 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)],[660]) ).
thf(315,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_zadd__assoc) ).
thf(1832,plain,
! [A: int,B: int,C: int] :
( ( 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)],[315]) ).
thf(401,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J) ).
thf(2126,plain,
! [A: int,B: int] :
( ( ( 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)],[401]) ).
thf(130,axiom,
! [A: nat,B: real,C: nat,D: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_320_power__le__dvd) ).
thf(1132,plain,
! [A: nat,B: real,C: nat,D: real] :
( ( 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)],[130]) ).
thf(301,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_zero__less__power) ).
thf(1792,plain,
! [A: nat,B: int] :
( ( 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)],[301]) ).
thf(204,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_divides__mul__r) ).
thf(1430,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[204]) ).
thf(668,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_685_self__quotient__aux2) ).
thf(3116,plain,
! [A: int,B: int,C: int] :
( ( 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)],[668]) ).
thf(8,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_real__mult__1) ).
thf(719,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,axiom,
! [A: real] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(917,plain,
! [A: real] :
( ( 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)],[66]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
<=> ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_less__bin__lemma) ).
thf(751,plain,
! [A: int,B: int] :
( ( ( 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)],[16]) ).
thf(474,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_number__of__Pls) ).
thf(2420,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(332,axiom,
! [A: int,B: int,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1892,plain,
! [A: int,B: int,C: nat] :
( ( 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)],[332]) ).
thf(195,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1398,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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)],[195]) ).
thf(343,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add__Bit0__Bit0) ).
thf(1931,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(258,axiom,
! [A: real,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_443_power2__le__imp__le) ).
thf(1641,plain,
! [A: real,B: real] :
( ( 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)],[258]) ).
thf(328,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_zadd__0__right) ).
thf(1875,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(596,axiom,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_number__of__is__id) ).
thf(2852,plain,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(506,axiom,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_add__Pls) ).
thf(2533,plain,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(33,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(817,plain,
! [A: nat] :
( ( 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)],[33]) ).
thf(549,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Bit1__def) ).
thf(2691,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(61,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_zcong__zdiff) ).
thf(902,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[61]) ).
thf(411,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_semiring__numeral__0__eq__0) ).
thf(2169,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(117,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zless__linear) ).
thf(1087,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(383,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2049,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(512,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_500_power__strict__increasing) ).
thf(2552,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[512]) ).
thf(81,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(969,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[81]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_exp__eq__1) ).
thf(1347,plain,
! [A: nat,B: nat] :
( ( ( ( power_power_nat @ A @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = one_one_nat )
| ( B = zero_zero_nat ) )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(94,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
<=> ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_add__0__iff) ).
thf(1013,plain,
! [A: real,B: real] :
( ( ( 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)],[94]) ).
thf(22,axiom,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_zcong__refl) ).
thf(770,plain,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(126,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_zcong__eq__trans) ).
thf(1115,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(533,axiom,
! [A: real,B: int] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ B ) )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_power__eq__0__iff__number__of) ).
thf(2635,plain,
! [A: real,B: int] :
( ( ( ( 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)],[533]) ).
thf(633,axiom,
! [A: real,B: 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 @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_power2__eq__imp__eq) ).
thf(2989,plain,
! [A: real,B: 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 @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(184,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1362,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(351,axiom,
ord_less_int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_rel__simps_I6_J) ).
thf(1963,plain,
ord_less_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(368,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_mult__numeral__1) ).
thf(2007,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(220,axiom,
! [A: real,B: nat,C: real] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_321_power__eq__imp__eq__base) ).
thf(1489,plain,
! [A: real,B: nat,C: real] :
( ( ( 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)],[220]) ).
thf(375,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_682_zdiv__mono2__lemma) ).
thf(2027,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( 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)],[375]) ).
thf(308,axiom,
! [A: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_zero__eq__power2) ).
thf(1811,plain,
! [A: real] :
( ( ( ( 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)],[308]) ).
thf(636,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
<=> ( B
= ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_number__of__reorient) ).
thf(2996,plain,
! [A: int,B: int] :
( ( ( ( number_number_of_int @ A )
= B )
=> ( B
= ( number_number_of_int @ A ) ) )
& ( ( B
= ( number_number_of_int @ A ) )
=> ( ( number_number_of_int @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(576,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_mult__2) ).
thf(2782,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_318_power__le__dvd) ).
thf(1109,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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)],[123]) ).
thf(437,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_rel__simps_I8_J) ).
thf(2259,plain,
! [A: int] :
( ( ( 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)],[437]) ).
thf(536,axiom,
! [A: nat,B: nat,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_316_dvd__power__le) ).
thf(2650,plain,
! [A: nat,B: nat,C: int,D: int] :
( ( 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)],[536]) ).
thf(201,axiom,
! [A: nat,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_363_power__mono) ).
thf(1418,plain,
! [A: nat,B: real,C: real] :
( ( 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)],[201]) ).
thf(324,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_616_zdiff__power3) ).
thf(1864,plain,
! [A: int,B: int] :
( ( 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)],[324]) ).
thf(242,axiom,
~ ! [A: int] :
~ ( ( 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/sandbox2/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(1581,plain,
~ ! [A: int] :
~ ( ( 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)],[242]) ).
thf(574,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_rel__simps_I37_J) ).
thf(2777,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(165,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1283,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[165]) ).
thf(372,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_zmult__1) ).
thf(2017,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(17,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(756,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(264,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_one__add__one__is__two) ).
thf(1664,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)],[264]) ).
thf(692,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_numeral__1__eq__1) ).
thf(3199,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(26,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
<=> ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_zcong__def) ).
thf(789,plain,
! [A: int,B: int,C: int] :
( ( ( 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)],[26]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(1828,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)],[313]) ).
thf(615,axiom,
! [A: real] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2925,plain,
! [A: real] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(358,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_614_zspecial__product) ).
thf(1978,plain,
! [A: int,B: int] :
( ( 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)],[358]) ).
thf(443,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_418_le__nat__number__of) ).
thf(2291,plain,
! [A: int,B: int] :
( ( ( 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)],[443]) ).
thf(95,axiom,
! [A: nat,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_295_power__gt1__lemma) ).
thf(1020,plain,
! [A: nat,B: real] :
( ( 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)],[95]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',fact_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(1677,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)],[267]) ).
thf(377,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_less__eq__int__code_I14_J) ).
thf(2034,plain,
! [A: int,B: int] :
( ( ( 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)],[377]) ).
thf(141,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_671_real__add__mult__distrib) ).
thf(1169,plain,
! [A: real,B: real,C: real] :
( ( 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)],[141]) ).
thf(342,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_223_right__distrib__number__of) ).
thf(1928,plain,
! [A: int,B: int,C: int] :
( ( 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)],[342]) ).
thf(187,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1377,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[187]) ).
thf(689,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_49_le__number__of__eq__not__less) ).
thf(3189,plain,
! [A: int,B: int] :
( ( ( 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)],[689]) ).
thf(12,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(734,plain,
! [A: real,B: real,C: real] :
( ( 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)],[12]) ).
thf(681,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_diff__bin__simps_I9_J) ).
thf(3157,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(404,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_int__0__neq__1) ).
thf(2137,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(585,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_zero__is__num__zero) ).
thf(2809,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(441,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( times_times_int @ A @ B ) )
=> ( ( dvd_dvd_int @ C @ A )
| ( dvd_dvd_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_zprime__zdvd__zmult__better) ).
thf(2286,plain,
! [A: int,B: int,C: int] :
( ( 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)],[441]) ).
thf(157,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_dvd__power__same) ).
thf(1242,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[157]) ).
thf(230,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_power__eq__0__iff) ).
thf(1521,plain,
! [A: nat,B: nat] :
( ( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) )
=> ( ( power_power_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(569,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_zmult__commute) ).
thf(2762,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(318,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_214_semiring__add__number__of) ).
thf(1843,plain,
! [A: int,B: int] :
( ( 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)],[318]) ).
thf(386,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_14_power2__eq__square__number__of) ).
thf(2058,plain,
! [A: int] :
( ( 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)],[386]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(877,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[51]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',fact_308_s1) ).
thf(2190,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)],[418]) ).
thf(111,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_585_zcong__zless__0) ).
thf(1072,plain,
! [A: int,B: int] :
( ( 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)],[111]) ).
thf(505,axiom,
! [A: real,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2530,plain,
! [A: real,B: nat] :
( ( 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)],[505]) ).
thf(127,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_double__eq__0__iff) ).
thf(1119,plain,
! [A: real] :
( ( ( ( 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)],[127]) ).
thf(464,axiom,
! [A: int,B: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ A )
= ( times_times_int @ A @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_power__commutes) ).
thf(2371,plain,
! [A: int,B: nat] :
( ( 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)],[464]) ).
thf(273,axiom,
! [A: int] :
( ( min
= ( bit1 @ A ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_rel__simps_I43_J) ).
thf(1696,plain,
! [A: int] :
( ( ( min
= ( bit1 @ A ) )
=> ( min = A ) )
& ( ( min = A )
=> ( min
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(520,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_503_int__pos__lt__two__imp__zero__or__one) ).
thf(2586,plain,
! [A: int] :
( ( 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)],[520]) ).
thf(624,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_319_power__le__dvd) ).
thf(2954,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( 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)],[624]) ).
thf(247,axiom,
! [A: real,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(1604,plain,
! [A: real,B: real] :
( ( 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)],[247]) ).
thf(67,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_power__mult) ).
thf(920,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[67]) ).
thf(271,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_605_Euler_Oaux1) ).
thf(1691,plain,
! [A: int,B: int] :
( ( 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)],[271]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_315_dvd__power__le) ).
thf(925,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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)],[69]) ).
thf(410,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_rel__simps_I28_J) ).
thf(2164,plain,
! [A: int] :
( ( ( 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)],[410]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_510_zero__less__power__nat__eq) ).
thf(1338,plain,
! [A: nat,B: nat] :
( ( ( 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)],[180]) ).
thf(382,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_407_zprime__power__zdvd__cancel__left) ).
thf(2047,plain,
! [A: nat,B: int,C: int,D: int] :
( ( 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)],[382]) ).
thf(651,axiom,
! [A: real,B: 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/sandbox2/benchmark/theBenchmark.p',fact_453_sum__power2__eq__zero__iff) ).
thf(3054,plain,
! [A: real,B: 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 ) )
=> ( ( 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)],[651]) ).
thf(6,axiom,
! [A: nat,B: nat,C: real,D: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_317_dvd__power__le) ).
thf(714,plain,
! [A: nat,B: nat,C: real,D: real] :
( ( 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)],[6]) ).
thf(285,axiom,
! [A: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_617_neg__one__power) ).
thf(1730,plain,
! [A: nat] :
( ( ( 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)],[285]) ).
thf(678,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(3151,plain,
! [A: nat,B: int] :
( ( 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)],[678]) ).
thf(663,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3097,plain,
! [A: int,B: int,C: int] :
( ( 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)],[663]) ).
thf(136,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(1153,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ B )
= ( times_times_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(761,plain,
! [A: nat,B: nat] :
( ( 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)],[19]) ).
thf(215,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_power__mult) ).
thf(1470,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[215]) ).
thf(338,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_semiring__one__add__one__is__two) ).
thf(1915,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(287,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_power__one__right) ).
thf(1736,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(530,axiom,
! [A: int,B: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_562_mult__nat__number__of) ).
thf(2621,plain,
! [A: int,B: int] :
( ( ( 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)],[530]) ).
thf(387,axiom,
? [A: int] :
( ( 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: int] :
( ( ( 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/sandbox2/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(2061,plain,
? [A: int] :
( ( 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: int] :
( ( ( 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)],[387]) ).
thf(572,axiom,
! [A: nat,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_494_power__strict__increasing__iff) ).
thf(2773,plain,
! [A: nat,B: nat,C: int] :
( ( 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)],[572]) ).
thf(256,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_semiring__norm_I110_J) ).
thf(1636,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(544,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat__mult__2) ).
thf(2673,plain,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(521,axiom,
~ ! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(2589,plain,
~ ! [A: int] :
( ( 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)],[521]) ).
thf(438,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2264,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(191,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1387,plain,
! [A: real,B: real,C: real] :
( ( 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)],[191]) ).
thf(562,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_426_odd__less__0) ).
thf(2733,plain,
! [A: int] :
( ( ( 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)],[562]) ).
thf(509,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__Bit1__Bit0) ).
thf(2541,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(229,axiom,
! [A: real,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_375_power__decreasing) ).
thf(1519,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[229]) ).
thf(34,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_sum__squares__ge__zero) ).
thf(820,plain,
! [A: real,B: real] : ( 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)],[34]) ).
thf(265,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_add__Bit0__Bit1) ).
thf(1666,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(219,axiom,
! [A: nat,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_292_power__less__power__Suc) ).
thf(1487,plain,
! [A: nat,B: real] :
( ( 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)],[219]) ).
thf(629,axiom,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_le__special_I1_J) ).
thf(2969,plain,
! [A: int] :
( ( ( 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)],[629]) ).
thf(654,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_semiring__one__add__one__is__two) ).
thf(3069,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)],[654]) ).
thf(523,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_semiring__mult__2__right) ).
thf(2601,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(477,axiom,
! [A: int,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_505_even__power__le__0__imp__0) ).
thf(2428,plain,
! [A: int,B: nat] :
( ( 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)],[477]) ).
thf(680,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_zadd__commute) ).
thf(3154,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(672,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_15_cube__square) ).
thf(3134,plain,
! [A: int] :
( ( 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)],[672]) ).
thf(311,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of) ).
thf(1824,plain,
! [A: int] :
( ( 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)],[311]) ).
thf(406,axiom,
! [A: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__special_I2_J) ).
thf(2150,plain,
! [A: int] :
( ( 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)],[406]) ).
thf(481,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_semiring__numeral__0__eq__0) ).
thf(2445,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(340,axiom,
! [A: int,B: int] :
( ( quadRes @ A @ B )
<=> ? [C: int] : ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_QuadRes__def) ).
thf(1920,plain,
! [A: int,B: int] :
( ( ( quadRes @ A @ B )
=> ? [C: int] : ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) )
& ( ? [C: int] : ( 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)],[340]) ).
thf(673,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I2_J) ).
thf(3137,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(37,axiom,
! [A: real,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_real ) )
=> ( dvd_dvd_real @ A @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_dvd__power) ).
thf(830,plain,
! [A: real,B: nat] :
( ( ( 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)],[37]) ).
thf(414,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_zero__power2) ).
thf(2179,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)],[414]) ).
thf(676,axiom,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_less__special_I1_J) ).
thf(3144,plain,
! [A: int] :
( ( ( 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)],[676]) ).
thf(415,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_222_right__distrib__number__of) ).
thf(2181,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[415]) ).
thf(149,axiom,
! [A: real,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_416_sum__squares__gt__zero__iff) ).
thf(1210,plain,
! [A: real,B: real] :
( ( ( 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)],[149]) ).
thf(98,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_real__le__refl) ).
thf(1027,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(564,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_603_xzgcda__linear__aux1) ).
thf(2741,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( 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)],[564]) ).
thf(255,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ one_one_int @ B )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_one__le__power) ).
thf(1634,plain,
! [A: nat,B: int] :
( ( 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)],[255]) ).
thf(398,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nat__1__add__1) ).
thf(2112,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)],[398]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(974,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[83]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1106,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[122]) ).
thf(185,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1365,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(531,axiom,
~ ! [A: int] :
~ ( 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/sandbox2/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(2628,plain,
~ ! [A: int] :
~ ( 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)],[531]) ).
thf(541,axiom,
! [A: int,B: nat] : ( 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/sandbox2/benchmark/theBenchmark.p',fact_482_zero__le__even__power_H) ).
thf(2663,plain,
! [A: int,B: nat] : ( 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)],[541]) ).
thf(591,axiom,
! [A: int] :
( ( zprime @ A )
<=> ( ( ord_less_int @ one_one_int @ A )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_zprime__def) ).
thf(2826,plain,
! [A: int] :
( ( ( zprime @ A )
=> ( ( ord_less_int @ one_one_int @ A )
& ! [B: int] :
( ( ( 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: int] :
( ( ( 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)],[591]) ).
thf(454,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(2344,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(494,axiom,
! [A: nat,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_297_power__gt1__lemma) ).
thf(2492,plain,
! [A: nat,B: int] :
( ( 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)],[494]) ).
thf(234,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_real__mult__right__cancel) ).
thf(1541,plain,
! [A: real,B: real,C: real] :
( ( 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)],[234]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_461_power__add) ).
thf(874,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[50]) ).
thf(302,axiom,
! [A: nat] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(1794,plain,
! [A: nat] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(305,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_618_Legendre__1mod4) ).
thf(1804,plain,
! [A: int] :
( ( 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)],[305]) ).
thf(460,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/sandbox2/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(2359,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)],[460]) ).
thf(322,axiom,
( ( t = one_one_int )
=> ? [A: int,B: 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(1856,plain,
( ( t = one_one_int )
=> ? [A: int,B: 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 ) ) ) ) )
= ( 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)],[322]) ).
thf(550,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zprime__2) ).
thf(2694,plain,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_178_crossproduct__noteq) ).
thf(1096,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( 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)],[121]) ).
thf(280,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1719,plain,
! [A: int,B: int,C: int] :
( ( 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)],[280]) ).
thf(669,axiom,
! [A: int] :
( ( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_583_power__0__left__number__of) ).
thf(3119,plain,
! [A: int] :
( ( ( ( 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)],[669]) ).
thf(657,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__eq__int__code_I15_J) ).
thf(3078,plain,
! [A: int,B: int] :
( ( ( 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)],[657]) ).
thf(48,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_325_zdvd__antisym__nonneg) ).
thf(869,plain,
! [A: int,B: int] :
( ( 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)],[48]) ).
thf(88,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_power__inject__exp) ).
thf(989,plain,
! [A: nat,B: nat,C: real] :
( ( 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)],[88]) ).
thf(685,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_613_zcong__square__zless) ).
thf(3176,plain,
! [A: int,B: int] :
( ( 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)],[685]) ).
thf(432,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_Bit1__Min) ).
thf(2245,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(345,axiom,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: int,B: 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(1936,plain,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: int,B: 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 ) ) ) ) )
= ( 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)],[345]) ).
thf(665,axiom,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_zero__eq__power2) ).
thf(3105,plain,
! [A: int] :
( ( ( ( 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)],[665]) ).
thf(245,axiom,
! [A: real,B: 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 ) ) ) ) ) )
<=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_sum__power2__gt__zero__iff) ).
thf(1592,plain,
! [A: real,B: 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 ) ) ) ) ) )
=> ( ( 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)],[245]) ).
thf(162,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1270,plain,
! [A: real,B: real,C: real] :
( ( 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)],[162]) ).
thf(622,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_rel__simps_I10_J) ).
thf(2946,plain,
! [A: int] :
( ( ( 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)],[622]) ).
thf(592,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_zadd__left__commute) ).
thf(2841,plain,
! [A: int,B: int,C: int] :
( ( 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)],[592]) ).
thf(177,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_385_add__scale__eq__noteq) ).
thf(1328,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( 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)],[177]) ).
thf(124,axiom,
ord_less_int @ min @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_bin__less__0__simps_I2_J) ).
thf(1111,plain,
ord_less_int @ min @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(152,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_584_zcong__zless__imp__eq) ).
thf(1227,plain,
! [A: int,B: int,C: int] :
( ( 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)],[152]) ).
thf(85,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ B )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(980,plain,
! [A: real,B: real] :
( ( 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)],[85]) ).
thf(243,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_615_zdiff__power2) ).
thf(1587,plain,
! [A: int,B: int] :
( ( 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)],[243]) ).
thf(329,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_rel__simps_I39_J) ).
thf(1878,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(559,axiom,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_zero__power2) ).
thf(2726,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)],[559]) ).
thf(486,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_240_arith__simps_I32_J) ).
thf(2460,plain,
! [A: int,B: int] :
( ( 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)],[486]) ).
thf(675,axiom,
! [A: int,B: int,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_243_add__number__of__left) ).
thf(3141,plain,
! [A: int,B: int,C: real] :
( ( 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)],[675]) ).
thf(352,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_semiring__mult__2) ).
thf(1964,plain,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(112,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1075,plain,
! [A: real,B: real,C: real] :
( ( 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)],[112]) ).
thf(200,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_386_add__scale__eq__noteq) ).
thf(1414,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( 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)],[200]) ).
thf(210,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_672_real__mult__less__mono2) ).
thf(1446,plain,
! [A: real,B: real,C: real] :
( ( 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)],[210]) ).
thf(148,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1207,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(4,axiom,
! [A: real,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_462_power__add) ).
thf(706,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[4]) ).
thf(449,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2323,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(686,axiom,
! [A: nat,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_589_neg__one__power__eq__mod__m) ).
thf(3179,plain,
! [A: nat,B: nat,C: int] :
( ( 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)],[686]) ).
thf(168,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1292,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[168]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_power__inject__exp) ).
thf(933,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[72]) ).
thf(662,axiom,
! [A: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_291_four__x__squared) ).
thf(3094,plain,
! [A: real] :
( ( 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)],[662]) ).
thf(288,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_mult__2__right) ).
thf(1739,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(446,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_double__eq__0__iff) ).
thf(2312,plain,
! [A: int] :
( ( ( ( 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)],[446]) ).
thf(639,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_mult__numeral__1__right) ).
thf(3010,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(690,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(3194,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[690]) ).
thf(456,axiom,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add__numeral__0__right) ).
thf(2349,plain,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(250,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_power3__eq__cube) ).
thf(1612,plain,
! [A: nat] :
( ( 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)],[250]) ).
thf(631,axiom,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_power__eq__0__iff__number__of) ).
thf(2978,plain,
! [A: int,B: int] :
( ( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) )
& ( ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) )
=> ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(137,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_643_zcong__less__eq) ).
thf(1155,plain,
! [A: int,B: int,C: int] :
( ( 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)],[137]) ).
thf(290,axiom,
! [A: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__special_I2_J) ).
thf(1744,plain,
! [A: int] :
( ( 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)],[290]) ).
thf(497,axiom,
! [A: int,B: int,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(2504,plain,
! [A: int,B: int,C: int,D: int] :
( ( 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)],[497]) ).
thf(1,conjecture,
? [A: int,B: 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: int,B: int] :
( ( 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(701,plain,
~ ? [A: int,B: 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 ) ) ) ) )
= ( 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(135,axiom,
! [A: nat,B: nat,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_492_power__strict__increasing__iff) ).
thf(1150,plain,
! [A: nat,B: nat,C: real] :
( ( 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)],[135]) ).
thf(212,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_641_nat__mult__dvd__cancel__disj_H) ).
thf(1451,plain,
! [A: nat,B: nat,C: nat] :
( ( ( 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)],[212]) ).
thf(189,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_675_real__mult__le__cancel__iff1) ).
thf(1382,plain,
! [A: real,B: real,C: real] :
( ( 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)],[189]) ).
thf(493,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_bin__less__0__simps_I3_J) ).
thf(2487,plain,
! [A: int] :
( ( ( 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)],[493]) ).
thf(458,axiom,
! [A: int,B: int,C: int] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_zcong__zmult__self) ).
thf(2355,plain,
! [A: int,B: int,C: int] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(64,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(911,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(700,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_int__0__less__1) ).
thf(3222,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(360,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/sandbox2/benchmark/theBenchmark.p',fact_305_s0p) ).
thf(1984,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)],[360]) ).
thf(384,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2052,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[384]) ).
thf(278,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_semiring__norm_I112_J) ).
thf(1715,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(405,axiom,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_power__eq__0__iff) ).
thf(2140,plain,
! [A: int,B: nat] :
( ( ( ( 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)],[405]) ).
thf(160,axiom,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_power__one) ).
thf(1263,plain,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(997,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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)],[90]) ).
thf(507,axiom,
! [A: int,B: int,C: int] :
( ~ ( 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/sandbox2/benchmark/theBenchmark.p',fact_502_Euler_Oaux____1) ).
thf(2536,plain,
! [A: int,B: int,C: int] :
( ~ ( 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)],[507]) ).
thf(170,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_676_real__mult__less__iff1) ).
thf(1297,plain,
! [A: real,B: real,C: real] :
( ( 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)],[170]) ).
thf(670,axiom,
! [A: int,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_159_power__even__eq) ).
thf(3126,plain,
! [A: int,B: nat] :
( ( 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)],[670]) ).
thf(161,axiom,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_realpow__pos__nth) ).
thf(1266,plain,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(407,axiom,
! [A: nat,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_406_power__Suc__less) ).
thf(2153,plain,
! [A: nat,B: int] :
( ( 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)],[407]) ).
thf(518,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_595_zdiff__zmult__distrib) ).
thf(2581,plain,
! [A: int,B: int,C: int] :
( ( 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)],[518]) ).
thf(488,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_mult__2) ).
thf(2465,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(515,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_408_zprime__power__zdvd__cancel__right) ).
thf(2566,plain,
! [A: nat,B: int,C: int,D: int] :
( ( 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)],[515]) ).
thf(304,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_rel__simps_I4_J) ).
thf(1799,plain,
! [A: int] :
( ( ( 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)],[304]) ).
thf(92,axiom,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_eq__number__of) ).
thf(1002,plain,
! [A: int,B: int] :
( ( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(587,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_zcong__zmult) ).
thf(2813,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[587]) ).
thf(658,axiom,
! [A: real] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_power2__less__0) ).
thf(3083,plain,
! [A: real] :
~ ( 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)],[658]) ).
thf(693,axiom,
~ ( ord_less_eq_int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_rel__simps_I20_J) ).
thf(3201,plain,
~ ( ord_less_eq_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(193,axiom,
! [A: nat,B: nat,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_298_power__le__imp__le__exp) ).
thf(1393,plain,
! [A: nat,B: nat,C: real] :
( ( 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)],[193]) ).
thf(254,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
<=> ? [D: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_zcong__iff__lin) ).
thf(1627,plain,
! [A: int,B: int,C: int] :
( ( ( zcong @ A @ B @ C )
=> ? [D: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) )
& ( ? [D: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) )
=> ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(698,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_rel__simps_I27_J) ).
thf(3215,plain,
! [A: int] :
( ( ( 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)],[698]) ).
thf(206,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1434,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(422,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_Int2_Oaux1) ).
thf(2203,plain,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(603,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_rel__simps_I40_J) ).
thf(2883,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(479,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_246_add__number__of__eq) ).
thf(2440,plain,
! [A: int,B: int] :
( ( 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)],[479]) ).
thf(470,axiom,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_zero__le__power2) ).
thf(2408,plain,
! [A: real] : ( 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)],[470]) ).
thf(333,axiom,
! [A: int] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_rel__simps_I45_J) ).
thf(1895,plain,
! [A: int] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(417,axiom,
ord_less_eq_int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_rel__simps_I23_J) ).
thf(2189,plain,
ord_less_eq_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(528,axiom,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_zcong__1) ).
thf(2617,plain,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
| ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_zdvd__bounds) ).
thf(953,plain,
! [A: int,B: int] :
( ( 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)],[76]) ).
thf(362,axiom,
! [A: real,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_158_power__even__eq) ).
thf(1991,plain,
! [A: real,B: nat] :
( ( 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)],[362]) ).
thf(578,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Bit0__def) ).
thf(2788,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(175,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_zdvd__not__zless) ).
thf(1318,plain,
! [A: int,B: int] :
( ( 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)],[175]) ).
thf(277,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1712,plain,
! [A: int,B: int,C: int] :
( ( 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)],[277]) ).
thf(319,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(1846,plain,
! [A: int,B: int] :
( ( 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)],[319]) ).
thf(166,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_real__zero__not__eq__one) ).
thf(1286,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(463,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2368,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(227,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_299_power__le__imp__le__exp) ).
thf(1515,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[227]) ).
thf(427,axiom,
! [A: int,B: int] :
( ( twoSqu512355103sum2sq @ B )
=> ( ( twoSqu512355103sum2sq @ A )
=> ( twoSqu512355103sum2sq @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq) ).
thf(2221,plain,
! [A: int,B: int] :
( ( twoSqu512355103sum2sq @ B )
=> ( ( twoSqu512355103sum2sq @ A )
=> ( twoSqu512355103sum2sq @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_373_power__less__imp__less__base) ).
thf(794,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[27]) ).
thf(364,axiom,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add__numeral__0) ).
thf(1996,plain,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_less__number__of) ).
thf(906,plain,
! [A: int,B: int] :
( ( ( 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)],[63]) ).
thf(619,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_420_number__of__Bit0) ).
thf(2936,plain,
! [A: int] :
( ( 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)],[619]) ).
thf(366,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_mult__numeral__1__right) ).
thf(2001,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_405_power__Suc__less) ).
thf(965,plain,
! [A: nat,B: nat] :
( ( 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)],[79]) ).
thf(472,axiom,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__power2) ).
thf(2413,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)],[472]) ).
thf(413,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_216_semiring__add__number__of) ).
thf(2176,plain,
! [A: int,B: int] :
( ( 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)],[413]) ).
thf(133,axiom,
! [A: nat,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_548_one__less__power) ).
thf(1146,plain,
! [A: nat,B: real] :
( ( 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)],[133]) ).
thf(435,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/sandbox2/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(2253,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)],[435]) ).
thf(163,axiom,
! [A: real,B: real,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1273,plain,
! [A: real,B: real,C: nat] :
( ( 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)],[163]) ).
thf(291,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(1747,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_509_nat__zero__less__power__iff) ).
thf(856,plain,
! [A: nat,B: nat] :
( ( ( 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)],[45]) ).
thf(607,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int )
<=> ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__special_I4_J) ).
thf(2894,plain,
! [A: int] :
( ( ( 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)],[607]) ).
thf(503,axiom,
! [A: nat,B: 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 @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_power2__eq__imp__eq) ).
thf(2524,plain,
! [A: nat,B: 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 @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(251,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(1615,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(579,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I19_J) ).
thf(2791,plain,
ord_less_eq_int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(41,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_real__le__antisym) ).
thf(843,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(595,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_288_prime__g__5) ).
thf(2849,plain,
! [A: int] :
( ( 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)],[595]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_order__le__neq__implies__less) ).
thf(772,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(253,axiom,
! [A: int,B: nat,C: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_561_nat__number__of__mult__left) ).
thf(1620,plain,
! [A: int,B: nat,C: int] :
( ( ( 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)],[253]) ).
thf(659,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( twoSqu2107342101sum2sq @ ( product_Pair_int_int @ A @ B ) ) @ ( twoSqu2107342101sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu2107342101sum2sq @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_611_mult__sum2sq) ).
thf(3086,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( twoSqu2107342101sum2sq @ ( product_Pair_int_int @ A @ B ) ) @ ( twoSqu2107342101sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu2107342101sum2sq @ ( 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)],[659]) ).
thf(260,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_semiring__numeral__1__eq__1) ).
thf(1652,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(516,axiom,
! [A: int,B: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_77_add__nat__number__of) ).
thf(2568,plain,
! [A: int,B: int] :
( ( ( 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)],[516]) ).
thf(233,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_real__mult__left__cancel) ).
thf(1535,plain,
! [A: real,B: real,C: real] :
( ( 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)],[233]) ).
thf(78,axiom,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_IntPrimes_Ozcong__zero) ).
thf(958,plain,
! [A: int,B: int] :
( ( ( zcong @ A @ B @ zero_zero_int )
=> ( A = B ) )
& ( ( A = B )
=> ( zcong @ A @ B @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(551,axiom,
! [A: int,B: 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/sandbox2/benchmark/theBenchmark.p',fact_454_sum__power2__eq__zero__iff) ).
thf(2695,plain,
! [A: int,B: 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 ) )
=> ( ( 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)],[551]) ).
thf(403,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_213_semiring__mult__number__of) ).
thf(2134,plain,
! [A: int,B: int] :
( ( 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)],[403]) ).
thf(626,axiom,
! [A: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_power__m1__even) ).
thf(2959,plain,
! [A: nat] :
( ( 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)],[626]) ).
thf(62,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_real__le__linear) ).
thf(904,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(688,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_zero__le__power) ).
thf(3187,plain,
! [A: nat,B: int] :
( ( 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)],[688]) ).
thf(223,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_674_real__mult__le__cancel__iff2) ).
thf(1503,plain,
! [A: real,B: real,C: real] :
( ( 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)],[223]) ).
thf(266,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A != zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_zero__less__power2) ).
thf(1669,plain,
! [A: real] :
( ( ( 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)],[266]) ).
thf(450,axiom,
! [A: int] :
( ( ( bit1 @ A )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_rel__simps_I47_J) ).
thf(2326,plain,
! [A: int] :
( ( ( ( bit1 @ A )
= min )
=> ( A = min ) )
& ( ( A = min )
=> ( ( bit1 @ A )
= min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(650,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_mult__Bit1) ).
thf(3051,plain,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(606,axiom,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_mult__Pls) ).
thf(2891,plain,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(563,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_207_times__numeral__code_I5_J) ).
thf(2738,plain,
! [A: int,B: int] :
( ( 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)],[563]) ).
thf(286,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_244_add__number__of__left) ).
thf(1733,plain,
! [A: int,B: int,C: int] :
( ( 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)],[286]) ).
thf(106,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
<=> ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_zcong__eq__zdvd__prop) ).
thf(1058,plain,
! [A: int,B: int] :
( ( ( 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)],[106]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1239,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[156]) ).
thf(178,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_651_Int2_Ozcong__zero) ).
thf(1332,plain,
! [A: int,B: int] :
( ( 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)],[178]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_549_one__less__power) ).
thf(1090,plain,
! [A: nat,B: nat] :
( ( 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)],[118]) ).
thf(485,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_mult__Bit0) ).
thf(2457,plain,
! [A: int,B: int] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(476,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_diff__bin__simps_I6_J) ).
thf(2425,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(3,axiom,
! [A: nat,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_dvd__power__same) ).
thf(704,plain,
! [A: nat,B: real,C: real] :
( ( 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(447,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(2319,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(385,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_242_number__of__mult) ).
thf(2055,plain,
! [A: int,B: int] :
( ( 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)],[385]) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_496_power__less__imp__less__exp) ).
thf(1092,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[119]) ).
thf(257,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_13_power2__eq__square__number__of) ).
thf(1638,plain,
! [A: int] :
( ( 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)],[257]) ).
thf(151,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1224,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(145,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( times_times_nat @ B @ A ) )
= ( times_times_nat @ ( plus_plus_nat @ B @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1194,plain,
! [A: nat,B: nat] :
( ( 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)],[145]) ).
thf(60,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zle__trans) ).
thf(900,plain,
! [A: int,B: int,C: int] :
( ( 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)],[60]) ).
thf(392,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_rel__simps_I38_J) ).
thf(2084,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(104,axiom,
! [A: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_333_power__0__left) ).
thf(1048,plain,
! [A: nat] :
( ( ( 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)],[104]) ).
thf(583,axiom,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_less__special_I2_J) ).
thf(2802,plain,
! [A: int] :
( ( ( 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)],[583]) ).
thf(143,axiom,
! [A: real,B: 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/sandbox2/benchmark/theBenchmark.p',fact_383_sum__squares__eq__zero__iff) ).
thf(1175,plain,
! [A: real,B: 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 ) )
=> ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(499,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(2510,plain,
! [A: int,B: int] :
( ( 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)],[499]) ).
thf(20,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_real__mult__commute) ).
thf(764,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(508,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_157_power__even__eq) ).
thf(2538,plain,
! [A: nat,B: nat] :
( ( 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)],[508]) ).
thf(321,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_semiring__mult__2) ).
thf(1853,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(473,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_less__special_I1_J) ).
thf(2415,plain,
! [A: int] :
( ( ( 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)],[473]) ).
thf(632,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_679_q__pos__lemma) ).
thf(2987,plain,
! [A: int,B: int,C: int] :
( ( 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)],[632]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_nat ) )
=> ( dvd_dvd_nat @ A @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_dvd__power) ).
thf(784,plain,
! [A: nat,B: nat] :
( ( ( 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)],[25]) ).
thf(646,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_208_zadd__zmult__distrib) ).
thf(3038,plain,
! [A: int,B: int,C: int] :
( ( 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)],[646]) ).
thf(475,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_power__mult) ).
thf(2422,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[475]) ).
thf(221,axiom,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_not__sum__squares__lt__zero) ).
thf(1492,plain,
! [A: real,B: real] :
~ ( 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)],[221]) ).
thf(246,axiom,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_pos2) ).
thf(1603,plain,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(281,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_sum__squares__ge__zero) ).
thf(1722,plain,
! [A: int,B: int] : ( 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)],[281]) ).
thf(132,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_zcong__trans) ).
thf(1144,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(297,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_mult__numeral__1) ).
thf(1771,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_order__le__neq__implies__less) ).
thf(737,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(691,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_zadd__strict__right__mono) ).
thf(3197,plain,
! [A: int,B: int,C: int] :
( ( 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)],[691]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_296_power__gt1__lemma) ).
thf(880,plain,
! [A: nat,B: nat] :
( ( 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)],[52]) ).
thf(687,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__eq__int__code_I13_J) ).
thf(3182,plain,
! [A: int,B: int] :
( ( ( 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)],[687]) ).
thf(653,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3066,plain,
! [A: int,B: int,C: int] :
( ( 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)],[653]) ).
thf(354,axiom,
! [A: nat,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_550_one__less__power) ).
thf(1969,plain,
! [A: nat,B: int] :
( ( 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)],[354]) ).
thf(682,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__number__of) ).
thf(3160,plain,
! [A: int,B: int] :
( ( ( 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)],[682]) ).
thf(56,axiom,
! [A: real,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_673_real__mult__order) ).
thf(890,plain,
! [A: real,B: real] :
( ( 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)],[56]) ).
thf(239,axiom,
! [A: nat,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_511_zero__less__power__nat__eq__number__of) ).
thf(1557,plain,
! [A: nat,B: int] :
( ( ( 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)],[239]) ).
thf(656,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__number__of) ).
thf(3073,plain,
! [A: int,B: int] :
( ( ( 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)],[656]) ).
thf(310,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_diff__bin__simps_I10_J) ).
thf(1821,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(29,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(799,plain,
! [A: real,B: real,C: real] :
( ( 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)],[29]) ).
thf(683,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
<=> ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_zless__add1__eq) ).
thf(3165,plain,
! [A: int,B: int] :
( ( ( 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)],[683]) ).
thf(43,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(848,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(601,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_le__imp__0__less) ).
thf(2874,plain,
! [A: int] :
( ( 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)],[601]) ).
thf(96,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_divides__add__revr) ).
thf(1022,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[96]) ).
thf(616,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_zless__imp__add1__zle) ).
thf(2928,plain,
! [A: int,B: int] :
( ( 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)],[616]) ).
thf(630,axiom,
! [A: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_odd__nonzero) ).
thf(2974,plain,
! [A: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(374,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_zero__power2) ).
thf(2025,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)],[374]) ).
thf(114,axiom,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_power__one) ).
thf(1080,plain,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(532,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_622_divides__cases) ).
thf(2632,plain,
! [A: nat,B: nat] :
( ( 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)],[532]) ).
thf(526,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__int__code_I16_J) ).
thf(2610,plain,
! [A: int,B: int] :
( ( ( 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)],[526]) ).
thf(643,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_209_zadd__zmult__distrib2) ).
thf(3027,plain,
! [A: int,B: int,C: int] :
( ( 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)],[643]) ).
thf(575,axiom,
! [A: nat,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_dvd__power__same) ).
thf(2780,plain,
! [A: nat,B: int,C: int] :
( ( 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)],[575]) ).
thf(439,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
<=> ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_zmult__eq__1__iff) ).
thf(2267,plain,
! [A: int,B: int] :
( ( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) )
& ( ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) )
=> ( ( times_times_int @ A @ B )
= one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(471,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ C @ B ) @ E )
<=> ( zcong @ A @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_zcong__zmult__prop1) ).
thf(2410,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[471]) ).
thf(614,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(2923,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)],[614]) ).
thf(317,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) )
<=> ( dvd_dvd_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_zdvd__reduce) ).
thf(1838,plain,
! [A: int,B: int,C: int] :
( ( ( 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)],[317]) ).
thf(577,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_660_self__quotient__aux1) ).
thf(2785,plain,
! [A: int,B: int,C: int] :
( ( 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)],[577]) ).
thf(99,axiom,
! [A: nat,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_336_power__strict__mono) ).
thf(1029,plain,
! [A: nat,B: real,C: real] :
( ( 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)],[99]) ).
thf(58,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(895,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(1556,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)],[238]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_625_mult__eq__if) ).
thf(1460,plain,
! [A: nat,B: nat] :
( ( ( 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)],[213]) ).
thf(535,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_number__of__Bit0) ).
thf(2647,plain,
! [A: int] :
( ( 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)],[535]) ).
thf(125,axiom,
! [A: real,B: real,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_218_left__distrib__number__of) ).
thf(1112,plain,
! [A: real,B: real,C: int] :
( ( 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)],[125]) ).
thf(517,axiom,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_power2__eq__square) ).
thf(2578,plain,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(558,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/sandbox2/benchmark/theBenchmark.p',fact_501_s) ).
thf(2725,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)],[558]) ).
thf(412,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zle__add1__eq__le) ).
thf(2171,plain,
! [A: int,B: int] :
( ( ( 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)],[412]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zle__antisym) ).
thf(827,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(570,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_rel__simps_I29_J) ).
thf(2765,plain,
! [A: int] :
( ( ( 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)],[570]) ).
thf(259,axiom,
! [A: real,B: 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 )
<=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_sum__power2__le__zero__iff) ).
thf(1643,plain,
! [A: real,B: 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 )
=> ( ( 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)],[259]) ).
thf(581,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__numeral__0) ).
thf(2797,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(445,axiom,
! [A: int,B: 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/sandbox2/benchmark/theBenchmark.p',fact_384_sum__squares__eq__zero__iff) ).
thf(2303,plain,
! [A: int,B: 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 ) )
=> ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(44,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__number__of) ).
thf(851,plain,
! [A: int,B: int] :
( ( ( 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)],[44]) ).
thf(423,axiom,
! [A: int] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2207,plain,
! [A: int] :
( ( 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)],[423]) ).
thf(272,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_380_power__strict__decreasing) ).
thf(1694,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[272]) ).
thf(356,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zpower__zpower) ).
thf(1973,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[356]) ).
thf(571,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ B )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2770,plain,
! [A: int,B: int] :
( ( 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)],[571]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(983,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[86]) ).
thf(627,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
<=> ( ord_less_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_rel__simps_I13_J) ).
thf(2962,plain,
! [A: int] :
( ( ( 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)],[627]) ).
thf(462,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_semiring__mult__2) ).
thf(2365,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(618,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_rel__simps_I21_J) ).
thf(2931,plain,
! [A: int] :
( ( ( 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)],[618]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_493_power__strict__increasing__iff) ).
thf(986,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[87]) ).
thf(442,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_463_power__add) ).
thf(2288,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[442]) ).
thf(431,axiom,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_p) ).
thf(2244,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)],[431]) ).
thf(91,axiom,
! [A: nat,B: nat,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_495_power__less__imp__less__exp) ).
thf(1000,plain,
! [A: nat,B: nat,C: real] :
( ( 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)],[91]) ).
thf(567,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_diff__bin__simps_I5_J) ).
thf(2752,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(283,axiom,
( ( twoSqu2107342101sum2sq @ ( 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/sandbox2/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(1726,plain,
( ( twoSqu2107342101sum2sq @ ( 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)],[283]) ).
thf(628,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_586_zprime__zdvd__zmult) ).
thf(2967,plain,
! [A: int,B: int,C: int] :
( ( 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)],[628]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1034,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[101]) ).
thf(307,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_one__not__neg__one__mod__m) ).
thf(1809,plain,
! [A: int] :
( ( 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)],[307]) ).
thf(395,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_number__of__mult) ).
thf(2096,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(327,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_444_power2__le__imp__le) ).
thf(1873,plain,
! [A: nat,B: nat] :
( ( 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)],[327]) ).
thf(542,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(2665,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(635,axiom,
! [A: real,B: real] : ( 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/sandbox2/benchmark/theBenchmark.p',fact_473_sum__power2__ge__zero) ).
thf(2994,plain,
! [A: real,B: real] : ( 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)],[635]) ).
thf(695,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ B @ C ) @ E )
<=> ( zcong @ A @ ( times_times_int @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_zcong__zmult__prop2) ).
thf(3206,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[695]) ).
thf(202,axiom,
ord_less_eq_int @ min @ min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_rel__simps_I24_J) ).
thf(1420,plain,
ord_less_eq_int @ min @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(70,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( times_times_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(927,plain,
! [A: real,B: real,C: real] :
( ( 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)],[70]) ).
thf(430,axiom,
! [A: int,B: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_621_Legendre__def) ).
thf(2234,plain,
! [A: int,B: int] :
( ( ( 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)],[430]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_169_crossproduct__eq) ).
thf(1134,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( 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)],[131]) ).
thf(15,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_zdvd__imp__le) ).
thf(749,plain,
! [A: int,B: int] :
( ( 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)],[15]) ).
thf(546,axiom,
! [A: int,B: int] : ( 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/sandbox2/benchmark/theBenchmark.p',fact_474_sum__power2__ge__zero) ).
thf(2684,plain,
! [A: int,B: int] : ( 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)],[546]) ).
thf(73,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(939,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(349,axiom,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_power2__less__0) ).
thf(1958,plain,
! [A: int] :
~ ( 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)],[349]) ).
thf(608,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_Pls__def) ).
thf(2899,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(9,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
<=> ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_zcong__zero__equiv__div) ).
thf(722,plain,
! [A: int,B: int] :
( ( ( 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)],[9]) ).
thf(347,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
<=> ( B = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_add__0__iff) ).
thf(1948,plain,
! [A: int,B: int] :
( ( ( 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)],[347]) ).
thf(294,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_eq__number__of) ).
thf(1758,plain,
! [A: int,B: int] :
( ( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(397,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__int__code_I14_J) ).
thf(2107,plain,
! [A: int,B: int] :
( ( ( 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)],[397]) ).
thf(537,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_zcong__zadd) ).
thf(2652,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[537]) ).
thf(490,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_412_sum__squares__le__zero__iff) ).
thf(2471,plain,
! [A: int,B: int] :
( ( ( 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)],[490]) ).
thf(483,axiom,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_power3__eq__cube) ).
thf(2449,plain,
! [A: real] :
( ( 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)],[483]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ B @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_zcong__not__zero) ).
thf(812,plain,
! [A: int,B: int] :
( ( 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)],[31]) ).
thf(225,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1509,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(2333,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)],[451]) ).
thf(436,axiom,
! [A: nat,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_219_left__distrib__number__of) ).
thf(2256,plain,
! [A: nat,B: nat,C: int] :
( ( 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)],[436]) ).
thf(500,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_210_plus__numeral__code_I9_J) ).
thf(2513,plain,
! [A: int,B: int] :
( ( 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)],[500]) ).
thf(444,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_le__special_I3_J) ).
thf(2298,plain,
! [A: int] :
( ( ( 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)],[444]) ).
thf(598,axiom,
! [A: int,B: int,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2863,plain,
! [A: int,B: int,C: int,D: int] :
( ( 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)],[598]) ).
thf(350,axiom,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_zprime__zdvd__power) ).
thf(1961,plain,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(55,axiom,
! [A: real,B: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ A )
= ( times_times_real @ A @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_power__commutes) ).
thf(887,plain,
! [A: real,B: nat] :
( ( 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)],[55]) ).
thf(240,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_179_crossproduct__noteq) ).
thf(1566,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ( 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)],[240]) ).
thf(671,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_le__special_I1_J) ).
thf(3129,plain,
! [A: int] :
( ( ( 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)],[671]) ).
thf(502,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_power__inject__exp) ).
thf(2518,plain,
! [A: nat,B: nat,C: int] :
( ( 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)],[502]) ).
thf(186,axiom,
! [A: real,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_411_sum__squares__le__zero__iff) ).
thf(1368,plain,
! [A: real,B: real] :
( ( ( 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)],[186]) ).
thf(696,axiom,
! [A: int,B: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__number__of__eq) ).
thf(3209,plain,
! [A: int,B: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(293,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_rel__simps_I9_J) ).
thf(1753,plain,
! [A: int] :
( ( ( 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)],[293]) ).
thf(231,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_487_power__increasing) ).
thf(1531,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[231]) ).
thf(605,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_248_number__of__add) ).
thf(2888,plain,
! [A: int,B: int] :
( ( 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)],[605]) ).
thf(548,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2689,plain,
! [A: int,B: int] :
( ( 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)],[548]) ).
thf(235,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_semiring__mult__2__right) ).
thf(1547,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(292,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_less__special_I3_J) ).
thf(1748,plain,
! [A: int] :
( ( ( 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)],[292]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_364_power__mono) ).
thf(1070,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[110]) ).
thf(666,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_369_zcong__zpower__zmult) ).
thf(3112,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( 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)],[666]) ).
thf(49,axiom,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_zcong__id) ).
thf(872,plain,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(153,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1230,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(218,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( times_times_real @ B @ A ) )
= ( times_times_real @ ( plus_plus_real @ B @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1484,plain,
! [A: real,B: real] :
( ( 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)],[218]) ).
thf(409,axiom,
! [A: real,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_504_even__power__le__0__imp__0) ).
thf(2160,plain,
! [A: real,B: nat] :
( ( 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)],[409]) ).
thf(300,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zadd__left__mono) ).
thf(1790,plain,
! [A: int,B: int,C: int] :
( ( 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)],[300]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_zero__le__power) ).
thf(1432,plain,
! [A: nat,B: nat] :
( ( 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)],[205]) ).
thf(652,axiom,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_power3__eq__cube) ).
thf(3063,plain,
! [A: int] :
( ( 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)],[652]) ).
thf(299,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_rel__simps_I32_J) ).
thf(1785,plain,
! [A: int,B: int] :
( ( ( 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)],[299]) ).
thf(453,axiom,
! [A: int] :
( ( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_582_power__0__left__number__of) ).
thf(2337,plain,
! [A: int] :
( ( ( ( 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)],[453]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',fact_5_t) ).
thf(1830,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)],[314]) ).
thf(116,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_579_zcong__not) ).
thf(1085,plain,
! [A: int,B: int,C: int] :
( ( 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)],[116]) ).
thf(684,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(3174,plain,
! [A: int,B: int] :
( ( 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)],[684]) ).
thf(647,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_684_zdiv__mono2__neg__lemma) ).
thf(3041,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( 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)],[647]) ).
thf(489,axiom,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_field__power__not__zero) ).
thf(2468,plain,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(539,axiom,
~ ( ord_less_int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_rel__simps_I3_J) ).
thf(2656,plain,
~ ( ord_less_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(566,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
<=> ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_int__one__le__iff__zero__less) ).
thf(2747,plain,
! [A: int] :
( ( ( 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)],[566]) ).
thf(171,axiom,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_power__eq__0__iff) ).
thf(1300,plain,
! [A: real,B: nat] :
( ( ( ( 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)],[171]) ).
thf(667,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_semiring__norm_I112_J) ).
thf(3114,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(344,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_680_q__neg__lemma) ).
thf(1934,plain,
! [A: int,B: int,C: int] :
( ( 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)],[344]) ).
thf(295,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_326_zdvd__mult__cancel) ).
thf(1766,plain,
! [A: int,B: int,C: int] :
( ( 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)],[295]) ).
thf(320,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_pos__zmult__eq__1__iff__lemma) ).
thf(1849,plain,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(150,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ ( times_times_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1221,plain,
! [A: real,B: real,C: real] :
( ( 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)],[150]) ).
thf(224,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1506,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[224]) ).
thf(10,axiom,
! [A: real,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(727,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[10]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_divides__mul__l) ).
thf(1094,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[120]) ).
thf(303,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( power_power_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_zpower__zdvd__prop1) ).
thf(1797,plain,
! [A: int,B: int,C: nat] :
( ( 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)],[303]) ).
thf(557,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_power__0) ).
thf(2722,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(620,axiom,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_less__0__number__of) ).
thf(2939,plain,
! [A: int] :
( ( ( 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)],[620]) ).
thf(655,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_numeral__1__eq__1) ).
thf(3071,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(584,axiom,
! [A: nat,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_300_power__le__imp__le__exp) ).
thf(2807,plain,
! [A: nat,B: nat,C: int] :
( ( 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)],[584]) ).
thf(638,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3007,plain,
! [A: int,B: int,C: int] :
( ( 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)],[638]) ).
thf(519,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_bin__less__0__simps_I1_J) ).
thf(2584,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(252,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1617,plain,
! [A: int,B: int,C: int] :
( ( 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)],[252]) ).
thf(197,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
<=> ( zcong @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_zcong__sym) ).
thf(1404,plain,
! [A: int,B: int,C: int] :
( ( ( zcong @ A @ B @ C )
=> ( zcong @ B @ A @ C ) )
& ( ( zcong @ B @ A @ C )
=> ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(433,axiom,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_power2__eq__square) ).
thf(2247,plain,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(634,axiom,
! [A: real,B: nat] : ( 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/sandbox2/benchmark/theBenchmark.p',fact_481_zero__le__even__power_H) ).
thf(2992,plain,
! [A: real,B: nat] : ( 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)],[634]) ).
thf(359,axiom,
! [A: int,B: nat,C: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_323_power__eq__imp__eq__base) ).
thf(1981,plain,
! [A: int,B: nat,C: int] :
( ( ( 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)],[359]) ).
thf(459,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_semiring__one__add__one__is__two) ).
thf(2357,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)],[459]) ).
thf(348,axiom,
! [A: int] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(1955,plain,
! [A: int] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(560,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_number__of__Bit1) ).
thf(2728,plain,
! [A: int] :
( ( 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)],[560]) ).
thf(279,axiom,
! [A: nat,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_365_power__mono) ).
thf(1717,plain,
! [A: nat,B: int,C: int] :
( ( 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)],[279]) ).
thf(376,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq) ).
thf(2030,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[376]) ).
thf(674,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_nat__number__of__Pls) ).
thf(3139,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(457,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right) ).
thf(2352,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(589,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rel__simps_I31_J) ).
thf(2818,plain,
! [A: int,B: int] :
( ( ( 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)],[589]) ).
thf(237,axiom,
! [A: int,B: int,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_237_mult__number__of__left) ).
thf(1553,plain,
! [A: int,B: int,C: real] :
( ( 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)],[237]) ).
thf(420,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rel__simps_I17_J) ).
thf(2194,plain,
! [A: int,B: int] :
( ( ( 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)],[420]) ).
thf(18,axiom,
! [A: nat,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_404_power__Suc__less) ).
thf(759,plain,
! [A: nat,B: real] :
( ( 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)],[18]) ).
thf(128,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1126,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(211,axiom,
! [A: real,B: real,C: real,D: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1448,plain,
! [A: real,B: real,C: real,D: real] :
( ( 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)],[211]) ).
thf(167,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1289,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(540,axiom,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_less__special_I2_J) ).
thf(2658,plain,
! [A: int] :
( ( ( 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)],[540]) ).
thf(203,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
<=> ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_real__less__def) ).
thf(1421,plain,
! [A: real,B: real] :
( ( ( 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)],[203]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(2013,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)],[370]) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(2045,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)],[381]) ).
thf(661,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_one__is__num__one) ).
thf(3092,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(455,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Bit0__Pls) ).
thf(2347,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(261,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_268_double__number__of__Bit0) ).
thf(1654,plain,
! [A: int] :
( ( 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)],[261]) ).
thf(199,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_512_nat__power__less__imp__less) ).
thf(1412,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[199]) ).
thf(425,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_10_power2__sum) ).
thf(2215,plain,
! [A: nat,B: nat] :
( ( 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)],[425]) ).
thf(228,axiom,
! [A: real,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_486_power__increasing) ).
thf(1517,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[228]) ).
thf(93,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_322_power__eq__imp__eq__base) ).
thf(1010,plain,
! [A: nat,B: nat,C: nat] :
( ( ( 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)],[93]) ).
thf(192,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1390,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[192]) ).
thf(580,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_zle__diff1__eq) ).
thf(2792,plain,
! [A: int,B: int] :
( ( ( 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)],[580]) ).
thf(306,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_semiring__numeral__0__eq__0) ).
thf(1807,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(480,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_472_power2__less__imp__less) ).
thf(2443,plain,
! [A: int,B: int] :
( ( 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)],[480]) ).
thf(440,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2283,plain,
! [A: int,B: int,C: int] :
( ( 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)],[440]) ).
thf(597,axiom,
! [A: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_334_power__0__left) ).
thf(2855,plain,
! [A: nat] :
( ( ( 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)],[597]) ).
thf(513,axiom,
! [A: real,B: 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/sandbox2/benchmark/theBenchmark.p',fact_659_realpow__two__sum__zero__iff) ).
thf(2554,plain,
! [A: real,B: 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 ) )
=> ( ( 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)],[513]) ).
thf(217,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1481,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(158,axiom,
! [A: real,B: 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/sandbox2/benchmark/theBenchmark.p',fact_677_real__two__squares__add__zero__iff) ).
thf(1244,plain,
! [A: real,B: 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 ) )
=> ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(89,axiom,
! [A: real,B: nat,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_372_power__less__imp__less__base) ).
thf(995,plain,
! [A: real,B: nat,C: real] :
( ( 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)],[89]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_add__0__iff) ).
thf(1276,plain,
! [A: nat,B: nat] :
( ( ( 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)],[164]) ).
thf(244,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).
thf(1590,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(159,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_168_crossproduct__eq) ).
thf(1253,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( 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)],[159]) ).
thf(553,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_610_inv__not__p__minus__1__aux) ).
thf(2707,plain,
! [A: int,B: int] :
( ( ( 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)],[553]) ).
thf(190,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_real__add__left__mono) ).
thf(1385,plain,
! [A: real,B: real,C: real] :
( ( 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)],[190]) ).
thf(522,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_rel__simps_I44_J) ).
thf(2594,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(590,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_mult__2__right) ).
thf(2823,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(699,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_488_power__increasing) ).
thf(3220,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[699]) ).
thf(586,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(2811,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)],[586]) ).
thf(367,axiom,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_not__sum__squares__lt__zero) ).
thf(2004,plain,
! [A: int,B: int] :
~ ( 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)],[367]) ).
thf(625,axiom,
! [A: int,B: 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 @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_power2__eq__imp__eq) ).
thf(2956,plain,
! [A: int,B: 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 @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(466,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_417_sum__squares__gt__zero__iff) ).
thf(2384,plain,
! [A: int,B: int] :
( ( ( 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)],[466]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(914,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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)],[65]) ).
thf(275,axiom,
! [A: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_double__number__of__Bit0) ).
thf(1706,plain,
! [A: int] :
( ( 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)],[275]) ).
thf(248,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_272_quartic__square__square) ).
thf(1607,plain,
! [A: int] :
( ( 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)],[248]) ).
thf(263,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1661,plain,
! [A: int,B: int,C: int] :
( ( 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)],[263]) ).
thf(495,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
<=> ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_less__special_I4_J) ).
thf(2494,plain,
! [A: int] :
( ( ( 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)],[495]) ).
thf(363,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_semiring__norm_I113_J) ).
thf(1994,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(482,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_zcong__scalar) ).
thf(2447,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(621,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_653_zcong__zmult__prop3) ).
thf(2944,plain,
! [A: int,B: int,C: int] :
( ( 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)],[621]) ).
thf(208,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_power__one__right) ).
thf(1440,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(677,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_656_zcong__zprime__prod__zero) ).
thf(3149,plain,
! [A: int,B: int,C: int] :
( ( 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)],[677]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(716,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[7]) ).
thf(139,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1161,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( 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)],[139]) ).
thf(465,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_170_crossproduct__eq) ).
thf(2374,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ( 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)],[465]) ).
thf(268,axiom,
! [A: int,B: int] :
~ ( 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/sandbox2/benchmark/theBenchmark.p',fact_478_not__sum__power2__lt__zero) ).
thf(1678,plain,
! [A: int,B: int] :
~ ( 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)],[268]) ).
thf(408,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_rel__simps_I26_J) ).
thf(2155,plain,
! [A: int] :
( ( ( 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)],[408]) ).
thf(194,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_646_divides__rev) ).
thf(1395,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[194]) ).
thf(664,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rel__simps_I5_J) ).
thf(3100,plain,
! [A: int] :
( ( ( 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)],[664]) ).
thf(623,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__mult__2__right) ).
thf(2951,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(588,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_211_semiring__mult__number__of) ).
thf(2815,plain,
! [A: int,B: int] :
( ( 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)],[588]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_376_power__decreasing) ).
thf(1148,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[134]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_zero__less__power) ).
thf(867,plain,
! [A: nat,B: nat] :
( ( 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)],[47]) ).
thf(46,axiom,
~ ( ord_less_int @ min @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_rel__simps_I7_J) ).
thf(865,plain,
~ ( ord_less_int @ min @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(694,axiom,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(3203,plain,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(426,axiom,
! [A: int,B: int] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_arith__simps_I32_J) ).
thf(2218,plain,
! [A: int,B: int] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(617,axiom,
twoSqu512355103sum2sq @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(2930,plain,
twoSqu512355103sum2sq @ ( 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)],[617]) ).
thf(400,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_59_zpower__zadd__distrib) ).
thf(2123,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[400]) ).
thf(226,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1512,plain,
! [A: real,B: real,C: real] :
( ( 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)],[226]) ).
thf(298,axiom,
! [A: int,B: 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 ) ) ) ) ) )
<=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_sum__power2__gt__zero__iff) ).
thf(1774,plain,
! [A: int,B: 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 ) ) ) ) ) )
=> ( ( 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)],[298]) ).
thf(80,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_zero__less__power) ).
thf(967,plain,
! [A: nat,B: real] :
( ( 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)],[80]) ).
thf(556,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_596_zdiff__zmult__distrib2) ).
thf(2719,plain,
! [A: int,B: int,C: int] :
( ( 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)],[556]) ).
thf(75,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_power__one__right) ).
thf(950,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(38,axiom,
! [A: nat,B: nat,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_301_power__increasing__iff) ).
thf(835,plain,
! [A: nat,B: nat,C: real] :
( ( 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)],[38]) ).
thf(188,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_379_power__strict__decreasing) ).
thf(1380,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[188]) ).
thf(524,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_diff__bin__simps_I3_J) ).
thf(2604,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(323,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_less__int__code_I15_J) ).
thf(1859,plain,
! [A: int,B: int] :
( ( ( 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)],[323]) ).
thf(582,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_le__imp__power__dvd) ).
thf(2800,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[582]) ).
thf(222,axiom,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
<=> ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_number__of__reorient) ).
thf(1495,plain,
! [A: int,B: real] :
( ( ( ( number267125858f_real @ A )
= B )
=> ( B
= ( number267125858f_real @ A ) ) )
& ( ( B
= ( number267125858f_real @ A ) )
=> ( ( number267125858f_real @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(179,axiom,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_field__power__not__zero) ).
thf(1335,plain,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(552,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_215_semiring__add__number__of) ).
thf(2704,plain,
! [A: int,B: int] :
( ( 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)],[552]) ).
thf(105,axiom,
! [A: real,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_378_power__strict__decreasing) ).
thf(1056,plain,
! [A: real,B: nat,C: nat] :
( ( 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)],[105]) ).
thf(146,axiom,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_not__real__square__gt__zero) ).
thf(1197,plain,
! [A: real] :
( ( ~ ( 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)],[146]) ).
thf(555,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rel__simps_I14_J) ).
thf(2714,plain,
! [A: int,B: int] :
( ( ( 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)],[555]) ).
thf(644,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__number__of__int__code) ).
thf(3030,plain,
! [A: int,B: int] :
( ( ( 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)],[644]) ).
thf(379,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_445_power2__le__imp__le) ).
thf(2040,plain,
! [A: int,B: int] :
( ( 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)],[379]) ).
thf(543,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J) ).
thf(2668,plain,
! [A: int,B: int] :
( ( ( 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)],[543]) ).
thf(77,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_power__0) ).
thf(955,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(249,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_semiring__numeral__1__eq__1) ).
thf(1610,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ A )
= ( times_times_nat @ A @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_power__commutes) ).
thf(796,plain,
! [A: nat,B: nat] :
( ( 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)],[28]) ).
thf(262,axiom,
! [A: int] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_rel__simps_I42_J) ).
thf(1657,plain,
! [A: int] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(452,axiom,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add__Pls__right) ).
thf(2334,plain,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(142,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_order__le__neq__implies__less) ).
thf(1172,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(21,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(767,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(611,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_rel__simps_I11_J) ).
thf(2913,plain,
! [A: int] :
( ( ( 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)],[611]) ).
thf(393,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_253_number__of__Bit1) ).
thf(2091,plain,
! [A: int] :
( ( 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)],[393]) ).
thf(428,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_rel__simps_I51_J) ).
thf(2223,plain,
! [A: int,B: int] :
( ( ( ( bit1 @ A )
= ( bit1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit1 @ A )
= ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_626_power__eq__if) ).
thf(1473,plain,
! [A: nat,B: nat] :
( ( ( 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)],[216]) ).
thf(529,axiom,
! [A: int,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_657_zpower__zdvd__prop2) ).
thf(2619,plain,
! [A: int,B: nat,C: int] :
( ( 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)],[529]) ).
thf(108,axiom,
! [A: real,B: real,C: real,D: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1065,plain,
! [A: real,B: real,C: real,D: real] :
( ( 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)],[108]) ).
thf(289,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_zcong__shift) ).
thf(1742,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(511,axiom,
! [A: real,B: real] :
~ ( 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/sandbox2/benchmark/theBenchmark.p',fact_477_not__sum__power2__lt__zero) ).
thf(2549,plain,
! [A: real,B: real] :
~ ( 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)],[511]) ).
thf(14,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
<=> ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(740,plain,
! [A: int,B: int] :
( ( ( 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)],[14]) ).
thf(155,axiom,
! [A: real,B: real,C: real,D: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1236,plain,
! [A: real,B: real,C: real,D: real] :
( ( 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)],[155]) ).
thf(561,axiom,
! [A: int,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_377_power__decreasing) ).
thf(2731,plain,
! [A: int,B: nat,C: nat] :
( ( 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)],[561]) ).
thf(129,axiom,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_divides__exp2) ).
thf(1129,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[129]) ).
thf(594,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_one__add__one__is__two) ).
thf(2847,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(492,axiom,
! [A: int,B: int,C: int,D: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_55_zadd__zless__mono) ).
thf(2485,plain,
! [A: int,B: int,C: int,D: int] :
( ( 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)],[492]) ).
thf(182,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_le__imp__power__dvd) ).
thf(1357,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[182]) ).
thf(341,axiom,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_power__one) ).
thf(1925,plain,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(335,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_681_unique__quotient__lemma) ).
thf(1902,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[335]) ).
thf(642,axiom,
! [A: real,B: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_470_power2__less__imp__less) ).
thf(3025,plain,
! [A: real,B: real] :
( ( 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)],[642]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',fact_286_p0) ).
thf(1827,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)],[312]) ).
thf(357,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_number__of__Pls) ).
thf(1976,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(236,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1550,plain,
! [A: int,B: int,C: int] :
( ( 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)],[236]) ).
thf(35,axiom,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
<=> ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_even__less__0__iff) ).
thf(822,plain,
! [A: real] :
( ( ( 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)],[35]) ).
thf(498,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2507,plain,
! [A: nat,B: nat] :
( ( 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)],[498]) ).
thf(640,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_rel__simps_I48_J) ).
thf(3013,plain,
! [A: int,B: int] :
( ( ( ( bit0 @ A )
= ( bit0 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit0 @ A )
= ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(176,axiom,
! [A: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_332_power__0__left) ).
thf(1320,plain,
! [A: nat] :
( ( ( 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)],[176]) ).
thf(514,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_371_zdvd__period) ).
thf(2563,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( 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)],[514]) ).
thf(697,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_598_number__of__diff) ).
thf(3212,plain,
! [A: int,B: int] :
( ( 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)],[697]) ).
thf(68,axiom,
! [A: nat,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_338_power__strict__mono) ).
thf(923,plain,
! [A: nat,B: int,C: int] :
( ( 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)],[68]) ).
thf(599,axiom,
! [A: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_add__special_I3_J) ).
thf(2866,plain,
! [A: int] :
( ( 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)],[599]) ).
thf(53,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(882,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(448,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_612_zcong__square) ).
thf(2321,plain,
! [A: int,B: int] :
( ( 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)],[448]) ).
thf(74,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_177_crossproduct__noteq) ).
thf(940,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( 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)],[74]) ).
thf(269,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_bin__less__0__simps_I4_J) ).
thf(1681,plain,
! [A: int] :
( ( ( 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)],[269]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
<=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_nat__power__eq__0__iff) ).
thf(1184,plain,
! [A: nat,B: nat] :
( ( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) )
& ( ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( power_power_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_nat__mult__eq__one) ).
thf(1037,plain,
! [A: nat,B: nat] :
( ( ( ( times_times_nat @ A @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( ( times_times_nat @ A @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(24,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
<=> ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_less__eq__real__def) ).
thf(775,plain,
! [A: real,B: real] :
( ( ( 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)],[24]) ).
thf(527,axiom,
! [A: int,B: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_401_pos__zmult__pos) ).
thf(2615,plain,
! [A: int,B: int] :
( ( 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)],[527]) ).
thf(296,axiom,
! [A: int] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_power2__ge__self) ).
thf(1769,plain,
! [A: int] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(339,axiom,
! [A: int,B: int,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_460_power__mult__distrib) ).
thf(1917,plain,
! [A: int,B: int,C: nat] :
( ( 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)],[339]) ).
thf(419,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_eq__number__of__Pls__Min) ).
thf(2191,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(147,axiom,
! [A: real,B: real,C: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1204,plain,
! [A: real,B: real,C: real] :
( ( 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)],[147]) ).
thf(214,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_real__le__trans) ).
thf(1468,plain,
! [A: real,B: real,C: real] :
( ( 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)],[214]) ).
thf(649,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_rel__simps_I49_J) ).
thf(3047,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(337,axiom,
! [A: nat,B: nat,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_303_power__increasing__iff) ).
thf(1912,plain,
! [A: nat,B: nat,C: int] :
( ( 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)],[337]) ).
thf(645,axiom,
! [A: nat,B: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_627_diff__square) ).
thf(3035,plain,
! [A: nat,B: nat] :
( ( 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)],[645]) ).
thf(326,axiom,
! [A: int,B: int,C: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_238_mult__number__of__left) ).
thf(1870,plain,
! [A: int,B: int,C: int] :
( ( 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)],[326]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_337_power__strict__mono) ).
thf(972,plain,
! [A: nat,B: nat,C: nat] :
( ( 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)],[82]) ).
thf(3345,plain,
$false,
inference(cvc4,[status(thm)],[892,2452,2094,1024,2744,2131,2072,2544,2199,3021,2876,846,2921,1031,2463,1899,1315,2499,2480,1083,1818,1295,1686,2250,2077,977,1158,2210,2644,1401,1939,1728,2099,2114,1437,730,1882,2231,1068,2395,2908,1443,2776,2527,3153,2676,2014,1971,1533,1078,1310,3004,2918,3044,2712,1233,814,1988,2901,2042,2607,2686,1867,2184,1164,1999,1063,2844,930,2360,898,1835,2432,1576,709,2010,2082,1724,2516,2405,2869,1887,2020,841,885,1046,2886,1359,2400,2067,1967,1904,1703,2654,1409,1709,2039,2755,838,802,1313,3089,1832,2126,1132,1792,1430,3116,719,917,751,2420,1892,1398,1931,1641,1875,2852,2533,817,2691,902,2169,1087,2049,2552,969,1347,1013,770,1115,2635,2989,1362,1963,2007,1489,2027,1811,2996,2782,1109,2259,2650,1418,1864,1581,2777,1283,2017,756,1664,3199,789,1828,2925,1978,2291,1020,1677,2034,1169,1928,1377,3189,734,3157,2137,2809,2286,1242,1521,2762,1843,2058,877,2190,1072,2530,1119,2371,1696,2586,2954,1604,920,1691,925,2164,1338,2047,3054,714,1730,3151,3097,1153,761,1470,1915,1736,2621,2061,2773,1636,2673,2589,2264,1387,2733,2541,1519,820,1666,1487,2969,3069,2601,2428,3154,3134,1824,2150,2445,1920,3137,830,2179,3144,2181,1210,1027,2741,1634,2112,974,1106,1365,2628,2663,2826,2344,2492,1541,874,1794,1804,2359,1856,2694,1096,1719,3119,3078,869,989,3176,2245,1936,3105,1592,1270,2946,2841,1328,1111,1227,980,1587,1878,2726,2460,3141,1964,1075,1414,1446,1207,706,2323,3179,1292,933,3094,1739,2312,3010,3194,2349,1612,2978,1155,1744,2504,701,1150,1451,1382,2487,2355,911,3222,1984,2052,1715,2140,1263,997,2536,1297,3126,1266,2153,2581,2465,2566,1799,1002,2813,3083,3201,1393,1627,3215,1434,2203,2883,2440,2408,1895,2189,2617,953,1991,2788,1318,1712,1846,1286,2368,1515,2221,794,1996,906,2936,2001,965,2413,2176,1146,2253,1273,1747,856,2894,2524,1615,2791,843,2849,772,1620,3086,1652,2568,1535,958,2695,2134,2959,904,3187,1503,1669,2326,3051,2891,2738,1733,1058,1239,1332,1090,2457,2425,704,2319,2055,1092,1638,1224,1194,900,2084,1048,2802,1175,2510,764,2538,1853,2415,2987,784,3038,2422,1492,1603,1722,1144,1771,737,3197,880,3182,3066,1969,3160,890,1557,3073,1821,799,3165,848,2874,1022,2928,2974,2025,1080,2632,2610,3027,2780,2267,2410,2923,1838,2785,1029,895,1556,1460,2647,1112,2578,2725,2171,827,2765,1643,2797,2303,851,2207,1694,1973,2770,983,2962,2365,2931,986,2288,2244,1000,2752,1726,2967,1034,1809,2096,1873,2665,2994,3206,1420,927,2234,1134,749,2684,939,1958,2899,722,1948,1758,2107,2652,2471,2449,812,1509,2333,2256,2513,2298,2863,1961,887,1566,3129,2518,1368,3209,1753,1531,2888,2689,1547,1748,1070,3112,872,1230,1484,2160,1790,1432,3063,1785,2337,1830,1085,3174,3041,2468,2656,2747,1300,3114,1934,1766,1849,1221,1506,727,1094,1797,2722,2939,3071,2807,3007,2584,1617,1404,2247,2992,1981,2357,1955,2728,1717,2030,3139,2352,2818,1553,2194,759,1126,1448,1289,2658,1421,2013,2045,3092,2347,1654,1412,2215,1517,1010,1390,2792,1807,2443,2283,2855,2554,1481,1244,995,1276,1590,1253,2707,1385,2594,2823,3220,2811,2004,2956,2384,914,1706,1607,1661,2494,1994,2447,2944,1440,3149,716,1161,2374,1678,2155,1395,3100,2951,2815,1148,867,865,3203,2218,2930,2123,1512,1774,967,2719,950,835,1380,2604,1859,2800,1495,1335,2704,1056,1197,2714,3030,2040,2668,955,1610,796,1657,2334,1172,767,2913,2091,2223,1473,2619,1065,1742,2549,740,1236,2731,1129,2847,2485,1357,1925,1902,3025,1827,1976,1550,822,2507,3013,1320,2563,3212,923,2866,882,2321,940,1681,1184,1037,775,2615,1769,1917,2191,1204,1468,3047,1912,3035,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM926_2 : TPTP v8.1.2. Released v5.3.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.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 17:40:33 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.10 % [INFO] Parsing done (259ms).
% 1.81/1.11 % [INFO] Running in sequential loop mode.
% 2.56/1.32 % [INFO] eprover registered as external prover.
% 2.56/1.32 % [INFO] cvc4 registered as external prover.
% 2.56/1.32 % [INFO] Scanning for conjecture ...
% 2.96/1.46 % [INFO] Found a conjecture and 698 axioms. Running axiom selection ...
% 3.45/1.58 % [INFO] Axiom selection finished. Selected 698 axioms (removed 0 axioms).
% 4.35/1.82 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.43/1.83 % [INFO] Type checking passed.
% 4.43/1.83 % [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 ...
% 16.70/4.54 % External prover 'cvc4' found a proof!
% 16.70/4.54 % [INFO] Killing All external provers ...
% 16.70/4.54 % Time passed: 4023ms (effective reasoning time: 3431ms)
% 16.70/4.54 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 16.70/4.56 % Axioms used in derivation (698): 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, 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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_461_power__add, 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_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, 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_286_p0, 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_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, 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, 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, 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
% 16.70/4.56 % No. of inferences in proof: 1400
% 16.70/4.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4023 ms resp. 3431 ms w/o parsing
% 17.70/4.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.03/4.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------