TSTP Solution File: NUM924_2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM924_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:42:32 EDT 2023
% Result : Theorem 14.00s 4.25s
% Output : Refutation 15.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 745
% Syntax : Number of formulae : 1446 ( 718 unt; 46 typ; 0 def)
% Number of atoms : 3020 (1326 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 13975 ( 279 ~; 82 |; 310 &;12076 @)
% ( 157 <=>;1071 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 13 con; 0-3 aty)
% Number of variables : 2695 ( 0 ^;2685 !; 10 ?;2695 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $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(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(m_type,type,
m: int ).
thf(s1_type,type,
s1: int ).
thf(s_type,type,
s: int ).
thf(t_type,type,
t: int ).
thf(588,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/sandbox/benchmark/theBenchmark.p',fact_351_nat__number__of__mult__left) ).
thf(2822,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)],[588]) ).
thf(484,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
<=> ( B = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__0__iff) ).
thf(2452,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)],[484]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1337,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)],[171]) ).
thf(380,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_rel__simps_I37_J) ).
thf(2094,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(536,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2612,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_690_divides__mul__r) ).
thf(760,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)],[16]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',fact_546_zprime__zdvd__zmult__better) ).
thf(1454,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)],[200]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',fact_64_sum__squares__le__zero__iff) ).
thf(1633,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)],[258]) ).
thf(373,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(2072,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)],[373]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',fact_10_sum__power2__gt__zero__iff) ).
thf(1729,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)],[283]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',fact_674_power__less__imp__less__exp) ).
thf(1237,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)],[145]) ).
thf(323,axiom,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( minus_minus_int @ B @ D ) ) @ ( times_times_int @ ( minus_minus_int @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_mult__diff__mult) ).
thf(1899,plain,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( minus_minus_int @ B @ D ) ) @ ( times_times_int @ ( minus_minus_int @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',fact_386_crossproduct__eq) ).
thf(1850,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)],[312]) ).
thf(517,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/sandbox/benchmark/theBenchmark.p',fact_56_semiring__mult__number__of) ).
thf(2544,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)],[517]) ).
thf(447,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_s) ).
thf(2331,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)],[447]) ).
thf(305,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(1818,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(420,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_semiring__one__add__one__is__two) ).
thf(2250,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)],[420]) ).
thf(406,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_semiring__norm_I113_J) ).
thf(2199,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(641,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/sandbox/benchmark/theBenchmark.p',fact_188_power3__eq__cube) ).
thf(3021,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)],[641]) ).
thf(610,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_zadd__0__right) ).
thf(2889,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(130,axiom,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_field__power__not__zero) ).
thf(1190,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)],[130]) ).
thf(354,axiom,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
<=> ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_number__of__reorient) ).
thf(1995,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)],[354]) ).
thf(424,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/sandbox/benchmark/theBenchmark.p',fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2263,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)],[424]) ).
thf(475,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_diff__bin__simps_I6_J) ).
thf(2427,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(349,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/sandbox/benchmark/theBenchmark.p',fact_487_zcong__not) ).
thf(1982,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)],[349]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',fact_236_zless__add1__eq) ).
thf(1956,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)],[341]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',fact_580_real__mult__le__cancel__iff1) ).
thf(1549,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)],[233]) ).
thf(429,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_mult__numeral__1__right) ).
thf(2280,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(683,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/sandbox/benchmark/theBenchmark.p',fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3172,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)],[683]) ).
thf(456,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/sandbox/benchmark/theBenchmark.p',fact_685_power__strict__decreasing) ).
thf(2363,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)],[456]) ).
thf(331,axiom,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_IntPrimes_Ozcong__zero) ).
thf(1924,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)],[331]) ).
thf(499,axiom,
~ ( ord_less_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_rel__simps_I3_J) ).
thf(2495,plain,
~ ( ord_less_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1443,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)],[198]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',fact_696_power__dvd__imp__le) ).
thf(1401,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)],[188]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',fact_633_one__le__power) ).
thf(1544,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)],[231]) ).
thf(669,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/sandbox/benchmark/theBenchmark.p',fact_102_less__nat__number__of) ).
thf(3108,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)],[669]) ).
thf(154,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_real__mult__commute) ).
thf(1269,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',fact_137_power2__eq__imp__eq) ).
thf(1793,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)],[298]) ).
thf(96,axiom,
! [A: int,B: int,C: int] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_zcong__zmult__self) ).
thf(1041,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)],[96]) ).
thf(210,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_real__le__refl) ).
thf(1486,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(506,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_power__0) ).
thf(2512,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(17,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
<=> ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_zcong__def) ).
thf(762,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)],[17]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_406_add__scale__eq__noteq) ).
thf(994,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)],[82]) ).
thf(649,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/sandbox/benchmark/theBenchmark.p',fact_80_zadd__zless__mono) ).
thf(3040,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)],[649]) ).
thf(193,axiom,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_zcong__refl) ).
thf(1422,plain,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(623,axiom,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_power__one) ).
thf(2947,plain,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(666,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_rel__simps_I9_J) ).
thf(3098,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)],[666]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(741,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(878,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)],[47]) ).
thf(461,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_less__special_I3_J) ).
thf(2380,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)],[461]) ).
thf(619,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_rel__simps_I11_J) ).
thf(2918,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)],[619]) ).
thf(441,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_rel__simps_I2_J) ).
thf(2316,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(482,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_Bit1__Min) ).
thf(2448,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1872,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)],[315]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',fact_567_real__mult__assoc) ).
thf(814,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)],[28]) ).
thf(485,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/sandbox/benchmark/theBenchmark.p',fact_383_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(2459,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)],[485]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',fact_649_power__le__dvd) ).
thf(945,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)],[67]) ).
thf(593,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/sandbox/benchmark/theBenchmark.p',fact_286_zprime__zdvd__power) ).
thf(2844,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)],[593]) ).
thf(363,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_zless__linear) ).
thf(2042,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)],[363]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',fact_37_times__numeral__code_I5_J) ).
thf(1458,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)],[202]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',fact_667_power__0__left) ).
thf(1078,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)],[103]) ).
thf(297,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/sandbox/benchmark/theBenchmark.p',fact_74_le__number__of__eq__not__less) ).
thf(1788,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)],[297]) ).
thf(402,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_semiring__mult__2) ).
thf(2184,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)],[402]) ).
thf(684,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_less__special_I1_J) ).
thf(3175,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)],[684]) ).
thf(491,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_int__0__less__1) ).
thf(2476,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(398,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_semiring__numeral__0__eq__0) ).
thf(2168,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',fact_555_one__not__neg__one__mod__m) ).
thf(1761,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)],[289]) ).
thf(173,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1342,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)],[173]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',fact_656_nat__power__less__imp__less) ).
thf(747,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)],[13]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',fact_627_zero__le__power) ).
thf(1354,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)],[175]) ).
thf(392,axiom,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_add__Pls__right) ).
thf(2146,plain,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_694_divides__exp2) ).
thf(1507,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)],[218]) ).
thf(62,axiom,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
thf(930,plain,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(454,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_p0) ).
thf(2360,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)],[454]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_310_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1095,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)],[108]) ).
thf(132,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(1196,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)],[132]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1001,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)],[84]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_570_real__add__left__mono) ).
thf(709,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)],[5]) ).
thf(609,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_mult__2__right) ).
thf(2886,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)],[609]) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',fact_470_pos__zmult__eq__1__iff__lemma) ).
thf(2173,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)],[400]) ).
thf(390,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/sandbox/benchmark/theBenchmark.p',fact_297_zdvd__period) ).
thf(2136,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)],[390]) ).
thf(469,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/sandbox/benchmark/theBenchmark.p',fact_270_zadd__power2) ).
thf(2405,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)],[469]) ).
thf(627,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
<=> ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_zcong__eq__zdvd__prop) ).
thf(2957,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)],[627]) ).
thf(286,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__eq__int__code_I14_J) ).
thf(1746,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)],[286]) ).
thf(667,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/sandbox/benchmark/theBenchmark.p',fact_429_q__pos__lemma) ).
thf(3103,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)],[667]) ).
thf(497,axiom,
ord_less_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_rel__simps_I6_J) ).
thf(2491,plain,
ord_less_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',fact_352_power__even__eq) ).
thf(1782,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)],[295]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',fact_659_power__less__imp__less__base) ).
thf(1391,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)],[184]) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',fact_148_sum__power2__ge__zero) ).
thf(1576,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)],[241]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_306_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(973,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)],[77]) ).
thf(98,axiom,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_mult__diff__mult) ).
thf(1046,plain,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(676,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/sandbox/benchmark/theBenchmark.p',fact_426_power__0__left__number__of) ).
thf(3140,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)],[676]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_584_real__mult__less__iff1) ).
thf(1475,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)],[206]) ).
thf(468,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_rel__simps_I33_J) ).
thf(2400,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)],[468]) ).
thf(226,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_power__one__right) ).
thf(1529,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',fact_276_self__quotient__aux2) ).
thf(1967,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)],[343]) ).
thf(275,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_one__add__one__is__two) ).
thf(1709,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',fact_380_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2328,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)],[446]) ).
thf(196,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
<=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_nat__power__eq__0__iff) ).
thf(1430,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)],[196]) ).
thf(585,axiom,
! [A: real] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2814,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)],[585]) ).
thf(670,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/sandbox/benchmark/theBenchmark.p',fact_549_neg__one__power) ).
thf(3116,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)],[670]) ).
thf(651,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/sandbox/benchmark/theBenchmark.p',fact_666_power__gt1__lemma) ).
thf(3046,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)],[651]) ).
thf(426,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2269,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(655,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/sandbox/benchmark/theBenchmark.p',fact_153_not__sum__squares__lt__zero) ).
thf(3061,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)],[655]) ).
thf(168,axiom,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
<=> ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_number__of__reorient) ).
thf(1323,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)],[168]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_574_real__mult__right__cancel) ).
thf(1132,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)],[119]) ).
thf(562,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_semiring__norm_I110_J) ).
thf(2703,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(313,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rel__simps_I22_J) ).
thf(1860,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)],[313]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_312_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1264,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)],[152]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_533_zcong__zmult__prop2) ).
thf(917,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)],[59]) ).
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/sandbox/benchmark/theBenchmark.p',fact_616_dvd__power__same) ).
thf(702,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(182,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/sandbox/benchmark/theBenchmark.p',fact_585_real__two__squares__add__zero__iff) ).
thf(1379,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)],[182]) ).
thf(599,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2857,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(221,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_number__of__diff) ).
thf(1514,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',fact_632_one__le__power) ).
thf(870,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)],[44]) ).
thf(251,axiom,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_power2__eq__square) ).
thf(1609,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)],[251]) ).
thf(239,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_real__le__linear) ).
thf(1572,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)],[239]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_309_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(770,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)],[19]) ).
thf(332,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_mult__2) ).
thf(1931,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)],[332]) ).
thf(358,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_less__int__code_I14_J) ).
thf(2024,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)],[358]) ).
thf(685,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/sandbox/benchmark/theBenchmark.p',fact_135_power2__eq__imp__eq) ).
thf(3180,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)],[685]) ).
thf(316,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/sandbox/benchmark/theBenchmark.p',fact_107_add1__zle__eq) ).
thf(1875,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)],[316]) ).
thf(700,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_semiring__numeral__1__eq__1) ).
thf(3231,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(463,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/sandbox/benchmark/theBenchmark.p',fact_113_le__imp__0__less) ).
thf(2388,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)],[463]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_57_mult__number__of__left) ).
thf(1100,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)],[110]) ).
thf(589,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/sandbox/benchmark/theBenchmark.p',fact_356_even__power__le__0__imp__0) ).
thf(2829,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)],[589]) ).
thf(330,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/sandbox/benchmark/theBenchmark.p',fact_493_zprime__zdvd__zmult) ).
thf(1922,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)],[330]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',fact_635_power__inject__exp) ).
thf(817,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)],[29]) ).
thf(558,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_rel__simps_I27_J) ).
thf(2691,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)],[558]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_504_zdiff__zmult__distrib) ).
thf(1398,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)],[187]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_605_power__mult__distrib) ).
thf(881,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)],[48]) ).
thf(436,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_rel__simps_I39_J) ).
thf(2301,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(304,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_mult__2__right) ).
thf(1815,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)],[304]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_655_le__imp__power__dvd) ).
thf(1494,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)],[213]) ).
thf(624,axiom,
( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(2950,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)],[624]) ).
thf(538,axiom,
~ ( ord_less_eq_int @ one_one_int @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
thf(2616,plain,
~ ( ord_less_eq_int @ one_one_int @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',fact_291_zprime__power__zdvd__cancel__left) ).
thf(1714,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)],[277]) ).
thf(383,axiom,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mult__Pls) ).
thf(2105,plain,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(549,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_diff__bin__simps_I4_J) ).
thf(2650,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(170,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_power__one__right) ).
thf(1334,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(361,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/sandbox/benchmark/theBenchmark.p',fact_184_double__number__of__Bit0) ).
thf(2034,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)],[361]) ).
thf(243,axiom,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(1581,plain,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(576,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
thf(2777,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(374,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_zprime__2) ).
thf(2073,plain,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_676_power__strict__increasing__iff) ).
thf(905,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)],[55]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1151,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)],[122]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_realpow__minus__mult) ).
thf(937,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(89,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_double__eq__0__iff) ).
thf(1020,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)],[89]) ).
thf(422,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_nat__1__add__1) ).
thf(2254,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)],[422]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',fact_245_number__of__Bit1) ).
thf(2367,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)],[458]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',fact_645_power__add) ).
thf(1215,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)],[139]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_42_zle__trans) ).
thf(956,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)],[71]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',fact_129_right__distrib__number__of) ).
thf(1622,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)],[255]) ).
thf(574,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_semiring__norm_I112_J) ).
thf(2772,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(83,axiom,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_right__diff__distrib__number__of) ).
thf(998,plain,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1405,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)],[190]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',fact_237_power2__eq__square__number__of) ).
thf(1600,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)],[248]) ).
thf(394,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/sandbox/benchmark/theBenchmark.p',fact_554_Legendre__1mod4) ).
thf(2154,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)],[394]) ).
thf(565,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/sandbox/benchmark/theBenchmark.p',fact_562_realpow__two__sum__zero__iff) ).
thf(2718,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)],[565]) ).
thf(539,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/sandbox/benchmark/theBenchmark.p',fact_542_zcong__not__zero) ).
thf(2618,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)],[539]) ).
thf(590,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/sandbox/benchmark/theBenchmark.p',fact_44_zpower__zadd__distrib) ).
thf(2833,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)],[590]) ).
thf(510,axiom,
! [A: int] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2523,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)],[510]) ).
thf(299,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/sandbox/benchmark/theBenchmark.p',fact_522_Euler_Oaux1) ).
thf(1796,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)],[299]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',fact_122_sum__squares__eq__zero__iff) ).
thf(1345,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)],[174]) ).
thf(580,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/sandbox/benchmark/theBenchmark.p',fact_551_zcong__zprime__prod__zero__contra) ).
thf(2799,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)],[580]) ).
thf(431,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/sandbox/benchmark/theBenchmark.p',fact_631_zero__less__power) ).
thf(2286,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)],[431]) ).
thf(698,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/sandbox/benchmark/theBenchmark.p',fact_530_zcong__square) ).
thf(3226,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)],[698]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',fact_598_power__strict__mono) ).
thf(1943,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)],[336]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1201,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)],[134]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_644_power__add) ).
thf(1242,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)],[147]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(849,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)],[38]) ).
thf(530,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/sandbox/benchmark/theBenchmark.p',fact_557_QuadRes__def) ).
thf(2586,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)],[530]) ).
thf(608,axiom,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(2884,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)],[608]) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',fact_681_power__increasing) ).
thf(1975,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)],[346]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_58_mult__number__of__left) ).
thf(1564,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)],[236]) ).
thf(250,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rel__simps_I32_J) ).
thf(1604,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)],[250]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',fact_629_zero__less__power) ).
thf(920,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)],[60]) ).
thf(66,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(942,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(408,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_number__of__add) ).
thf(2204,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)],[408]) ).
thf(271,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_semiring__mult__2__right) ).
thf(1691,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)],[271]) ).
thf(526,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_rel__simps_I16_J) ).
thf(2574,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)],[526]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_eq__number__of) ).
thf(793,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)],[25]) ).
thf(328,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
<=> ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_zcong__zero__equiv__div) ).
thf(1915,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)],[328]) ).
thf(568,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/sandbox/benchmark/theBenchmark.p',fact_404_zero__le__even__power_H) ).
thf(2737,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)],[568]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1311,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)],[164]) ).
thf(415,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_zmult__1__right) ).
thf(2232,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(435,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_bin__less__0__simps_I3_J) ).
thf(2296,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)],[435]) ).
thf(438,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/sandbox/benchmark/theBenchmark.p',fact_531_zspecial__product) ).
thf(2307,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)],[438]) ).
thf(648,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/sandbox/benchmark/theBenchmark.p',fact_432_zdiv__mono2__lemma) ).
thf(3037,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)],[648]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_559_mult__eq__if) ).
thf(1163,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)],[125]) ).
thf(563,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/sandbox/benchmark/theBenchmark.p',fact_112_add__nat__number__of) ).
thf(2705,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)],[563]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',fact_144_power2__less__imp__less) ).
thf(1723,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)],[281]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(825,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)],[31]) ).
thf(428,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/sandbox/benchmark/theBenchmark.p',fact_95_zadd__zmult__distrib2) ).
thf(2277,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)],[428]) ).
thf(630,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_one__is__num__one) ).
thf(2969,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(657,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_zero__is__num__zero) ).
thf(3069,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(679,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_rel__simps_I46_J) ).
thf(3154,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(360,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/sandbox/benchmark/theBenchmark.p',fact_66_sum__squares__ge__zero) ).
thf(2032,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)],[360]) ).
thf(223,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
<=> ( zcong @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_zcong__sym) ).
thf(1519,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)],[223]) ).
thf(532,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_mult__numeral__1) ).
thf(2596,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',fact_688_divides__exp) ).
thf(1570,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)],[238]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_375_crossproduct__noteq) ).
thf(1174,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)],[127]) ).
thf(267,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(1676,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)],[267]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',fact_601_real__le__trans) ).
thf(1502,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)],[216]) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',fact_518_xzgcda__linear__aux1) ).
thf(1751,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)],[287]) ).
thf(308,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_add__Bit1__Bit0) ).
thf(1824,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)],[308]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',fact_623_power__mono) ).
thf(1370,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)],[179]) ).
thf(693,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_rel__simps_I40_J) ).
thf(3207,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(466,axiom,
~ ( ord_less_eq_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_rel__simps_I20_J) ).
thf(2396,plain,
~ ( ord_less_eq_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',fact_497_zcong__neg__1__impl__ne__1) ).
thf(1920,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)],[329]) ).
thf(604,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/sandbox/benchmark/theBenchmark.p',fact_678_power__strict__increasing__iff) ).
thf(2872,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)],[604]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',fact_185_double__number__of__Bit0) ).
thf(1888,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)],[319]) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',fact_139_power2__le__imp__le) ).
thf(1819,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)],[306]) ).
thf(535,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/sandbox/benchmark/theBenchmark.p',fact_273_cube__square) ).
thf(2609,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)],[535]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
<=> ( B
= ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_number__of__reorient) ).
thf(889,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)],[51]) ).
thf(310,axiom,
! [A: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_add__special_I3_J) ).
thf(1836,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)],[310]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',fact_626_zero__le__power) ).
thf(1210,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)],[137]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_412_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1027,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)],[90]) ).
thf(644,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/sandbox/benchmark/theBenchmark.p',fact_134_zmult__zless__mono2) ).
thf(3028,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)],[644]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_576_real__add__mult__distrib) ).
thf(1291,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)],[159]) ).
thf(487,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(2464,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)],[487]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',fact_624_power__mono) ).
thf(847,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)],[37]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',fact_40_le__number__of) ).
thf(1365,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)],[178]) ).
thf(555,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/sandbox/benchmark/theBenchmark.p',fact_147_sum__power2__le__zero__iff) ).
thf(2670,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)],[555]) ).
thf(477,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/sandbox/benchmark/theBenchmark.p',fact_651_dvd__power__le) ).
thf(2433,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)],[477]) ).
thf(492,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/sandbox/benchmark/theBenchmark.p',fact_138_power2__le__imp__le) ).
thf(2477,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)],[492]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',fact_630_zero__less__power) ).
thf(852,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)],[39]) ).
thf(448,axiom,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
<=> ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_power__eq__0__iff) ).
thf(2332,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)],[448]) ).
thf(587,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/sandbox/benchmark/theBenchmark.p',fact_634_one__le__power) ).
thf(2820,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)],[587]) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',fact_489_four__x__squared) ).
thf(2313,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)],[440]) ).
thf(498,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/sandbox/benchmark/theBenchmark.p',fact_280_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2492,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)],[498]) ).
thf(518,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/sandbox/benchmark/theBenchmark.p',fact_427_power__0__left__number__of) ).
thf(2547,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)],[518]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',fact_296_zdvd__reduce) ).
thf(2344,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)],[450]) ).
thf(284,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/sandbox/benchmark/theBenchmark.p',fact_539_zdiff__power2) ).
thf(1740,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)],[284]) ).
thf(326,axiom,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_zcong__1) ).
thf(1910,plain,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(842,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(550,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/sandbox/benchmark/theBenchmark.p',fact_523_zle__diff1__eq) ).
thf(2653,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)],[550]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',fact_653_le__imp__power__dvd) ).
thf(1106,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)],[112]) ).
thf(668,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/sandbox/benchmark/theBenchmark.p',fact_295_zdvd__mult__cancel) ).
thf(3105,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)],[668]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1541,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)],[230]) ).
thf(395,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__eq__int__code_I16_J) ).
thf(2157,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)],[395]) ).
thf(340,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/sandbox/benchmark/theBenchmark.p',fact_244_number__of__Bit0) ).
thf(1953,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)],[340]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',fact_16_zero__less__power2) ).
thf(1804,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)],[302]) ).
thf(592,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/sandbox/benchmark/theBenchmark.p',fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2841,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)],[592]) ).
thf(696,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/sandbox/benchmark/theBenchmark.p',fact_108_zle__add1__eq__le) ).
thf(3218,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)],[696]) ).
thf(245,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_rel__simps_I51_J) ).
thf(1587,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)],[245]) ).
thf(504,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_numeral__1__eq__1) ).
thf(2509,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_384_crossproduct__eq) ).
thf(1138,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)],[120]) ).
thf(671,axiom,
( ( ord_less_eq_int @ zero_zero_int @ s )
& ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_s0p) ).
thf(3119,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)],[671]) ).
thf(692,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/sandbox/benchmark/theBenchmark.p',fact_51_zadd__left__mono) ).
thf(3205,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)],[692]) ).
thf(663,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_rel__simps_I8_J) ).
thf(3087,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)],[663]) ).
thf(507,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_diff__bin__simps_I3_J) ).
thf(2515,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(382,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/sandbox/benchmark/theBenchmark.p',fact_527_inv__not__p__minus__1__aux) ).
thf(2100,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)],[382]) ).
thf(460,axiom,
( ( t = zero_zero_int )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
thf(2377,plain,
( ( t = zero_zero_int )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(581,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/sandbox/benchmark/theBenchmark.p',fact_548_zpower__zdvd__prop1) ).
thf(2801,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)],[581]) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',fact_695_divides__div__not) ).
thf(1375,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)],[181]) ).
thf(632,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_number__of__Pls) ).
thf(2973,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_564_real__le__eq__diff) ).
thf(1121,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)],[116]) ).
thf(114,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 )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_realpow__pos__nth__unique) ).
thf(1111,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 )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(344,axiom,
! [A: int,B: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_add__number__of__eq) ).
thf(1970,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)],[344]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_677_power__strict__increasing__iff) ).
thf(1227,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)],[143]) ).
thf(545,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
<=> ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_rel__simps_I25_J) ).
thf(2638,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)],[545]) ).
thf(115,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_number__of__mult) ).
thf(1118,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)],[115]) ).
thf(237,axiom,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_realpow__minus__mult) ).
thf(1567,plain,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( twoSqu512355103sum2sq @ B )
=> ( ( twoSqu512355103sum2sq @ A )
=> ( twoSqu512355103sum2sq @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_is__mult__sum2sq) ).
thf(884,plain,
! [A: int,B: int] :
( ( twoSqu512355103sum2sq @ B )
=> ( ( twoSqu512355103sum2sq @ A )
=> ( twoSqu512355103sum2sq @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(444,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/sandbox/benchmark/theBenchmark.p',fact_217_add__number__of__left) ).
thf(2323,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)],[444]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',fact_528_zcong__eq__trans) ).
thf(933,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)],[63]) ).
thf(203,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_real__le__antisym) ).
thf(1461,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)],[203]) ).
thf(602,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/sandbox/benchmark/theBenchmark.p',fact_140_power2__le__imp__le) ).
thf(2868,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)],[602]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_313_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1075,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)],[102]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',fact_305_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1424,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)],[194]) ).
thf(451,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/sandbox/benchmark/theBenchmark.p',fact_131_zadd__left__commute) ).
thf(2349,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)],[451]) ).
thf(136,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1207,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(260,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_one__power2) ).
thf(1644,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)],[260]) ).
thf(521,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_Numeral1__eq1__nat) ).
thf(2561,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(694,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_rel__simps_I4_J) ).
thf(3210,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)],[694]) ).
thf(646,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/sandbox/benchmark/theBenchmark.p',fact_553_zpower__zdvd__prop2) ).
thf(3032,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)],[646]) ).
thf(334,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/sandbox/benchmark/theBenchmark.p',fact_136_power2__eq__imp__eq) ).
thf(1937,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)],[334]) ).
thf(384,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/sandbox/benchmark/theBenchmark.p',fact_187_power3__eq__cube) ).
thf(2108,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)],[384]) ).
thf(199,axiom,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_eq__number__of) ).
thf(1446,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)],[199]) ).
thf(252,axiom,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zero__power2) ).
thf(1612,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)],[252]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_596_power__strict__mono) ).
thf(1039,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)],[95]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(970,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1,conjecture,
ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(701,plain,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1478,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)],[207]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_divides__ge) ).
thf(911,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)],[57]) ).
thf(500,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/sandbox/benchmark/theBenchmark.p',fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(2497,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)],[500]) ).
thf(338,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
<=> ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_le__special_I4_J) ).
thf(1947,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)],[338]) ).
thf(350,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Bit0__Pls) ).
thf(1984,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(560,axiom,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_le__special_I2_J) ).
thf(2697,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)],[560]) ).
thf(427,axiom,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_less__0__number__of) ).
thf(2272,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)],[427]) ).
thf(483,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_numeral__1__eq__1) ).
thf(2450,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(388,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/sandbox/benchmark/theBenchmark.p',fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(2125,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)],[388]) ).
thf(514,axiom,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_field__power__not__zero) ).
thf(2536,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)],[514]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',fact_683_power__Suc__less) ).
thf(1297,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)],[161]) ).
thf(591,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_rel__simps_I26_J) ).
thf(2836,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)],[591]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',fact_662_power__less__power__Suc) ).
thf(1456,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)],[201]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',fact_657_nat__zero__less__power__iff) ).
thf(1552,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)],[234]) ).
thf(596,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/sandbox/benchmark/theBenchmark.p',fact_145_power2__less__imp__less) ).
thf(2851,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)],[596]) ).
thf(419,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/sandbox/benchmark/theBenchmark.p',fact_350_mult__nat__number__of) ).
thf(2243,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)],[419]) ).
thf(488,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_semiring__numeral__1__eq__1) ).
thf(2465,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_power__eq__0__iff) ).
thf(1060,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)],[100]) ).
thf(523,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_add__numeral__0) ).
thf(2566,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(300,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Pls__def) ).
thf(1799,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(656,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/sandbox/benchmark/theBenchmark.p',fact_86_le__special_I2_J) ).
thf(3064,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)],[656]) ).
thf(280,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1720,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',fact_28_add__special_I3_J) ).
thf(1979,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)],[348]) ).
thf(659,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_diff__bin__simps_I10_J) ).
thf(3074,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)],[659]) ).
thf(691,axiom,
! [A: int] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_rel__simps_I45_J) ).
thf(3201,plain,
! [A: int] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(185,axiom,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_add__diff__add) ).
thf(1393,plain,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(459,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_rel__simps_I44_J) ).
thf(2370,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(695,axiom,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power2__less__0) ).
thf(3215,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)],[695]) ).
thf(677,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(3147,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',fact_482_zcong__scalar2) ).
thf(1086,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)],[104]) ).
thf(561,axiom,
ord_less_eq_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_rel__simps_I23_J) ).
thf(2702,plain,
ord_less_eq_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(686,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_less__int__code_I13_J) ).
thf(3183,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)],[686]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',fact_550_zcong__zmult__prop3) ).
thf(2057,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)],[368]) ).
thf(570,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/sandbox/benchmark/theBenchmark.p',fact_697_divides__cases) ).
thf(2748,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)],[570]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_481_zcong__scalar) ).
thf(1035,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)],[93]) ).
thf(129,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_order__le__neq__implies__less) ).
thf(1187,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)],[129]) ).
thf(412,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/sandbox/benchmark/theBenchmark.p',fact_540_zdiff__power3) ).
thf(2221,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)],[412]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_668_power__0__left) ).
thf(773,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)],[20]) ).
thf(512,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
<=> ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_less__bin__lemma) ).
thf(2529,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)],[512]) ).
thf(618,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/sandbox/benchmark/theBenchmark.p',fact_11_sum__power2__eq__zero__iff) ).
thf(2909,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)],[618]) ).
thf(470,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult__Bit0) ).
thf(2408,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)],[470]) ).
thf(688,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_semiring__one__add__one__is__two) ).
thf(3190,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)],[688]) ).
thf(547,axiom,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_zero__le__power2) ).
thf(2645,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)],[547]) ).
thf(636,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/sandbox/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2995,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)],[636]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(953,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)],[70]) ).
thf(553,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/sandbox/benchmark/theBenchmark.p',fact_220_add__number__of__eq) ).
thf(2662,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)],[553]) ).
thf(416,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_int__0__neq__1) ).
thf(2235,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',fact_658_power__less__imp__less__base) ).
thf(1510,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)],[219]) ).
thf(288,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_double__eq__0__iff) ).
thf(1754,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)],[288]) ).
thf(616,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_mult__2) ).
thf(2904,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)],[616]) ).
thf(111,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1103,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(393,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__eq__int__code_I13_J) ).
thf(2149,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)],[393]) ).
thf(661,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_mult__numeral__1__right) ).
thf(3079,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',fact_94_zadd__zmult__distrib) ).
thf(1595,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)],[246]) ).
thf(612,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_semiring__numeral__1__eq__1) ).
thf(2894,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(680,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(3158,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(150,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/sandbox/benchmark/theBenchmark.p',fact_385_crossproduct__eq) ).
thf(1251,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)],[150]) ).
thf(472,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/sandbox/benchmark/theBenchmark.p',fact_672_power__strict__increasing) ).
thf(2413,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)],[472]) ).
thf(650,axiom,
! [A: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_odd__nonzero) ).
thf(3042,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)],[650]) ).
thf(529,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rel__simps_I19_J) ).
thf(2585,plain,
ord_less_eq_int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(123,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
<=> ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_add__0__iff) ).
thf(1154,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)],[123]) ).
thf(566,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
<=> ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_less__special_I4_J) ).
thf(2727,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)],[566]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_307_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1007,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)],[86]) ).
thf(365,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/sandbox/benchmark/theBenchmark.p',fact_491_zcong__zless__imp__eq) ).
thf(2048,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)],[365]) ).
thf(595,axiom,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_zcong__id) ).
thf(2849,plain,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(496,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/sandbox/benchmark/theBenchmark.p',fact_433_unique__quotient__lemma__neg) ).
thf(2489,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)],[496]) ).
thf(465,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_semiring__mult__2) ).
thf(2393,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)],[465]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',fact_441_zprime__def) ).
thf(1652,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)],[263]) ).
thf(183,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1388,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(467,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/sandbox/benchmark/theBenchmark.p',fact_149_sum__power2__ge__zero) ).
thf(2398,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)],[467]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',fact_536_zcong__zpower) ).
thf(1965,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)],[342]) ).
thf(586,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/sandbox/benchmark/theBenchmark.p',fact_279_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2817,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)],[586]) ).
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/sandbox/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1488,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(46,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/sandbox/benchmark/theBenchmark.p',fact_534_zcong__zmult__prop1) ).
thf(875,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)],[46]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',fact_671_power__strict__increasing) ).
thf(711,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)],[6]) ).
thf(228,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_power__0) ).
thf(1535,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(583,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/sandbox/benchmark/theBenchmark.p',fact_73_le__number__of__eq__not__less) ).
thf(2806,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)],[583]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(958,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)],[72]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',fact_679_power__increasing) ).
thf(1403,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)],[189]) ).
thf(697,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/sandbox/benchmark/theBenchmark.p',fact_490_zcong__zless__0) ).
thf(3223,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)],[697]) ).
thf(660,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/sandbox/benchmark/theBenchmark.p',fact_422_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(3077,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)],[660]) ).
thf(23,axiom,
! [A: int,B: int] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_arith__simps_I32_J) ).
thf(787,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)],[23]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_397_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)],[146]) ).
thf(672,axiom,
zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_s1) ).
thf(3123,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)],[672]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1092,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)],[107]) ).
thf(520,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_rel__simps_I49_J) ).
thf(2557,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',fact_72_le__number__of__eq__not__less) ).
thf(704,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)],[4]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1224,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)],[142]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',fact_483_zcong__zmult) ).
thf(1356,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)],[176]) ).
thf(682,axiom,
~ ( ord_less_int @ min @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_rel__simps_I7_J) ).
thf(3170,plain,
~ ( ord_less_int @ min @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(359,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/sandbox/benchmark/theBenchmark.p',fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2029,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)],[359]) ).
thf(445,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/sandbox/benchmark/theBenchmark.p',fact_183_zadd__strict__right__mono) ).
thf(2326,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)],[445]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',fact_430_q__neg__lemma) ).
thf(1707,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)],[274]) ).
thf(434,axiom,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_add__numeral__0__right) ).
thf(2293,plain,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(713,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)],[7]) ).
thf(314,axiom,
! [A: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_eq__0__number__of) ).
thf(1865,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)],[314]) ).
thf(291,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_rel__simps_I21_J) ).
thf(1765,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)],[291]) ).
thf(106,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_zcong__trans) ).
thf(1090,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)],[106]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fact_693_divides__rev) ).
thf(1464,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)],[204]) ).
thf(68,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(947,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(79,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_right__diff__distrib__number__of) ).
thf(979,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_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)],[79]) ).
thf(509,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/sandbox/benchmark/theBenchmark.p',fact_431_unique__quotient__lemma) ).
thf(2521,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)],[509]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',fact_637_power__inject__exp) ).
thf(2119,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)],[387]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_560_power__eq__if) ).
thf(831,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)],[33]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',fact_38_less__eq__number__of__int__code) ).
thf(1408,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)],[191]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',fact_303_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1282,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)],[156]) ).
thf(414,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ ( number_number_of_int @ B ) @ C ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_add__number__of__diff1) ).
thf(2229,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ ( number_number_of_int @ B ) @ C ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',fact_583_real__mult__order) ).
thf(1574,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)],[240]) ).
thf(381,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/sandbox/benchmark/theBenchmark.p',fact_275_self__quotient__aux1) ).
thf(2097,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)],[381]) ).
thf(598,axiom,
ord_less_int @ t @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(2856,plain,
ord_less_int @ t @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(613,axiom,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_zero__le__power2) ).
thf(2896,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)],[613]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_501_zcong__zdiff) ).
thf(863,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)],[41]) ).
thf(376,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/sandbox/benchmark/theBenchmark.p',fact_484_zcong__zadd) ).
thf(2079,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)],[376]) ).
thf(455,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_bin__less__0__simps_I1_J) ).
thf(2361,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_124_left__distrib__number__of) ).
thf(900,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)],[53]) ).
thf(556,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/sandbox/benchmark/theBenchmark.p',fact_418_power__eq__0__iff__number__of) ).
thf(2679,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)],[556]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',fact_488_zcong__iff__lin) ).
thf(2415,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)],[473]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',fact_90_less__number__of__int__code) ).
thf(1894,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)],[322]) ).
thf(635,axiom,
! [A: int,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= one_one_int ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= ( times_times_int @ A @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_realpow__num__eq__if) ).
thf(2987,plain,
! [A: int,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= one_one_int ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= ( times_times_int @ A @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',fact_152_not__sum__squares__lt__zero) ).
thf(784,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)],[22]) ).
thf(474,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_rel__simps_I10_J) ).
thf(2422,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)],[474]) ).
thf(575,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
thf(2774,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(224,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_power__0) ).
thf(1524,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(626,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/sandbox/benchmark/theBenchmark.p',fact_440_Euler_Oaux____1) ).
thf(2955,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)],[626]) ).
thf(249,axiom,
ord_less_int @ min @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_bin__less__0__simps_I2_J) ).
thf(1603,plain,
ord_less_int @ min @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(97,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1043,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',fact_434_zdiv__mono2__neg__lemma) ).
thf(1801,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)],[301]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',fact_246_number__of__Bit1) ).
thf(1667,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)],[264]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',fact_606_power__mult__distrib) ).
thf(811,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)],[27]) ).
thf(643,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/sandbox/benchmark/theBenchmark.p',fact_32_qf1pt) ).
thf(3027,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)],[643]) ).
thf(389,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_rel__simps_I38_J) ).
thf(2129,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(385,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/sandbox/benchmark/theBenchmark.p',fact_423_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2111,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)],[385]) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',fact_541_zcong__less__eq) ).
thf(1630,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)],[257]) ).
thf(577,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_rel__simps_I30_J) ).
thf(2780,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)],[577]) ).
thf(307,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_zmult__1) ).
thf(1821,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(9,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
<=> ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_less__eq__real__def) ).
thf(726,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)],[9]) ).
thf(481,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/sandbox/benchmark/theBenchmark.p',fact_477_Euler_Oaux2) ).
thf(2446,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)],[481]) ).
thf(689,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_rel__simps_I50_J) ).
thf(3192,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',fact_405_add__scale__eq__noteq) ).
thf(964,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)],[74]) ).
thf(421,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_nat__number__of__Pls) ).
thf(2252,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(270,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/sandbox/benchmark/theBenchmark.p',fact_222_number__of__add) ).
thf(1688,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)],[270]) ).
thf(674,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/sandbox/benchmark/theBenchmark.p',fact_269_zadd__power3) ).
thf(3133,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)],[674]) ).
thf(653,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/sandbox/benchmark/theBenchmark.p',fact_109_semiring__add__number__of) ).
thf(3055,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)],[653]) ).
thf(647,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_semiring__mult__2) ).
thf(3034,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)],[647]) ).
thf(620,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/sandbox/benchmark/theBenchmark.p',fact_469_zmult__eq__1__iff) ).
thf(2923,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)],[620]) ).
thf(578,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/sandbox/benchmark/theBenchmark.p',fact_151_sum__squares__gt__zero__iff) ).
thf(2785,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)],[578]) ).
thf(638,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_power__one__right) ).
thf(3006,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(516,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_semiring__norm_I110_J) ).
thf(2542,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(548,axiom,
! [A: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__special_I2_J) ).
thf(2647,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)],[548]) ).
thf(678,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/sandbox/benchmark/theBenchmark.p',fact_407_add__scale__eq__noteq) ).
thf(3150,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)],[678]) ).
thf(339,axiom,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_pos2) ).
thf(1952,plain,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1171,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)],[126]) ).
thf(540,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/sandbox/benchmark/theBenchmark.p',fact_442_prime__g__5) ).
thf(2620,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)],[540]) ).
thf(391,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/sandbox/benchmark/theBenchmark.p',fact_425_power__0__left__number__of) ).
thf(2139,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)],[391]) ).
thf(370,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
thf(2064,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)],[370]) ).
thf(432,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/sandbox/benchmark/theBenchmark.p',fact_628_zero__le__power) ).
thf(2288,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)],[432]) ).
thf(293,axiom,
! [A: int] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_power2__ge__self) ).
thf(1775,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)],[293]) ).
thf(543,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/sandbox/benchmark/theBenchmark.p',fact_8_not__sum__power2__lt__zero) ).
thf(2633,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)],[543]) ).
thf(214,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1496,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',fact_160_pos__zmult__eq__1__iff) ).
thf(2207,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)],[409]) ).
thf(372,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_order__le__neq__implies__less) ).
thf(2069,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)],[372]) ).
thf(133,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_real__mult__1) ).
thf(1198,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_650_dvd__power__le) ).
thf(1396,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)],[186]) ).
thf(628,axiom,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_less__special_I2_J) ).
thf(2962,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)],[628]) ).
thf(457,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/sandbox/benchmark/theBenchmark.p',fact_684_power__Suc__less) ).
thf(2365,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)],[457]) ).
thf(366,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(2051,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',fact_41_zmult__assoc) ).
thf(1245,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)],[148]) ).
thf(629,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_zero__power2) ).
thf(2967,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)],[629]) ).
thf(464,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/sandbox/benchmark/theBenchmark.p',fact_240_power2__sum) ).
thf(2390,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)],[464]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',fact_15_zero__less__power2) ).
thf(1694,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)],[272]) ).
thf(61,axiom,
! [A: real,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= one_one_real ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= ( times_times_real @ A @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_realpow__num__eq__if) ).
thf(922,plain,
! [A: real,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= one_one_real ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= ( times_times_real @ A @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(634,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/sandbox/benchmark/theBenchmark.p',fact_486_power__m1__even) ).
thf(2984,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)],[634]) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',fact_143_power2__less__imp__less) ).
thf(1973,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)],[345]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',fact_63_sum__squares__le__zero__iff) ).
thf(1413,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)],[192]) ).
thf(639,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/sandbox/benchmark/theBenchmark.p',fact_377_crossproduct__noteq) ).
thf(3009,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)],[639]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(2054,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)],[367]) ).
thf(625,axiom,
! [A: real,B: real] :
( ( power_power_real @ ( minus_minus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_power2__diff) ).
thf(2952,plain,
! [A: real,B: real] :
( ( power_power_real @ ( minus_minus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_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)],[625]) ).
thf(554,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/sandbox/benchmark/theBenchmark.p',fact_254_odd__less__0) ).
thf(2665,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)],[554]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',fact_594_realpow__num__eq__if) ).
thf(1467,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)],[205]) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',fact_292_zpower__zpower) ).
thf(2318,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)],[442]) ).
thf(362,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_less__int__code_I15_J) ).
thf(2037,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)],[362]) ).
thf(606,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_diff__bin__simps_I5_J) ).
thf(2878,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_573_real__mult__left__cancel) ).
thf(749,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)],[14]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',fact_661_power__less__power__Suc) ).
thf(1340,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)],[172]) ).
thf(615,axiom,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__special_I1_J) ).
thf(2899,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)],[615]) ).
thf(528,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/sandbox/benchmark/theBenchmark.p',fact_496_neg__one__power__eq__mod__m) ).
thf(2582,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)],[528]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_150_sum__squares__gt__zero__iff) ).
thf(1049,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)],[99]) ).
thf(681,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/sandbox/benchmark/theBenchmark.p',fact_123_sum__squares__eq__zero__iff) ).
thf(3161,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)],[681]) ).
thf(325,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_less__eq__int__code_I15_J) ).
thf(1905,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)],[325]) ).
thf(353,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_rel__simps_I5_J) ).
thf(1990,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)],[353]) ).
thf(652,axiom,
! [A: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zero__eq__power2) ).
thf(3048,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)],[652]) ).
thf(594,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_power2__eq__square) ).
thf(2846,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)],[594]) ).
thf(423,axiom,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zero__eq__power2) ).
thf(2256,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)],[423]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_647_power__le__dvd) ).
thf(968,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)],[75]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',fact_665_power__gt1__lemma) ).
thf(823,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)],[30]) ).
thf(292,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_rel__simps_I28_J) ).
thf(1770,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)],[292]) ).
thf(564,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_nat__mult__2) ).
thf(2715,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)],[564]) ).
thf(552,axiom,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_p) ).
thf(2661,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)],[552]) ).
thf(285,axiom,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1743,plain,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',fact_417_power__eq__0__iff__number__of) ).
thf(2012,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)],[356]) ).
thf(567,axiom,
! [A: int,B: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_less__number__of) ).
thf(2732,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)],[567]) ).
thf(508,axiom,
( ~ ( quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
!= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(2518,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)],[508]) ).
thf(699,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/sandbox/benchmark/theBenchmark.p',fact_55_semiring__mult__number__of) ).
thf(3228,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)],[699]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_652_dvd__power__le) ).
thf(1098,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)],[109]) ).
thf(601,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_rel__simps_I14_J) ).
thf(2863,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)],[601]) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',fact_675_power__less__imp__less__exp) ).
thf(1598,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)],[247]) ).
thf(101,axiom,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
<=> ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_even__less__0__iff) ).
thf(1070,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)],[101]) ).
thf(45,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_order__le__neq__implies__less) ).
thf(872,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)],[45]) ).
thf(662,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_bin__less__0__simps_I4_J) ).
thf(3082,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)],[662]) ).
thf(404,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/sandbox/benchmark/theBenchmark.p',fact_625_power__mono) ).
thf(2192,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)],[404]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_614_dvd__power__same) ).
thf(1267,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)],[153]) ).
thf(654,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/sandbox/benchmark/theBenchmark.p',fact_271_int__pos__lt__two__imp__zero__or__one) ).
thf(3058,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)],[654]) ).
thf(144,axiom,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_not__real__square__gt__zero) ).
thf(1230,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)],[144]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',fact_689_divides__mul__l) ).
thf(1484,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)],[209]) ).
thf(524,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/sandbox/benchmark/theBenchmark.p',fact_218_add__number__of__left) ).
thf(2569,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)],[524]) ).
thf(379,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zero__power2) ).
thf(2092,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)],[379]) ).
thf(397,axiom,
! [A: real] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_power2__less__0) ).
thf(2165,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)],[397]) ).
thf(557,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/sandbox/benchmark/theBenchmark.p',fact_126_left__distrib__number__of) ).
thf(2688,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)],[557]) ).
thf(296,axiom,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1785,plain,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',fact_547_Int2_Ozcong__zero) ).
thf(1711,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)],[276]) ).
thf(640,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/sandbox/benchmark/theBenchmark.p',fact_299_zdvd__imp__le) ).
thf(3019,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)],[640]) ).
thf(215,axiom,
! [A: real] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1499,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)],[215]) ).
thf(352,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/sandbox/benchmark/theBenchmark.p',fact_242_power2__sum) ).
thf(1987,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)],[352]) ).
thf(278,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(1716,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(413,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
<=> ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_even__less__0__iff) ).
thf(2224,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)],[413]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1317,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)],[166]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',fact_403_zero__le__even__power_H) ).
thf(1763,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)],[290]) ).
thf(229,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1538,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(495,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/sandbox/benchmark/theBenchmark.p',fact_294_zdvd__antisym__nonneg) ).
thf(2486,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)],[495]) ).
thf(533,axiom,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_less__special_I1_J) ).
thf(2599,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)],[533]) ).
thf(157,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_left__diff__distrib__number__of) ).
thf(1285,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( minus_minus_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)],[157]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1218,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)],[140]) ).
thf(665,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/sandbox/benchmark/theBenchmark.p',fact_241_power2__sum) ).
thf(3095,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)],[665]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_add__0__iff) ).
thf(1358,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)],[177]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',fact_130_zadd__assoc) ).
thf(1934,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)],[333]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',fact_282__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(2113,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)],[386]) ).
thf(673,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
<=> ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zless__le) ).
thf(3124,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)],[673]) ).
thf(273,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
<=> ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_int__one__le__iff__zero__less) ).
thf(1702,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)],[273]) ).
thf(453,axiom,
! [A: int] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2357,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)],[453]) ).
thf(527,axiom,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_add__numeral__0) ).
thf(2579,plain,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',fact_581_real__mult__le__cancel__iff2) ).
thf(1427,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)],[195]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1504,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)],[217]) ).
thf(505,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(2511,plain,
ord_less_eq_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(600,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_mult__Bit1) ).
thf(2860,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)],[600]) ).
thf(279,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/sandbox/benchmark/theBenchmark.p',fact_54_semiring__mult__number__of) ).
thf(1717,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)],[279]) ).
thf(621,axiom,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_less__special_I2_J) ).
thf(2939,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)],[621]) ).
thf(658,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/sandbox/benchmark/theBenchmark.p',fact_128_right__distrib__number__of) ).
thf(3071,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)],[658]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_exp__eq__1) ).
thf(1272,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)],[155]) ).
thf(425,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_diff__bin__simps_I7_J) ).
thf(2266,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)],[425]) ).
thf(471,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_one__add__one__is__two) ).
thf(2411,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)],[471]) ).
thf(501,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/sandbox/benchmark/theBenchmark.p',fact_660_power__less__imp__less__base) ).
thf(2500,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)],[501]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',fact_311_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(744,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)],[12]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1221,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)],[141]) ).
thf(633,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/sandbox/benchmark/theBenchmark.p',fact_12_sum__power2__eq__zero__iff) ).
thf(2975,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)],[633]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',fact_485_power__m1__even) ).
thf(1670,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)],[265]) ).
thf(642,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/sandbox/benchmark/theBenchmark.p',fact_529_zcong__square__zless) ).
thf(3024,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)],[642]) ).
thf(180,axiom,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_left__diff__distrib__number__of) ).
thf(1372,plain,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(611,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/sandbox/benchmark/theBenchmark.p',fact_543_zdvd__bounds) ).
thf(2892,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)],[611]) ).
thf(81,axiom,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_power__one) ).
thf(991,plain,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(254,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_rel__simps_I29_J) ).
thf(1617,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)],[254]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',fact_9_sum__power2__gt__zero__iff) ).
thf(1839,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)],[311]) ).
thf(493,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
<=> ( ord_less_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_rel__simps_I13_J) ).
thf(2479,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)],[493]) ).
thf(378,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/sandbox/benchmark/theBenchmark.p',fact_355_even__power__le__0__imp__0) ).
thf(2088,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)],[378]) ).
thf(269,axiom,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_add__diff__add) ).
thf(1685,plain,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(559,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(2696,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)],[559]) ).
thf(603,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/sandbox/benchmark/theBenchmark.p',fact_424_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2870,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)],[603]) ).
thf(117,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1126,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(403,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_less__special_I3_J) ).
thf(2187,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)],[403]) ).
thf(546,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/sandbox/benchmark/theBenchmark.p',fact_535_zcong__shift) ).
thf(2643,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)],[546]) ).
thf(551,axiom,
! [A: int,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_realpow__minus__mult) ).
thf(2658,plain,
! [A: int,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(617,axiom,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_two__realpow__ge__one) ).
thf(2907,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)],[617]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_608_power__commutes) ).
thf(1108,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)],[113]) ).
thf(605,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/sandbox/benchmark/theBenchmark.p',fact_435_quartic__square__square) ).
thf(2875,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)],[605]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',fact_278_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(1940,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)],[335]) ).
thf(478,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/sandbox/benchmark/theBenchmark.p',fact_607_power__mult__distrib) ).
thf(2435,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)],[478]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_682_power__Suc__less) ).
thf(845,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)],[36]) ).
thf(542,axiom,
! [A: int] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_eq__number__of__0) ).
thf(2626,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)],[542]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',fact_239_power2__eq__square__number__of) ).
thf(1649,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)],[262]) ).
thf(452,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/sandbox/benchmark/theBenchmark.p',fact_216_less__number__of) ).
thf(2352,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)],[452]) ).
thf(364,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_zadd__0) ).
thf(2045,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(664,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_semiring__mult__2__right) ).
thf(3092,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)],[664]) ).
thf(439,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/sandbox/benchmark/theBenchmark.p',fact_561_diff__square) ).
thf(2310,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)],[439]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(976,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)],[78]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_664_power__gt1__lemma) ).
thf(903,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)],[54]) ).
thf(687,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/sandbox/benchmark/theBenchmark.p',fact_654_le__imp__power__dvd) ).
thf(3188,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)],[687]) ).
thf(405,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/sandbox/benchmark/theBenchmark.p',fact_30__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(2194,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)],[405]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',fact_238_power2__eq__square__number__of) ).
thf(2215,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)],[410]) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',fact_597_power__strict__mono) ).
thf(1517,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)],[222]) ).
thf(87,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
<=> ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_real__less__def) ).
thf(1010,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)],[87]) ).
thf(437,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/sandbox/benchmark/theBenchmark.p',fact_293_zdvd__not__zless) ).
thf(2305,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)],[437]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',fact_552_zcong__zprime__prod__zero) ).
thf(2342,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)],[449]) ).
thf(531,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/sandbox/benchmark/theBenchmark.p',fact_84_le__special_I4_J) ).
thf(2591,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)],[531]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_60_arith__simps_I32_J) ).
thf(961,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)],[73]) ).
thf(430,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/sandbox/benchmark/theBenchmark.p',fact_26_add__special_I2_J) ).
thf(2283,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)],[430]) ).
thf(519,axiom,
! [A: int] :
( ( minus_minus_int @ ( times_times_int @ A @ A ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ ( minus_minus_int @ A @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_real__squared__diff__one__factored) ).
thf(2554,plain,
! [A: int] :
( ( minus_minus_int @ ( times_times_int @ A @ A ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ ( minus_minus_int @ A @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(208,axiom,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_real__squared__diff__one__factored) ).
thf(1481,plain,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(584,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/sandbox/benchmark/theBenchmark.p',fact_289_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(2811,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)],[584]) ).
thf(631,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_semiring__numeral__0__eq__0) ).
thf(2971,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(573,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_rel__simps_I48_J) ).
thf(2764,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)],[573]) ).
thf(675,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_Int2_Oaux1) ).
thf(3136,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)],[675]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
thf(781,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(511,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/sandbox/benchmark/theBenchmark.p',fact_610_power__commutes) ).
thf(2526,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)],[511]) ).
thf(261,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_semiring__mult__2__right) ).
thf(1646,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)],[261]) ).
thf(480,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/sandbox/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
thf(2443,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)],[480]) ).
thf(597,axiom,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_diff__bin__simps_I1_J) ).
thf(2853,plain,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(433,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_add__Bit0__Bit0) ).
thf(2290,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)],[433]) ).
thf(622,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/sandbox/benchmark/theBenchmark.p',fact_93_plus__numeral__code_I9_J) ).
thf(2944,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)],[622]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',fact_301_le__nat__number__of) ).
thf(2081,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)],[377]) ).
thf(294,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_rel__simps_I17_J) ).
thf(1777,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)],[294]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1440,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)],[197]) ).
thf(163,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1308,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(371,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/sandbox/benchmark/theBenchmark.p',fact_413_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2066,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)],[371]) ).
thf(131,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1193,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(396,axiom,
! [A: nat] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2162,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)],[396]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_509_number__of__diff) ).
thf(1212,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)],[138]) ).
thf(321,axiom,
ord_less_int @ t @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(1893,plain,
ord_less_int @ t @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(569,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/sandbox/benchmark/theBenchmark.p',fact_347_zero__less__power__nat__eq__number__of) ).
thf(2739,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)],[569]) ).
thf(541,axiom,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_add__Pls) ).
thf(2623,plain,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(91,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1030,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(212,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1491,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(579,axiom,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_power2__eq__square) ).
thf(2796,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)],[579]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fact_411_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(914,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)],[58]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_62_number__of__mult) ).
thf(1294,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)],[160]) ).
thf(486,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_semiring__norm_I112_J) ).
thf(2462,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(8,axiom,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
<=> ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_power__eq__0__iff) ).
thf(716,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)],[8]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_502_zdvd__zdiffD) ).
thf(1161,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)],[124]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_354_power__even__eq) ).
thf(1614,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)],[253]) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',fact_419_power__eq__0__iff__number__of) ).
thf(2003,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)],[355]) ).
thf(411,axiom,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_add__numeral__0__right) ).
thf(2218,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(259,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_nat__numeral__1__eq__1) ).
thf(1642,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(220,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_zle__refl) ).
thf(1512,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(282,axiom,
! [A: int] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_rel__simps_I42_J) ).
thf(1725,plain,
! [A: int] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',fact_243_number__of__Bit0) ).
thf(1578,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)],[242]) ).
thf(513,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_semiring__numeral__0__eq__0) ).
thf(2534,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(950,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)],[69]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1546,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)],[232]) ).
thf(256,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_rel__simps_I12_J) ).
thf(1625,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)],[256]) ).
thf(534,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__special_I1_J) ).
thf(2604,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)],[534]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_617_power__mult) ).
thf(867,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)],[43]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',fact_673_power__less__imp__less__exp) ).
thf(865,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)],[42]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',fact_636_power__inject__exp) ).
thf(735,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)],[10]) ).
thf(462,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_diff__bin__simps_I9_J) ).
thf(2385,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)],[462]) ).
thf(268,axiom,
! [A: int] :
( ( min
= ( bit1 @ A ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_rel__simps_I43_J) ).
thf(1678,plain,
! [A: int] :
( ( ( min
= ( bit1 @ A ) )
=> ( min = A ) )
& ( ( min = A )
=> ( min
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_nat__mult__eq__one) ).
thf(854,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)],[40]) ).
thf(351,axiom,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_t__l__p) ).
thf(1986,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)],[351]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',fact_65_sum__squares__ge__zero) ).
thf(1527,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)],[225]) ).
thf(121,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1148,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',fact_125_left__distrib__number__of) ).
thf(1673,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)],[266]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1248,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)],[149]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_381_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(790,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)],[24]) ).
thf(544,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/sandbox/benchmark/theBenchmark.p',fact_648_power__le__dvd) ).
thf(2636,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)],[544]) ).
thf(571,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_mult__numeral__1) ).
thf(2751,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',fact_382_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1314,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)],[165]) ).
thf(525,axiom,
( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(2572,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)],[525]) ).
thf(235,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_zle__antisym) ).
thf(1561,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)],[235]) ).
thf(357,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_eq__number__of__Pls__Min) ).
thf(2021,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_618_power__mult) ).
thf(886,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)],[50]) ).
thf(407,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/sandbox/benchmark/theBenchmark.p',fact_619_power__mult) ).
thf(2201,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)],[407]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_376_crossproduct__noteq) ).
thf(801,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)],[26]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_609_power__commutes) ).
thf(897,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)],[52]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fact_127_right__distrib__number__of) ).
thf(767,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)],[18]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_691_divides__add__revr) ).
thf(1033,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)],[92]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1288,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)],[158]) ).
thf(690,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_rel__simps_I34_J) ).
thf(3196,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)],[690]) ).
thf(320,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/sandbox/benchmark/theBenchmark.p',fact_492_zcong__zpower__zmult) ).
thf(1891,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)],[320]) ).
thf(645,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/sandbox/benchmark/theBenchmark.p',fact_106_zless__imp__add1__zle) ).
thf(3030,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)],[645]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(828,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)],[32]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(839,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)],[34]) ).
thf(476,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/sandbox/benchmark/theBenchmark.p',fact_186_power3__eq__cube) ).
thf(2430,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)],[476]) ).
thf(614,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(2898,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(489,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_power2__diff) ).
thf(2467,plain,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_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)],[489]) ).
thf(56,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(908,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',fact_663_power__less__power__Suc) ).
thf(2507,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)],[503]) ).
thf(515,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/sandbox/benchmark/theBenchmark.p',fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2539,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)],[515]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_285_zero__less__power__nat__eq) ).
thf(1299,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)],[162]) ).
thf(324,axiom,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ ( number267125858f_real @ B ) @ C ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_add__number__of__diff1) ).
thf(1902,plain,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ ( number267125858f_real @ B ) @ C ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(502,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_le__special_I3_J) ).
thf(2502,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)],[502]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',fact_290_zprime__power__zdvd__cancel__right) ).
thf(2241,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)],[418]) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',fact_615_dvd__power__same) ).
thf(1977,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)],[347]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',fact_304_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1129,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)],[118]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',fact_146_sum__power2__le__zero__iff) ).
thf(1827,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)],[309]) ).
thf(151,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1261,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(582,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/sandbox/benchmark/theBenchmark.p',fact_111_semiring__add__number__of) ).
thf(2803,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)],[582]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',fact_503_zdiff__zmult__distrib2) ).
thf(1532,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)],[227]) ).
thf(244,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_less__int__code_I16_J) ).
thf(1582,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)],[244]) ).
thf(88,axiom,
ord_less_eq_int @ min @ min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_rel__simps_I24_J) ).
thf(1019,plain,
ord_less_eq_int @ min @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_692_nat__mult__dvd__cancel__disj_H) ).
thf(982,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)],[80]) ).
thf(317,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
<=> ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_le__special_I3_J) ).
thf(1880,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)],[317]) ).
thf(85,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1004,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(494,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_number__of__Pls) ).
thf(2484,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(318,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/sandbox/benchmark/theBenchmark.p',fact_558_real__sum__squared__expand) ).
thf(1885,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)],[318]) ).
thf(169,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1331,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(572,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/sandbox/benchmark/theBenchmark.p',fact_556_Legendre__def) ).
thf(2754,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)],[572]) ).
thf(167,axiom,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_power__one) ).
thf(1320,plain,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',fact_420_pos__zmult__pos) ).
thf(1945,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)],[337]) ).
thf(637,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/sandbox/benchmark/theBenchmark.p',fact_669_power__0__left) ).
thf(2998,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)],[637]) ).
thf(369,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_rel__simps_I15_J) ).
thf(2059,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)],[369]) ).
thf(490,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/sandbox/benchmark/theBenchmark.p',fact_283__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(2470,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)],[490]) ).
thf(327,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Bit1__def) ).
thf(1912,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(401,axiom,
! [A: int] :
( ( ( bit1 @ A )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_rel__simps_I47_J) ).
thf(2177,plain,
! [A: int] :
( ( ( ( bit1 @ A )
= min )
=> ( A = min ) )
& ( ( A = min )
=> ( ( bit1 @ A )
= min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(443,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_semiring__one__add__one__is__two) ).
thf(2321,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',fact_670_power__strict__increasing) ).
thf(940,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)],[65]) ).
thf(522,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_add__Bit0__Bit1) ).
thf(2563,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)],[522]) ).
thf(607,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/sandbox/benchmark/theBenchmark.p',fact_110_semiring__add__number__of) ).
thf(2881,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)],[607]) ).
thf(128,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_real__zero__not__eq__one) ).
thf(1184,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(375,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
<=> ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_less__special_I4_J) ).
thf(2074,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)],[375]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',fact_680_power__increasing) ).
thf(1037,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)],[94]) ).
thf(479,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_rel__simps_I31_J) ).
thf(2438,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)],[479]) ).
thf(417,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_nat__mult__2__right) ).
thf(2238,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)],[417]) ).
thf(537,axiom,
quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(2615,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)],[537]) ).
thf(15,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__number__of) ).
thf(755,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)],[15]) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',fact_646_power__add) ).
thf(2170,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)],[399]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_582_real__mult__less__mono2) ).
thf(1088,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)],[105]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1204,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)],[135]) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',fact_353_power__even__eq) ).
thf(1812,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)],[303]) ).
thf(3233,plain,
$false,
inference(e,[status(thm)],[2822,2452,1337,2094,2612,760,1454,1633,2072,1729,1237,1899,1850,2544,2331,1818,2250,2199,3021,2889,1190,1995,2263,2427,1982,1956,1549,2280,3172,2363,1924,2495,1443,1401,1544,3108,1269,1793,1041,1486,2512,762,994,3040,1422,2947,3098,741,878,2380,2918,2316,2448,1872,814,2459,945,2844,2042,1458,1078,1788,2184,3175,2476,2168,1761,1342,747,1354,2146,1507,930,2360,1095,1196,1001,709,2886,2173,2136,2405,2957,1746,3103,2491,1782,1391,1576,973,1046,3140,1475,2400,1529,1967,1709,2328,1430,2814,3116,3046,2269,3061,1323,1132,2703,1860,1264,917,702,1379,2857,1514,870,1609,1572,770,1931,2024,3180,1875,3231,2388,1100,2829,1922,817,2691,1398,881,2301,1815,1494,2950,2616,1714,2105,2650,1334,2034,1581,2777,2073,905,1151,937,1020,2254,2367,1215,956,1622,2772,998,1405,1600,2154,2718,2618,2833,2523,1796,1345,2799,2286,3226,1943,1201,1242,849,2586,2884,1975,1564,1604,920,942,2204,1691,2574,793,1915,2737,1311,2232,2296,2307,3037,1163,2705,1723,825,2277,2969,3069,3154,2032,1519,2596,1570,1174,1676,1502,1751,1824,1370,3207,2396,1920,2872,1888,1819,2609,889,1836,1210,1027,3028,1291,2464,847,1365,2670,2433,2477,852,2332,2820,2313,2492,2547,2344,1740,1910,842,2653,1106,3105,1541,2157,1953,1804,2841,3218,1587,2509,1138,3119,3205,3087,2515,2100,2377,2801,1375,2973,1121,1111,1970,1227,2638,1118,1567,884,2323,933,1461,2868,1075,1424,2349,1207,1644,2561,3210,3032,1937,2108,1446,1612,1039,970,701,1478,911,2497,1947,1984,2697,2272,2450,2125,2536,1297,2836,1456,1552,2851,2243,2465,1060,2566,1799,3064,1720,1979,3074,3201,1393,2370,3215,3147,1086,2702,3183,2057,2748,1035,1187,2221,773,2529,2909,2408,3190,2645,2995,953,2662,2235,1510,1754,2904,1103,2149,3079,1595,2894,3158,1251,2413,3042,2585,1154,2727,1007,2048,2849,2489,2393,1652,1388,2398,1965,2817,1488,875,711,1535,2806,958,1403,3223,3077,787,1239,3123,1092,2557,704,1224,1356,3170,2029,2326,1707,2293,713,1865,1765,1090,1464,947,979,2521,2119,831,1408,1282,2229,1574,2097,2856,2896,863,2079,2361,900,2679,2415,1894,2987,784,2422,2774,1524,2955,1603,1043,1801,1667,811,3027,2129,2111,1630,2780,1821,726,2446,3192,964,2252,1688,3133,3055,3034,2923,2785,3006,2542,2647,3150,1952,1171,2620,2139,2064,2288,1775,2633,1496,2207,2069,1198,1396,2962,2365,2051,1245,2967,2390,1694,922,2984,1973,1413,3009,2054,2952,2665,1467,2318,2037,2878,749,1340,2899,2582,1049,3161,1905,1990,3048,2846,2256,968,823,1770,2715,2661,1743,2012,2732,2518,3228,1098,2863,1598,1070,872,3082,2192,1267,3058,1230,1484,2569,2092,2165,2688,1785,1711,3019,1499,1987,1716,2224,1317,1763,1538,2486,2599,1285,1218,3095,1358,1934,2113,3124,1702,2357,2579,1427,1504,2511,2860,1717,2939,3071,1272,2266,2411,2500,744,1221,2975,1670,3024,1372,2892,991,1617,1839,2479,2088,1685,2696,2870,1126,2187,2643,2658,2907,1108,2875,1940,2435,845,2626,1649,2352,2045,3092,2310,976,903,3188,2194,2215,1517,1010,2305,2342,2591,961,2283,2554,1481,2811,2971,2764,3136,781,2526,1646,2443,2853,2290,2944,2081,1777,1440,1308,2066,1193,2162,1212,1893,2739,2623,1030,1491,2796,914,1294,2462,716,1161,1614,2003,2218,1642,1512,1725,1578,2534,950,1546,1625,2604,867,865,735,2385,1678,854,1986,1527,1148,1673,1248,790,2636,2751,1314,2572,1561,2021,886,2201,801,897,767,1033,1288,3196,1891,3030,828,839,2430,2898,2467,908,2507,2539,1299,1902,2502,2241,1977,1129,1827,1261,2803,1532,1582,1019,982,1880,1004,2484,1885,1331,2754,1320,1945,2998,2059,2470,1912,2177,2321,940,2563,2881,1184,2074,1037,2438,2238,2615,755,2170,1088,1204,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM924_2 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n016.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 17:38:12 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.93/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.95/1.22 % [INFO] Parsing done (341ms).
% 2.24/1.23 % [INFO] Running in sequential loop mode.
% 2.77/1.46 % [INFO] eprover registered as external prover.
% 2.77/1.47 % [INFO] cvc4 registered as external prover.
% 2.77/1.47 % [INFO] Scanning for conjecture ...
% 3.05/1.61 % [INFO] Found a conjecture and 698 axioms. Running axiom selection ...
% 3.86/1.74 % [INFO] Axiom selection finished. Selected 698 axioms (removed 0 axioms).
% 4.62/2.00 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.62/2.02 % [INFO] Type checking passed.
% 4.62/2.02 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 14.00/4.24 % External prover 'e' found a proof!
% 14.00/4.24 % [INFO] Killing All external provers ...
% 14.00/4.24 % Time passed: 3706ms (effective reasoning time: 3003ms)
% 14.00/4.24 % 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)>
% 14.00/4.25 % Axioms used in derivation (698): fact_290_zprime__power__zdvd__cancel__right, fact_347_zero__less__power__nat__eq__number__of, fact_189_semiring__mult__2, fact_169_Bit0__Pls, fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_81_nat__number__of__Pls, fact_360_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_266_less__special_I2_J, fact_21_zero__power2, fact_590_realpow__minus__mult, fact_653_le__imp__power__dvd, fact_652_dvd__power__le, fact_353_power__even__eq, fact_670_power__strict__increasing, fact_25_add__special_I2_J, fact_108_zle__add1__eq__le, fact_193_mult__2, fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_681_power__increasing, fact_45_less__eq__int__code_I16_J, fact_434_zdiv__mono2__neg__lemma, fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_82_semiring__norm_I113_J, fact_407_add__scale__eq__noteq, fact_383_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_46_rel__simps_I34_J, fact_618_power__mult, fact_691_divides__add__revr, fact_91_zmult__1__right, fact_267_less__special_I2_J, fact_11_sum__power2__eq__zero__iff, fact_228_rel__simps_I4_J, fact_692_nat__mult__dvd__cancel__disj_H, fact_277_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_205_semiring__numeral__0__eq__0, fact_168_rel__simps_I38_J, fact_27_add__special_I3_J, fact_56_semiring__mult__number__of, fact_479_zcong__1, fact_661_power__less__power__Suc, fact_540_zdiff__power3, fact_449_rel__simps_I40_J, fact_281__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096, fact_405_add__scale__eq__noteq, fact_286_zprime__zdvd__power, fact_478_IntPrimes_Ozcong__zero, fact_100_less__int__code_I14_J, fact_236_zless__add1__eq, fact_663_power__less__power__Suc, fact_616_dvd__power__same, fact_294_zdvd__antisym__nonneg, fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_, fact_648_power__le__dvd, fact_474_order__le__neq__implies__less, fact_43_zle__antisym, fact_129_right__distrib__number__of, fact_408_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_32_qf1pt, fact_641_power__0, fact_584_real__mult__less__iff1, fact_257_less__special_I1_J, fact_599_real__le__refl, fact_482_zcong__scalar2, fact_627_zero__le__power, fact_552_zcong__zprime__prod__zero, fact_182_zadd__0, fact_215_less__number__of, fact_155_mult__numeral__1, fact_455_rel__simps_I13_J, fact_280_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_491_zcong__zless__imp__eq, fact_54_semiring__mult__number__of, fact_292_zpower__zpower, fact_484_zcong__zadd, fact_578_mult__diff__mult, fact_260_semiring__one__add__one__is__two, fact_602_real__le__antisym, fact_514_diff__bin__simps_I9_J, fact_41_zmult__assoc, fact_428_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_606_power__mult__distrib, fact_303_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_633_one__le__power, fact_580_real__mult__le__cancel__iff1, fact_432_zdiv__mono2__lemma, fact_208_number__of__Pls, fact_95_zadd__zmult__distrib2, fact_556_Legendre__def, fact_579_mult__diff__mult, fact_605_power__mult__distrib, fact_381_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_248_semiring__numeral__1__eq__1, fact_207_number__of__Pls, fact_77_rel__simps_I32_J, fact_194_semiring__mult__2__right, fact_672_power__strict__increasing, fact_643_power__0, fact_269_zadd__power3, fact_240_power2__sum, fact_89_mult__Bit0, fact_296_zdvd__reduce, fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_695_divides__div__not, fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_522_Euler_Oaux1, fact_508_number__of__diff, fact_210_semiring__norm_I112_J, fact_298_zprime__2, fact_90_less__number__of__int__code, fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_635_power__inject__exp, fact_548_zpower__zdvd__prop1, fact_173_rel__simps_I2_J, fact_596_power__strict__mono, fact_433_unique__quotient__lemma__neg, fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_75_rel__simps_I22_J, fact_49_rel__simps_I31_J, fact_625_power__mono, fact_48_less__eq__int__code_I13_J, fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_503_zdiff__zmult__distrib2, fact_687_divides__ge, fact_688_divides__exp, fact_223_rel__simps_I12_J, fact_382_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_679_power__increasing, fact_685_power__strict__decreasing, fact_504_zdiff__zmult__distrib, fact_176_int__0__neq__1, fact_516_diff__bin__simps_I3_J, fact_694_divides__exp2, fact_498__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, fact_658_power__less__imp__less__base, fact_502_zdvd__zdiffD, fact_567_real__mult__assoc, fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_16_zero__less__power2, fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_293_zdvd__not__zless, fact_630_zero__less__power, fact_588_real__squared__diff__one__factored, fact_573_real__mult__left__cancel, fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_200_power2__eq__square, fact_460_bin__less__0__simps_I2_J, fact_174_less__int__code_I13_J, fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_42_zle__trans, fact_621_power__one__right, fact_531_zspecial__product, fact_629_zero__less__power, fact_614_dvd__power__same, fact_83_le__special_I4_J, fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_175_rel__simps_I14_J, fact_544_zcong__zero__equiv__div, fact_299_zdvd__imp__le, fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_307_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_212_add__numeral__0, fact_403_zero__le__even__power_H, fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_386_crossproduct__eq, fact_427_power__0__left__number__of, fact_422_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_513_left__diff__distrib__number__of, fact_489_four__x__squared, fact_140_power2__le__imp__le, fact_34_number__of__is__id, fact_349_nat__mult__2, fact_0__096t_A_060_A0_096, fact_459_rel__simps_I8_J, fact_125_left__distrib__number__of, fact_306_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_231_add__Bit1__Bit0, fact_468_rel__simps_I25_J, fact_52_eq__number__of__0, fact_623_power__mono, fact_465_rel__simps_I28_J, fact_148_sum__power2__ge__zero, fact_4_calculation_I2_J, fact_133_zero__is__num__zero, fact_270_zadd__power2, fact_676_power__strict__increasing__iff, fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_159_mult__Bit1, fact_135_power2__eq__imp__eq, fact_101_rel__simps_I15_J, fact_506_diff__bin__simps_I1_J, fact_569_real__mult__1, fact_50_zless__le, fact_264_less__special_I4_J, fact_206_semiring__numeral__0__eq__0, fact_612_power__one, fact_119_rel__simps_I51_J, fact_673_power__less__imp__less__exp, fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_471_zcong__sym, fact_527_inv__not__p__minus__1__aux, fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_33_zle__refl, fact_376_crossproduct__noteq, fact_680_power__increasing, fact_121_zless__linear, fact_177_add__Pls__right, fact_445__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_423_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_256_less__special_I3_J, fact_671_power__strict__increasing, fact_684_power__Suc__less, fact_242_power2__sum, fact_62_number__of__mult, fact_114_eq__number__of, fact_59_arith__simps_I32_J, fact_237_power2__eq__square__number__of, fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_515_diff__bin__simps_I10_J, fact_655_le__imp__power__dvd, fact_585_real__two__squares__add__zero__iff, fact_144_power2__less__imp__less, fact_350_mult__nat__number__of, fact_20_zero__power2, fact_458_rel__simps_I6_J, fact_19_one__power2, fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_631_zero__less__power, fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_613_power__one, fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_387_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_509_number__of__diff, fact_418_power__eq__0__iff__number__of, fact_51_zadd__left__mono, fact_252_semiring__norm_I110_J, fact_537_power2__diff, fact_510_right__diff__distrib__number__of, fact_214_add__numeral__0__right, fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_600_real__le__linear, fact_297_zdvd__period, fact_66_sum__squares__ge__zero, fact_494__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_142_zero__le__power2, fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_73_le__number__of__eq__not__less, fact_549_neg__one__power, fact_14_power2__less__0, fact_470_pos__zmult__eq__1__iff__lemma, fact_528_zcong__eq__trans, fact_300_is__mult__sum2sq, fact_273_cube__square, fact_476_order__le__neq__implies__less, fact_678_power__strict__increasing__iff, fact_526_diff__bin__simps_I5_J, fact_439_s, fact_105_Numeral1__eq1__nat, fact_477_Euler_Oaux2, fact_696_power__dvd__imp__le, fact_501_zcong__zdiff, fact_261_semiring__one__add__one__is__two, fact_660_power__less__imp__less__base, fact_160_pos__zmult__eq__1__iff, fact_523_zle__diff1__eq, fact_426_power__0__left__number__of, fact_128_right__distrib__number__of, fact_646_power__add, fact_624_power__mono, fact_632_one__le__power, fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_13_power2__less__0, fact_157_mult__numeral__1__right, fact_487_zcong__not, fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_430_q__neg__lemma, fact_271_int__pos__lt__two__imp__zero__or__one, fact_282__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1, fact_137_power2__eq__imp__eq, fact_225_rel__simps_I16_J, fact_35_zmult__commute, fact_3_t, fact_550_zcong__zmult__prop3, fact_185_double__number__of__Bit0, fact_31_p, fact_511_right__diff__distrib__number__of, fact_485_power__m1__even, fact_249_semiring__numeral__1__eq__1, fact_657_nat__zero__less__power__iff, fact_127_right__distrib__number__of, fact_475_order__le__neq__implies__less, fact_63_sum__squares__le__zero__iff, fact_235_odd__nonzero, fact_446_Bit1__Min, fact_99_rel__simps_I33_J, fact_554_Legendre__1mod4, fact_693_divides__rev, fact_542_zcong__not__zero, fact_39_le__number__of, fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_583_real__mult__order, fact_425_power__0__left__number__of, fact_451_rel__simps_I42_J, fact_359_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_490_zcong__zless__0, fact_88_mult__Pls, fact_183_zadd__strict__right__mono, fact_493_zprime__zdvd__zmult, fact_312_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_126_left__distrib__number__of, fact_139_power2__le__imp__le, fact_492_zcong__zpower__zmult, fact_697_divides__cases, fact_541_zcong__less__eq, fact_553_zpower__zdvd__prop2, fact_74_le__number__of__eq__not__less, fact_355_even__power__le__0__imp__0, fact_278_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_60_arith__simps_I32_J, fact_519_zcong__def, fact_603_field__power__not__zero, fact_284_s1, fact_163_rel__simps_I46_J, fact_172_rel__simps_I17_J, fact_190_semiring__mult__2, fact_258_less__special_I1_J, fact_453_rel__simps_I7_J, fact_5__096_126_A1_A_060_061_At_096, fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_488_zcong__iff__lin, fact_682_power__Suc__less, fact_180_Bit0__def, fact_448_rel__simps_I47_J, fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_164_rel__simps_I39_J, fact_420_pos__zmult__pos, fact_309_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_94_zadd__zmult__distrib, fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_615_dvd__power__same, fact_104_nat__numeral__1__eq__1, fact_222_number__of__add, fact_689_divides__mul__l, fact_507_Int2_Oaux1, fact_593_realpow__num__eq__if, fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_452_rel__simps_I45_J, fact_67_le__special_I3_J, fact_481_zcong__scalar, fact_171_less__int__code_I16_J, fact_276_self__quotient__aux2, fact_651_dvd__power__le, fact_466_eq__number__of__Pls__Min, fact_385_crossproduct__eq, fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_517_less__bin__lemma, fact_289_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_7_not__sum__power2__lt__zero, fact_103_int__one__le__iff__zero__less, fact_628_zero__le__power, fact_364_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_429_q__pos__lemma, fact_497_zcong__neg__1__impl__ne__1, fact_98_less__eq__int__code_I15_J, fact_58_mult__number__of__left, fact_595_realpow__num__eq__if, fact_247_semiring__numeral__1__eq__1, fact_92_zmult__1, fact_186_power3__eq__cube, fact_263_one__add__one__is__two, fact_647_power__le__dvd, fact_442_prime__g__5, fact_505_diff__bin__simps_I7_J, fact_61_number__of__mult, fact_220_add__number__of__eq, fact_76_less__eq__int__code_I14_J, fact_113_le__imp__0__less, fact_167_rel__simps_I44_J, fact_179_add__Bit0__Bit0, fact_467_rel__simps_I11_J, fact_639_power__eq__0__iff, fact_192_mult__2, fact_545_zcong__eq__zdvd__prop, fact_463_rel__simps_I23_J, fact_304_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_656_nat__power__less__imp__less, fact_68_le__special_I3_J, fact_581_real__mult__le__cancel__iff2, fact_195_semiring__mult__2__right, fact_184_double__number__of__Bit0, fact_211_add__numeral__0, fact_597_power__strict__mono, fact_78_rel__simps_I27_J, fact_574_real__mult__right__cancel, fact_107_add1__zle__eq, fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_262_one__add__one__is__two, fact_272_s0p, fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_64_sum__squares__le__zero__iff, fact_198_mult__2__right, fact_424_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_532_zcong__id, fact_9_sum__power2__gt__zero__iff, fact_145_power2__less__imp__less, fact_555_one__not__neg__one__mod__m, fact_216_less__number__of, fact_251_numeral__1__eq__1, fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096, fact_122_sum__squares__eq__zero__iff, fact_239_power2__eq__square__number__of, fact_102_less__nat__number__of, fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_354_power__even__eq, fact_6_p0, fact_472_zcong__refl, fact_375_crossproduct__noteq, fact_178_add__Pls, fact_123_sum__squares__eq__zero__iff, fact_55_semiring__mult__number__of, fact_10_sum__power2__gt__zero__iff, fact_38_less__eq__number__of__int__code, fact_352_power__even__eq, fact_480_zcong__zmult__self, fact_130_zadd__assoc, fact_23_zero__eq__power2, fact_536_zcong__zpower, fact_118_number__of__reorient, fact_197_mult__2__right, fact_443_pos2, fact_348_nat__mult__2__right, fact_638_power__eq__0__iff, fact_156_mult__numeral__1__right, fact_464_rel__simps_I20_J, fact_158_one__is__num__one, fact_219_add__number__of__eq, fact_246_number__of__Bit1, fact_275_self__quotient__aux1, fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_668_power__0__left, fact_310_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_561_diff__square, fact_534_zcong__zmult__prop1, fact_243_number__of__Bit0, fact_512_left__diff__distrib__number__of, fact_518_xzgcda__linear__aux1, fact_226_bin__less__0__simps_I4_J, fact_690_divides__mul__r, fact_610_power__commutes, fact_565_real__less__def, fact_165_rel__simps_I50_J, fact_611_power__one, fact_608_power__commutes, fact_440_Euler_Oaux____1, fact_667_power__0__left, fact_665_power__gt1__lemma, fact_285_zero__less__power__nat__eq, fact_592_two__realpow__ge__one, fact_520_add__number__of__diff1, fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_686_realpow__pos__nth__unique, fact_87_nat__1__add__1, fact_8_not__sum__power2__lt__zero, fact_450_rel__simps_I37_J, fact_109_semiring__add__number__of, fact_626_zero__le__power, fact_650_dvd__power__le, fact_17_one__power2, fact_217_add__number__of__left, fact_15_zero__less__power2, fact_370_add__0__iff, fact_589_realpow__minus__mult, fact_71_less__0__number__of, fact_29_t__l__p, fact_161_double__eq__0__iff, fact_351_nat__number__of__mult__left, fact_371_add__0__iff, fact_563_real__zero__not__eq__one, fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_666_power__gt1__lemma, fact_411_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_147_sum__power2__le__zero__iff, fact_640_power__eq__0__iff, fact_12_sum__power2__eq__zero__iff, fact_150_sum__squares__gt__zero__iff, fact_586_exp__eq__1, fact_283__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_, fact_154_mult__numeral__1, fact_65_sum__squares__ge__zero, fact_152_not__sum__squares__lt__zero, fact_96_rel__simps_I29_J, fact_253_semiring__norm_I110_J, fact_151_sum__squares__gt__zero__iff, fact_564_real__le__eq__diff, fact_406_add__scale__eq__noteq, fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_97_rel__simps_I5_J, fact_53_eq__0__number__of, fact_259_semiring__one__add__one__is__two, fact_369_add__0__iff, fact_188_power3__eq__cube, fact_654_le__imp__power__dvd, fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_295_zdvd__mult__cancel, fact_642_power__0, fact_591_realpow__minus__mult, fact_218_add__number__of__left, fact_110_semiring__add__number__of, fact_291_zprime__power__zdvd__cancel__left, fact_499__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_634_one__le__power, fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_559_mult__eq__if, fact_560_power__eq__if, fact_232_add__Bit0__Bit1, fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_620_power__one__right, fact_191_semiring__mult__2, fact_409_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_22_zero__power2, fact_120_rel__simps_I48_J, fact_1_calculation_I1_J, fact_637_power__inject__exp, fact_568_real__mult__commute, fact_84_le__special_I4_J, fact_435_quartic__square__square, fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_582_real__mult__less__mono2, fact_234_Bit1__def, fact_85_le__special_I2_J, fact_601_real__le__trans, fact_622_power__one__right, fact_456_rel__simps_I9_J, fact_535_zcong__shift, fact_221_number__of__add, fact_617_power__mult, fact_305_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_18_one__power2, fact_201_power2__eq__square, fact_358_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_607_power__mult__distrib, fact_213_add__numeral__0__right, fact_669_power__0__left, fact_37_times__numeral__code_I5_J, fact_153_not__sum__squares__lt__zero, fact_162_double__eq__0__iff, fact_136_power2__eq__imp__eq, fact_40_le__number__of, fact_117_number__of__reorient, fact_233_int__0__less__1, fact_587_real__squared__diff__one__factored, fact_143_power2__less__imp__less, fact_662_power__less__power__Suc, fact_26_add__special_I2_J, fact_204_semiring__numeral__0__eq__0, fact_486_power__m1__even, fact_265_less__special_I4_J, fact_469_zmult__eq__1__iff, fact_619_power__mult, fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_529_zcong__square__zless, fact_570_real__add__left__mono, fact_199_power2__eq__square, fact_356_even__power__le__0__imp__0, fact_571_add__diff__add, fact_461_rel__simps_I26_J, fact_250_numeral__1__eq__1, fact_447_rel__simps_I43_J, fact_86_le__special_I2_J, fact_203_even__less__0__iff, fact_116_number__of__reorient, fact_106_zless__imp__add1__zle, fact_44_zpower__zadd__distrib, fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_419_power__eq__0__iff__number__of, fact_138_power2__le__imp__le, fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_495__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_543_zdvd__bounds, fact_677_power__strict__increasing__iff, fact_245_number__of__Bit1, fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_454_rel__simps_I24_J, fact_674_power__less__imp__less__exp, fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_530_zcong__square, fact_576_real__add__mult__distrib, fact_566_less__eq__real__def, fact_413_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_313_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_572_add__diff__add, fact_57_mult__number__of__left, fact_28_add__special_I3_J, fact_181_zadd__0__right, fact_279_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_636_power__inject__exp, fact_196_semiring__mult__2__right, fact_577_nat__power__eq__0__iff, fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_389_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_645_power__add, fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_146_sum__power2__le__zero__iff, fact_170_Pls__def, fact_524_diff__bin__simps_I4_J, fact_72_le__number__of__eq__not__less, fact_412_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_539_zdiff__power2, fact_410_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_70_le__special_I1_J, fact_546_zprime__zdvd__zmult__better, fact_462_rel__simps_I30_J, fact_402_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_255_less__special_I3_J, fact_124_left__distrib__number__of, fact_609_power__commutes, fact_93_plus__numeral__code_I9_J, fact_538_power2__diff, fact_557_QuadRes__def, fact_421_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_112_add__nat__number__of, fact_166_rel__simps_I49_J, fact_683_power__Suc__less, fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_659_power__less__imp__less__base, fact_230_bin__less__0__simps_I3_J, fact_227_rel__simps_I10_J, fact_496_neg__one__power__eq__mod__m, fact_380_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_604_field__power__not__zero, fact_594_realpow__num__eq__if, fact_675_power__less__imp__less__exp, fact_575_nat__mult__eq__one, fact_244_number__of__Bit0, fact_111_semiring__add__number__of, fact_417_power__eq__0__iff__number__of, fact_598_power__strict__mono, fact_562_realpow__two__sum__zero__iff, fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_483_zcong__zmult, fact_36_zle__linear, fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_547_Int2_Ozcong__zero, fact_301_le__nat__number__of, fact_644_power__add, fact_457_rel__simps_I3_J, fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_47_rel__simps_I19_J, fact_551_zcong__zprime__prod__zero__contra, fact_274_power2__ge__self, fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_229_bin__less__0__simps_I1_J, fact_115_eq__number__of, fact_390_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_134_zmult__zless__mono2, fact_311_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_132_zadd__commute, fact_404_zero__le__even__power_H, fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_80_zadd__zless__mono, fact_238_power2__eq__square__number__of, fact_209_semiring__norm_I112_J, fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_649_power__le__dvd, fact_149_sum__power2__ge__zero, fact_187_power3__eq__cube, fact_268__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096, fact_521_add__number__of__diff1, fact_500_not__real__square__gt__zero, fact_141_zero__le__power2, fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_69_le__special_I1_J, fact_131_zadd__left__commute, fact_473_zcong__trans, fact_431_unique__quotient__lemma, fact_384_crossproduct__eq, fact_224_less__int__code_I15_J, fact_558_real__sum__squared__expand, fact_533_zcong__zmult__prop2, fact_254_odd__less__0, fact_202_even__less__0__iff, fact_525_diff__bin__simps_I6_J, fact_24_zero__eq__power2, fact_79_rel__simps_I21_J, fact_241_power2__sum, fact_377_crossproduct__noteq, fact_441_zprime__def, fact_664_power__gt1__lemma
% 14.00/4.25 % No. of inferences in proof: 1400
% 14.00/4.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3706 ms resp. 3003 ms w/o parsing
% 15.06/4.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.06/4.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------