TSTP Solution File: NUM924+6 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:42:56 EDT 2023
% Result : Theorem 13.64s 4.02s
% Output : Refutation 14.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 712
% Syntax : Number of formulae : 1364 ( 450 unt; 62 typ; 0 def)
% Number of atoms : 3207 ( 936 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 17822 ( 204 ~; 83 |; 304 &;15713 @)
% ( 135 <=>;1383 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 62 usr; 11 con; 0-3 aty)
% Number of variables : 2563 ( 0 ^;2553 !; 10 ?;2563 :)
% Comments :
%------------------------------------------------------------------------------
thf(ord_less_type,type,
ord_less: $i > $i > $i > $o ).
thf(int_type,type,
int: $i ).
thf(plus_plus_type,type,
plus_plus: $i > $i > $i > $i ).
thf(power_power_type,type,
power_power: $i > $i > $i > $i ).
thf(s_type,type,
s: $i ).
thf(number_number_of_type,type,
number_number_of: $i > $i > $i ).
thf(nat_type,type,
nat: $i ).
thf(bit0_type,type,
bit0: $i > $i ).
thf(bit1_type,type,
bit1: $i > $i ).
thf(pls_type,type,
pls: $i ).
thf(one_one_type,type,
one_one: $i > $i ).
thf(zero_zero_type,type,
zero_zero: $i > $i ).
thf(power_type,type,
power: $i > $o ).
thf(real_type,type,
real: $i ).
thf(ord_less_eq_type,type,
ord_less_eq: $i > $i > $i > $o ).
thf(ab_group_add_type,type,
ab_group_add: $i > $o ).
thf(minus_minus_type,type,
minus_minus: $i > $i > $i > $i ).
thf(ti_type,type,
ti: $i > $i > $i ).
thf(dvd_type,type,
dvd: $i > $o ).
thf(times_times_type,type,
times_times: $i > $i > $i > $i ).
thf(linordered_semidom_type,type,
linordered_semidom: $i > $o ).
thf(semiring_type,type,
semiring: $i > $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1: $i > $o ).
thf(dvd_dvd_type,type,
dvd_dvd: $i > $i > $i > $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct: $i > $o ).
thf(number_type,type,
number: $i > $o ).
thf(no_zero_divisors_type,type,
no_zero_divisors: $i > $o ).
thf(zero_neq_one_type,type,
zero_neq_one: $i > $o ).
thf(zcong_type,type,
zcong: $i > $i > $i > $o ).
thf(linord626643107strict_type,type,
linord626643107strict: $i > $o ).
thf(comm_ring_1_type,type,
comm_ring_1: $i > $o ).
thf(order_type,type,
order: $i > $o ).
thf(bool_type,type,
bool: $i ).
thf(linordered_idom_type,type,
linordered_idom: $i > $o ).
thf(ordered_ring_type,type,
ordered_ring: $i > $o ).
thf(number_ring_type,type,
number_ring: $i > $o ).
thf(mult_zero_type,type,
mult_zero: $i > $o ).
thf(ring_char_0_type,type,
ring_char_0: $i > $o ).
thf(number_semiring_type,type,
number_semiring: $i > $o ).
thf(undefined_type,type,
undefined: $i > $i ).
thf(linord219039673up_add_type,type,
linord219039673up_add: $i > $o ).
thf(linordered_ring_type,type,
linordered_ring: $i > $o ).
thf(semiring_1_type,type,
semiring_1: $i > $o ).
thf(comm_semiring_type,type,
comm_semiring: $i > $o ).
thf(comm_monoid_mult_type,type,
comm_monoid_mult: $i > $o ).
thf(linorder_type,type,
linorder: $i > $o ).
thf(monoid_mult_type,type,
monoid_mult: $i > $o ).
thf(linord581940658strict_type,type,
linord581940658strict: $i > $o ).
thf(ordere453448008miring_type,type,
ordere453448008miring: $i > $o ).
thf(ring_11004092258visors_type,type,
ring_11004092258visors: $i > $o ).
thf(ring_1_type,type,
ring_1: $i > $o ).
thf(semiring_0_type,type,
semiring_0: $i > $o ).
thf(ring_type,type,
ring: $i > $o ).
thf(ring_n68954251visors_type,type,
ring_n68954251visors: $i > $o ).
thf(s1_type,type,
s1: $i ).
thf(m_type,type,
m: $i ).
thf(zprime_type,type,
zprime: $i > $o ).
thf(min_type,type,
min: $i ).
thf(twoSqu420862341sum2sq_type,type,
twoSqu420862341sum2sq: $i > $o ).
thf(legendre_type,type,
legendre: $i > $i > $i ).
thf(quadRes_type,type,
quadRes: $i > $i > $o ).
thf(t_type,type,
t: $i ).
thf(148,axiom,
! [A: $i] :
( ( times_times @ int @ ( one_one @ int ) @ A )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zmult__1) ).
thf(1036,plain,
! [A: $i] :
( ( times_times @ int @ ( one_one @ int ) @ A )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(286,axiom,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ! [B: $i] :
( ( ( ( number_number_of @ nat @ B )
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( one_one @ A ) ) )
& ( ( ( number_number_of @ nat @ B )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_power__0__left__number__of) ).
thf(1501,plain,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ! [B: $i] :
( ( ( ( number_number_of @ nat @ B )
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( one_one @ A ) ) )
& ( ( ( number_number_of @ nat @ B )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ A @ ( ti @ int @ B ) @ C )
<=> ( zcong @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg2) ).
thf(2094,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ A @ ( ti @ int @ B ) @ C )
=> ( zcong @ A @ B @ C ) )
& ( ( zcong @ A @ B @ C )
=> ( zcong @ A @ ( ti @ int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( ( zcong @ A @ ( zero_zero @ int ) @ B )
=> ( ( legendre @ A @ B )
= ( zero_zero @ int ) ) )
& ( ~ ( zcong @ A @ ( zero_zero @ int ) @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( one_one @ int ) ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of @ int @ min ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_Legendre__def) ).
thf(1633,plain,
! [A: $i,B: $i] :
( ( ( zcong @ A @ ( zero_zero @ int ) @ B )
=> ( ( legendre @ A @ B )
= ( zero_zero @ int ) ) )
& ( ~ ( zcong @ A @ ( zero_zero @ int ) @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( one_one @ int ) ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of @ int @ min ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
thf(1729,plain,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(550,axiom,
! [A: $i,B: $i] : ( zcong @ A @ B @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_zcong__1) ).
thf(2412,plain,
! [A: $i,B: $i] : ( zcong @ A @ B @ ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( zcong @ B @ ( zero_zero @ int ) @ C )
=> ( ( zcong @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd @ int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_Euler_Oaux____1) ).
thf(2595,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( zcong @ B @ ( zero_zero @ int ) @ C )
=> ( ( zcong @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd @ int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(193,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_power2__eq__imp__eq) ).
thf(1179,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(58,axiom,
linordered_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring) ).
thf(777,plain,
linordered_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] : ( zcong @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ C @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_zcong__zmult__self) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i] : ( zcong @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ C @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( times_times @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
= ( number_number_of @ int @ ( times_times @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_times__numeral__code_I5_J) ).
thf(1956,plain,
! [A: $i,B: $i] :
( ( times_times @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
= ( number_number_of @ int @ ( times_times @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( ( ti @ int @ D )
= ( ti @ int @ B ) )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_zcong__eq__trans) ).
thf(1879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( ( ti @ int @ D )
= ( ti @ int @ B ) )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ real @ A @ B )
<=> ( ( ord_less @ real @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_less__eq__real__def) ).
thf(1337,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ real @ A @ B )
=> ( ( ord_less @ real @ A @ B )
| ( A = B ) ) )
& ( ( ( ord_less @ real @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ nat @ ( number_number_of @ nat @ A ) @ ( number_number_of @ nat @ B ) )
<=> ( ~ ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ A @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_le__nat__number__of) ).
thf(1718,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ A ) @ ( number_number_of @ nat @ B ) )
=> ( ~ ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ A @ pls ) ) )
& ( ( ~ ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ A @ pls ) )
=> ( ord_less_eq @ nat @ ( number_number_of @ nat @ A ) @ ( number_number_of @ nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(519,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(2295,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(51,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ B @ ( times_times @ A @ C @ D ) )
= ( times_times @ A @ C @ ( times_times @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(760,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ B @ ( times_times @ A @ C @ D ) )
= ( times_times @ A @ C @ ( times_times @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_zle__diff1__eq) ).
thf(2109,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less_eq @ int @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(269,axiom,
! [A: $i] :
( ( ( number @ A )
& ( semiring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ ( times_times @ A @ ( number_number_of @ A @ B ) @ C ) @ ( times_times @ A @ ( number_number_of @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_right__distrib__number__of) ).
thf(1454,plain,
! [A: $i] :
( ( ( number @ A )
& ( semiring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ ( times_times @ A @ ( number_number_of @ A @ B ) @ C ) @ ( times_times @ A @ ( number_number_of @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
<=> ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_nat__mult__eq__one) ).
thf(893,plain,
! [A: $i,B: $i] :
( ( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
=> ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) )
& ( ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) )
=> ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( minus_minus @ nat @ ( ti @ nat @ A ) @ B )
= ( minus_minus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_arg1) ).
thf(1840,plain,
! [A: $i,B: $i] :
( ( minus_minus @ nat @ ( ti @ nat @ A ) @ B )
= ( minus_minus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(122,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(962,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd @ int @ C @ ( times_times @ int @ A @ B ) )
=> ( ( dvd_dvd @ int @ C @ A )
| ( dvd_dvd @ int @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_zprime__zdvd__zmult__better) ).
thf(2427,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd @ int @ C @ ( times_times @ int @ A @ B ) )
=> ( ( dvd_dvd @ int @ C @ A )
| ( dvd_dvd @ int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_zcong__scalar2) ).
thf(2480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(514,axiom,
dvd @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Odvd) ).
thf(2280,plain,
dvd @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(298,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( ( ti @ int @ A )
= ( zero_zero @ int ) )
| ( ( ti @ int @ A )
= ( one_one @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_int__pos__lt__two__imp__zero__or__one) ).
thf(1554,plain,
! [A: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( ( ti @ int @ A )
= ( zero_zero @ int ) )
| ( ( ti @ int @ A )
= ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(579,axiom,
! [A: $i] :
( ( bit0 @ ( ti @ int @ A ) )
= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
thf(2512,plain,
! [A: $i] :
( ( bit0 @ ( ti @ int @ A ) )
= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(16,axiom,
! [A: $i] :
( ( dvd @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( B
= ( times_times @ A @ C @ D ) )
=> ( dvd_dvd @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_dvdI) ).
thf(683,plain,
! [A: $i] :
( ( dvd @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( B
= ( times_times @ A @ C @ D ) )
=> ( dvd_dvd @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(396,axiom,
ord_less @ int @ min @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_bin__less__0__simps_I2_J) ).
thf(1882,plain,
ord_less @ int @ min @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(157,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I22_J) ).
thf(1068,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(545,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ A @ C @ D )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less_eq @ A @ ( power_power @ A @ C @ B ) @ ( power_power @ A @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_power__mono) ).
thf(2395,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ A @ C @ D )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less_eq @ A @ ( power_power @ A @ C @ B ) @ ( power_power @ A @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(266,axiom,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( zero_zero @ A )
!= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_zero__neq__one) ).
thf(1443,plain,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( zero_zero @ A )
!= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(253,axiom,
! [A: $i] :
( ( minus_minus @ int @ A @ pls )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_diff__bin__simps_I1_J) ).
thf(1401,plain,
! [A: $i] :
( ( minus_minus @ int @ A @ pls )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( twoSqu420862341sum2sq @ B )
=> ( ( twoSqu420862341sum2sq @ A )
=> ( twoSqu420862341sum2sq @ ( times_times @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_is__mult__sum2sq) ).
thf(1073,plain,
! [A: $i,B: $i] :
( ( twoSqu420862341sum2sq @ B )
=> ( ( twoSqu420862341sum2sq @ A )
=> ( twoSqu420862341sum2sq @ ( times_times @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(631,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( times_times @ A @ ( power_power @ A @ B @ ( minus_minus @ nat @ C @ ( one_one @ nat ) ) ) @ B )
= ( power_power @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_realpow__minus__mult) ).
thf(2671,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( times_times @ A @ ( power_power @ A @ B @ ( minus_minus @ nat @ C @ ( one_one @ nat ) ) ) @ B )
= ( power_power @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(202,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( zero_zero @ A )
= ( number_number_of @ A @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_semiring__norm_I112_J) ).
thf(1205,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( zero_zero @ A )
= ( number_number_of @ A @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(292,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
<=> ( ord_less_eq @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__number__of) ).
thf(1533,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
=> ( ord_less_eq @ int @ B @ C ) )
& ( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(340,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
thf(1692,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(191,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_rel__simps_I40_J) ).
thf(1173,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(536,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ min @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_rel__simps_I26_J) ).
thf(2363,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ min @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ min @ A ) )
& ( ( ord_less_eq @ int @ min @ A )
=> ( ord_less_eq @ int @ min @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(387,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ord_less_eq @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
<=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_power__increasing__iff) ).
thf(1855,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ( ord_less_eq @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
=> ( ord_less_eq @ nat @ B @ C ) )
& ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(314,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I19_J) ).
thf(1596,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(465,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ ( plus_plus @ A @ B @ C ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ A @ ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_power2__sum) ).
thf(2104,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ ( plus_plus @ A @ B @ C ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ A @ ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(260,axiom,
! [A: $i] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls
= ( ti @ int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_rel__simps_I38_J) ).
thf(1422,plain,
! [A: $i] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls
= ( ti @ int @ A ) ) )
& ( ( pls
= ( ti @ int @ A ) )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(1569,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(417,axiom,
! [A: $i] :
( ( times_times @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_nat__mult__2__right) ).
thf(1939,plain,
! [A: $i] :
( ( times_times @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(502,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( minus_minus @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( minus_minus @ A @ ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_add__number__of__diff1) ).
thf(2248,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( minus_minus @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( minus_minus @ A @ ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(463,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ D @ C ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ D )
=> ( ord_less @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_power__less__imp__less__base) ).
thf(2099,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ D @ C ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ D )
=> ( ord_less @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(311,axiom,
! [A: $i] :
( ( mult_zero @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_mult__zero__right) ).
thf(1591,plain,
! [A: $i] :
( ( mult_zero @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(468,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_bin__less__0__simps_I1_J) ).
thf(2114,plain,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(182,axiom,
zcong @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_s1) ).
thf(1142,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)],[182]) ).
thf(150,axiom,
comm_monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(1041,plain,
comm_monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(97,axiom,
! [A: $i] : ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_two__realpow__ge__one) ).
thf(861,plain,
! [A: $i] : ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(346,axiom,
( ( ti @ int @ min )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OMin_res) ).
thf(1705,plain,
( ( ti @ int @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(160,axiom,
! [A: $i] :
( ( times_times @ int @ A @ ( one_one @ int ) )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zmult__1__right) ).
thf(1078,plain,
! [A: $i] :
( ( times_times @ int @ A @ ( one_one @ int ) )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(180,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
thf(1137,plain,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(229,axiom,
! [A: $i] :
( ( times_times @ real @ ( one_one @ real ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_real__mult__1) ).
thf(1310,plain,
! [A: $i] :
( ( times_times @ real @ ( one_one @ real ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(447,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_sum__power2__ge__zero) ).
thf(2035,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ B @ C )
=> ( ( ord_less_eq @ int @ C @ A )
=> ( ord_less_eq @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zle__trans) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ B @ C )
=> ( ( ord_less_eq @ int @ C @ A )
=> ( ord_less_eq @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ord_less @ int @ C @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ C ) @ ( times_times @ nat @ ( number_number_of @ nat @ A ) @ B ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ C @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ C ) @ ( times_times @ nat @ ( number_number_of @ nat @ A ) @ B ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_nat__number__of__mult__left) ).
thf(2459,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ord_less @ int @ C @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ C ) @ ( times_times @ nat @ ( number_number_of @ nat @ A ) @ B ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ C @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ C ) @ ( times_times @ nat @ ( number_number_of @ nat @ A ) @ B ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(602,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(2580,plain,
ring_11004092258visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
thf(1354,plain,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(189,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ A @ D @ E )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( dvd_dvd @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_dvd__power__le) ).
thf(1164,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ A @ D @ E )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( dvd_dvd @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ord_less @ C @ ( ti @ C @ A ) @ B )
<=> ( ord_less @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_arg1) ).
thf(1999,plain,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ( ord_less @ C @ ( ti @ C @ A ) @ B )
=> ( ord_less @ C @ A @ B ) )
& ( ( ord_less @ C @ A @ B )
=> ( ord_less @ C @ ( ti @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( dvd_dvd @ C @ A @ ( ti @ C @ B ) )
<=> ( dvd_dvd @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Rings_Odvd__class_Odvd_arg2) ).
thf(814,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( ( dvd_dvd @ C @ A @ ( ti @ C @ B ) )
=> ( dvd_dvd @ C @ A @ B ) )
& ( ( dvd_dvd @ C @ A @ B )
=> ( dvd_dvd @ C @ A @ ( ti @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(233,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sum__power2__gt__zero__iff) ).
thf(1327,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ord_less @ C @ A @ ( ti @ C @ B ) )
<=> ( ord_less @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_arg2) ).
thf(2491,plain,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ( ord_less @ C @ A @ ( ti @ C @ B ) )
=> ( ord_less @ C @ A @ B ) )
& ( ( ord_less @ C @ A @ B )
=> ( ord_less @ C @ A @ ( ti @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ int @ D @ E )
=> ( ( dvd_dvd @ int @ D @ ( plus_plus @ int @ B @ C ) )
<=> ( dvd_dvd @ int @ D @ ( plus_plus @ int @ ( plus_plus @ int @ B @ ( times_times @ int @ A @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_zdvd__period) ).
thf(1576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ int @ D @ E )
=> ( ( ( dvd_dvd @ int @ D @ ( plus_plus @ int @ B @ C ) )
=> ( dvd_dvd @ int @ D @ ( plus_plus @ int @ ( plus_plus @ int @ B @ ( times_times @ int @ A @ E ) ) @ C ) ) )
& ( ( dvd_dvd @ int @ D @ ( plus_plus @ int @ ( plus_plus @ int @ B @ ( times_times @ int @ A @ E ) ) @ C ) )
=> ( dvd_dvd @ int @ D @ ( plus_plus @ int @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(264,axiom,
twoSqu420862341sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_qf1pt) ).
thf(1441,plain,
twoSqu420862341sum2sq @ ( 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)],[264]) ).
thf(105,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(885,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(321,axiom,
! [A: $i] :
( ( plus_plus @ int @ A @ ( zero_zero @ int ) )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_zadd__0__right) ).
thf(1613,plain,
! [A: $i] :
( ( plus_plus @ int @ A @ ( zero_zero @ int ) )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_less__int__code_I14_J) ).
thf(1921,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(239,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( ~ ( ord_less @ A @ B @ C )
=> ( ord_less @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_linorder__neqE__linordered__idom) ).
thf(1359,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( ~ ( ord_less @ A @ B @ C )
=> ( ord_less @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(317,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_power2__eq__square) ).
thf(1601,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(547,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
thf(2400,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ ( number_number_of @ nat @ B ) ) )
<=> ( ( ( number_number_of @ nat @ B )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_zero__less__power__nat__eq__number__of) ).
thf(1518,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ ( number_number_of @ nat @ B ) ) )
=> ( ( ( number_number_of @ nat @ B )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) )
& ( ( ( ( number_number_of @ nat @ B )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ ( number_number_of @ nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(87,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ ( times_times @ A @ B @ C ) @ D )
=> ( dvd_dvd @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_dvd__mult__left) ).
thf(829,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ ( times_times @ A @ B @ C ) @ D )
=> ( dvd_dvd @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ( ( ti @ int @ C )
= ( plus_plus @ int @ A @ ( times_times @ int @ C @ B ) ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ B @ ( one_one @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_self__quotient__aux2) ).
thf(1095,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ( ( ti @ int @ 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)],[166]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times @ int @ B @ C ) @ E )
<=> ( zcong @ A @ ( times_times @ int @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_zcong__zmult__prop2) ).
thf(1623,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( ( zcong @ A @ ( times_times @ int @ B @ C ) @ E )
=> ( zcong @ A @ ( times_times @ int @ B @ D ) @ E ) )
& ( ( zcong @ A @ ( times_times @ int @ B @ D ) @ E )
=> ( zcong @ A @ ( times_times @ int @ B @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(280,axiom,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_zero__power2) ).
thf(1482,plain,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult_zero @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_arg2) ).
thf(724,plain,
! [A: $i,B: $i,C: $i] :
( ( mult_zero @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(526,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_semiring__norm_I113_J) ).
thf(2328,plain,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ A @ B )
= ( plus_plus @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
thf(1792,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ A @ B )
= ( plus_plus @ int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(430,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_power2__less__imp__less) ).
thf(1985,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(333,axiom,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ! [B: $i] :
( ( ( plus_plus @ A @ B @ B )
= ( zero_zero @ A ) )
<=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_double__eq__0__iff) ).
thf(1660,plain,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ! [B: $i] :
( ( ( ( plus_plus @ A @ B @ B )
= ( zero_zero @ A ) )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) )
& ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
=> ( ( plus_plus @ A @ B @ B )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(642,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ A @ ( one_one @ A ) @ ( power_power @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_one__less__power) ).
thf(2708,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ A @ ( one_one @ A ) @ ( power_power @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(575,axiom,
! [A: $i] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_rel__simps_I45_J) ).
thf(2501,plain,
! [A: $i] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(389,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(1860,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(231,axiom,
! [A: $i] :
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ ( one_one @ int ) ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_Legendre__1mod4) ).
thf(1323,plain,
! [A: $i] :
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ ( one_one @ int ) ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(635,axiom,
zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_p) ).
thf(2682,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)],[635]) ).
thf(230,axiom,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) )
<=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_sum__squares__gt__zero__iff) ).
thf(1313,plain,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) )
=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_add__Bit1__Bit0) ).
thf(2185,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(571,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ C ) )
= ( times_times @ A @ ( plus_plus @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(2488,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ C ) )
= ( times_times @ A @ ( plus_plus @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(197,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ C @ D )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ A @ ( power_power @ A @ C @ B ) @ ( power_power @ A @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_power__strict__mono) ).
thf(1191,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ C @ D )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ A @ ( power_power @ A @ C @ B ) @ ( power_power @ A @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(563,axiom,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( one_one @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_one__power2) ).
thf(2466,plain,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( one_one @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd @ int @ B @ ( times_times @ int @ C @ A ) )
=> ( ( dvd_dvd @ int @ B @ C )
| ( dvd_dvd @ int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_zprime__zdvd__zmult) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd @ int @ B @ ( times_times @ int @ C @ A ) )
=> ( ( dvd_dvd @ int @ B @ C )
| ( dvd_dvd @ int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
<=> ( ( ord_less_eq @ int @ A @ B )
& ( ( ti @ int @ A )
!= ( ti @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(917,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ A @ B )
=> ( ( ord_less_eq @ int @ A @ B )
& ( ( ti @ int @ A )
!= ( ti @ int @ B ) ) ) )
& ( ( ( ord_less_eq @ int @ A @ B )
& ( ( ti @ int @ A )
!= ( ti @ int @ B ) ) )
=> ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ ( times_times @ int @ A @ B ) @ C )
= ( times_times @ int @ A @ ( times_times @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zmult__assoc) ).
thf(1462,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ ( times_times @ int @ A @ B ) @ C )
= ( times_times @ int @ A @ ( times_times @ int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(154,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ ( plus_plus @ A @ D @ E ) )
= ( plus_plus @ A @ ( plus_plus @ A @ B @ D ) @ ( plus_plus @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1059,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ ( plus_plus @ A @ D @ E ) )
= ( plus_plus @ A @ ( plus_plus @ A @ B @ D ) @ ( plus_plus @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(601,axiom,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) @ ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_sum__squares__le__zero__iff) ).
thf(2571,plain,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) @ ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) )
=> ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(534,axiom,
! [A: $i] :
( ( ord_less @ int @ min @ ( bit1 @ A ) )
<=> ( ord_less @ int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_rel__simps_I9_J) ).
thf(2356,plain,
! [A: $i] :
( ( ( ord_less @ int @ min @ ( bit1 @ A ) )
=> ( ord_less @ int @ min @ A ) )
& ( ( ord_less @ int @ min @ A )
=> ( ord_less @ int @ min @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus @ int @ B @ A ) @ ( plus_plus @ int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_zcong__shift) ).
thf(1087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus @ int @ B @ A ) @ ( plus_plus @ int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(400,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(1890,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(236,axiom,
! [A: $i] :
( ( ( bit0 @ A )
= pls )
<=> ( ( ti @ int @ A )
= pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_rel__simps_I44_J) ).
thf(1347,plain,
! [A: $i] :
( ( ( ( bit0 @ A )
= pls )
=> ( ( ti @ int @ A )
= pls ) )
& ( ( ( ti @ int @ A )
= pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ A @ ( minus_minus @ int @ B @ C ) )
= ( minus_minus @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_zdiff__zmult__distrib2) ).
thf(1398,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ A @ ( minus_minus @ int @ B @ C ) )
= ( minus_minus @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(413,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( number_number_of @ A @ ( bit0 @ B ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) ) @ ( number_number_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_number__of__Bit0) ).
thf(1931,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( number_number_of @ A @ ( bit0 @ B ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) ) @ ( number_number_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(651,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq @ int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_rel__simps_I11_J) ).
thf(2730,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ min )
=> ( ord_less_eq @ int @ A @ min ) )
& ( ( ord_less_eq @ int @ A @ min )
=> ( ord_less @ int @ ( bit0 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ A @ B @ ( ti @ int @ C ) )
<=> ( zcong @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg3) ).
thf(1362,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ A @ B @ ( ti @ int @ C ) )
=> ( zcong @ A @ B @ C ) )
& ( ( zcong @ A @ B @ C )
=> ( zcong @ A @ B @ ( ti @ int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(363,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__1__add__1) ).
thf(1778,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)],[363]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( ti @ C @ ( power_power @ C @ A @ B ) )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_res) ).
thf(2388,plain,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( ti @ C @ ( power_power @ C @ A @ B ) )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(78,axiom,
ring_11004092258visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(817,plain,
ring_11004092258visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(110,axiom,
linorder @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(902,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( times_times @ int @ ( bit1 @ A ) @ B )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_mult__Bit1) ).
thf(1479,plain,
! [A: $i,B: $i] :
( ( times_times @ int @ ( bit1 @ A ) @ B )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) )
=> ( ( ord_less @ int @ C @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_q__pos__lemma) ).
thf(1609,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) )
=> ( ( ord_less @ int @ C @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( quadRes @ ( ti @ int @ A ) @ B )
<=> ( quadRes @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Residues_OQuadRes_arg1) ).
thf(1815,plain,
! [A: $i,B: $i] :
( ( ( quadRes @ ( ti @ int @ A ) @ B )
=> ( quadRes @ A @ B ) )
& ( ( quadRes @ A @ B )
=> ( quadRes @ ( ti @ int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_rel__simps_I48_J) ).
thf(1494,plain,
! [A: $i,B: $i] :
( ( ( ( bit0 @ A )
= ( bit0 @ B ) )
=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) )
& ( ( ( ti @ int @ A )
= ( ti @ int @ B ) )
=> ( ( bit0 @ A )
= ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(561,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ B @ ( times_times @ nat @ C @ D ) )
= ( power_power @ A @ ( power_power @ A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_power__mult) ).
thf(2456,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ B @ ( times_times @ nat @ C @ D ) )
= ( power_power @ A @ ( power_power @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(273,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_pos2) ).
thf(1465,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
thf(756,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ ( power_power @ nat @ B @ A ) @ ( power_power @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_divides__exp) ).
thf(1811,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ ( power_power @ nat @ B @ A ) @ ( power_power @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(505,axiom,
( ( zero_zero @ real )
!= ( one_one @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_real__zero__not__eq__one) ).
thf(2259,plain,
( ( zero_zero @ real )
!= ( one_one @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(258,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
= ( plus_plus @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_semiring__mult__2) ).
thf(1418,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
= ( plus_plus @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times @ real @ ( plus_plus @ real @ A @ B ) @ C )
= ( plus_plus @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_real__add__mult__distrib) ).
thf(937,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times @ real @ ( plus_plus @ real @ A @ B ) @ C )
= ( plus_plus @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ real @ A @ B )
| ( ord_less_eq @ real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_real__le__linear) ).
thf(806,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ real @ A @ B )
| ( ord_less_eq @ real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( minus_minus @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_diff__bin__simps_I7_J) ).
thf(2335,plain,
! [A: $i,B: $i] :
( ( minus_minus @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(82,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ B @ ( times_times @ A @ C @ D ) )
= ( times_times @ A @ ( times_times @ A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(821,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ B @ ( times_times @ A @ C @ D ) )
= ( times_times @ A @ ( times_times @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ~ ( dvd_dvd @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_zdvd__not__zless) ).
thf(2017,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ~ ( dvd_dvd @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(499,axiom,
! [A: $i] :
( ( ti @ int @ ( bit1 @ A ) )
= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
thf(2237,plain,
! [A: $i] :
( ( ti @ int @ ( bit1 @ A ) )
= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(257,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ B @ C )
= ( plus_plus @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1415,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ B @ C )
= ( plus_plus @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_zdiff__power3) ).
thf(1109,plain,
! [A: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(564,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ord_less @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
<=> ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_power__strict__increasing__iff) ).
thf(2469,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ( ord_less @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
=> ( ord_less @ nat @ B @ C ) )
& ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(335,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_semiring__numeral__0__eq__0) ).
thf(1682,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(90,axiom,
zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(834,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)],[90]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd @ int @ D @ C )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ ( times_times @ int @ B @ C ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_zprime__power__zdvd__cancel__right) ).
thf(1858,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd @ int @ D @ C )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ ( times_times @ int @ B @ C ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(391,axiom,
ring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
thf(1864,plain,
ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd @ int @ C @ ( power_power @ int @ A @ B ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( dvd_dvd @ int @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_zpower__zdvd__prop2) ).
thf(1843,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd @ int @ C @ ( power_power @ int @ A @ B ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( dvd_dvd @ int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I34_J) ).
thf(2281,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(102,axiom,
! [A: $i] :
( ( plus_plus @ int @ pls @ A )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_add__Pls) ).
thf(877,plain,
! [A: $i] :
( ( plus_plus @ int @ pls @ A )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(99,axiom,
~ ! [A: $i] :
~ ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192__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(866,plain,
~ ! [A: $i] :
~ ( ( 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)],[99]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg1) ).
thf(660,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(316,axiom,
comm_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).
thf(1600,plain,
comm_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(342,axiom,
ord_less @ int @ t @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(1696,plain,
ord_less @ int @ t @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ A ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ B ) ) )
& ( ~ ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__nat__number__of) ).
thf(2437,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ A ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ B ) ) )
& ( ~ ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(553,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) )
= ( times_times @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2424,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) )
= ( times_times @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult_zero @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_arg1) ).
thf(774,plain,
! [A: $i,B: $i,C: $i] :
( ( mult_zero @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(435,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
= ( number_number_of @ A @ ( times_times @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_arith__simps_I32_J) ).
thf(2002,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
= ( number_number_of @ A @ ( times_times @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(133,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ord_less @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_power__less__imp__less__exp) ).
thf(998,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ord_less @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(516,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__number__of__Pls) ).
thf(2286,plain,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(623,axiom,
? [A: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ! [B: $i] :
( ( ( 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 ) ) ) )
=> ( ( ti @ int @ B )
= ( ti @ int @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191__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(2639,plain,
? [A: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ! [B: $i] :
( ( ( 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 ) ) ) )
=> ( ( ti @ int @ B )
= ( ti @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(419,axiom,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B @ C ) )
<=> ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
& ( ord_less_eq @ A @ ( zero_zero @ A ) @ C ) )
| ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
& ( ord_less_eq @ A @ C @ ( zero_zero @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_zero__le__mult__iff) ).
thf(1943,plain,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B @ C ) )
=> ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
& ( ord_less_eq @ A @ ( zero_zero @ A ) @ C ) )
| ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
& ( ord_less_eq @ A @ C @ ( zero_zero @ A ) ) ) ) )
& ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
& ( ord_less_eq @ A @ ( zero_zero @ A ) @ C ) )
| ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
& ( ord_less_eq @ A @ C @ ( zero_zero @ A ) ) ) )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd @ int @ C @ ( power_power @ int @ A @ B ) )
=> ( dvd_dvd @ int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_zprime__zdvd__power) ).
thf(1201,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( dvd_dvd @ int @ C @ ( power_power @ int @ A @ B ) )
=> ( dvd_dvd @ int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(343,axiom,
~ ( ord_less @ int @ min @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_rel__simps_I7_J) ).
thf(1697,plain,
~ ( ord_less @ int @ min @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(211,axiom,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ! [B: $i,C: $i] :
( ( ( power_power @ A @ B @ C )
= ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( C
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_power__eq__0__iff) ).
thf(1242,plain,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ( power_power @ A @ B @ C )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( C
!= ( zero_zero @ nat ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( C
!= ( zero_zero @ nat ) ) )
=> ( ( power_power @ A @ B @ C )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ int @ A @ ( plus_plus @ int @ B @ ( times_times @ int @ A @ C ) ) )
<=> ( dvd_dvd @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_zdvd__reduce) ).
thf(849,plain,
! [A: $i,B: $i,C: $i] :
( ( ( dvd_dvd @ int @ A @ ( plus_plus @ int @ B @ ( times_times @ int @ A @ C ) ) )
=> ( dvd_dvd @ int @ A @ B ) )
& ( ( dvd_dvd @ int @ A @ B )
=> ( dvd_dvd @ int @ A @ ( plus_plus @ int @ B @ ( times_times @ int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ A @ B @ C )
<=> ( dvd_dvd @ int @ C @ ( minus_minus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_zcong__def) ).
thf(1604,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ A @ B @ C )
=> ( dvd_dvd @ int @ C @ ( minus_minus @ int @ A @ B ) ) )
& ( ( dvd_dvd @ int @ C @ ( minus_minus @ int @ A @ B ) )
=> ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(438,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(2011,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(339,axiom,
semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(1691,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(67,axiom,
dvd @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Odvd) ).
thf(793,plain,
dvd @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(114,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ( power_power @ A @ D @ B )
= ( power_power @ A @ D @ C ) )
<=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_power__inject__exp) ).
thf(925,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ( ( power_power @ A @ D @ B )
= ( power_power @ A @ D @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( power_power @ A @ D @ B )
= ( power_power @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(185,axiom,
! [A: $i] :
( ( power_power @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_quartic__square__square) ).
thf(1153,plain,
! [A: $i] :
( ( power_power @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(74,axiom,
linord581940658strict @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring__strict) ).
thf(810,plain,
linord581940658strict @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_less__int__code_I13_J) ).
thf(2047,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(574,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) )
<=> ( ord_less_eq @ int @ B @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_le__special_I3_J) ).
thf(2496,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) )
=> ( ord_less_eq @ int @ B @ pls ) )
& ( ( ord_less_eq @ int @ B @ pls )
=> ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( ( power_power @ nat @ A @ B )
= ( zero_zero @ nat ) )
<=> ( ( B
!= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_nat__power__eq__0__iff) ).
thf(2061,plain,
! [A: $i,B: $i] :
( ( ( ( power_power @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( B
!= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
!= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( power_power @ nat @ A @ B )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(276,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(1470,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( number_number_of @ B @ ( ti @ int @ A ) )
= ( number_number_of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(1915,plain,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( number_number_of @ B @ ( ti @ int @ A ) )
= ( number_number_of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(348,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ min )
<=> ( ord_less_eq @ int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_rel__simps_I30_J) ).
thf(1708,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ min )
=> ( ord_less_eq @ int @ A @ min ) )
& ( ( ord_less_eq @ int @ A @ min )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(498,axiom,
! [A: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__0__number__of) ).
thf(2232,plain,
! [A: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(520,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
thf(2296,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) )
=> ( ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(627,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ nat @ C @ D )
=> ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less @ A @ B @ ( one_one @ A ) )
=> ( ord_less @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_power__strict__decreasing) ).
thf(2660,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ nat @ C @ D )
=> ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less @ A @ B @ ( one_one @ A ) )
=> ( ord_less @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(362,axiom,
! [A: $i] :
( ( ring_n68954251visors @ A )
=> ! [B: $i,C: $i] :
( ( ( times_times @ A @ B @ C )
= ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_mult__eq__0__iff) ).
thf(1768,plain,
! [A: $i] :
( ( ring_n68954251visors @ A )
=> ! [B: $i,C: $i] :
( ( ( ( times_times @ A @ B @ C )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
= ( zero_zero @ A ) ) )
=> ( ( times_times @ A @ B @ C )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(32,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( times_times @ A @ B @ ( times_times @ A @ C @ ( times_times @ A @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(714,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( times_times @ A @ B @ ( times_times @ A @ C @ ( times_times @ A @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(540,axiom,
! [A: $i] :
( ( ( monoid_mult @ A )
& ( number @ A ) )
=> ! [B: $i] :
( ( power_power @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_power2__eq__square__number__of) ).
thf(2382,plain,
! [A: $i] :
( ( ( monoid_mult @ A )
& ( number @ A ) )
=> ! [B: $i] :
( ( power_power @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_zdvd__imp__le) ).
thf(1057,plain,
! [A: $i,B: $i] :
( ( dvd_dvd @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(188,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(1163,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2264,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_less__eq__number__of__int__code) ).
thf(957,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg1) ).
thf(746,plain,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(612,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) )
= ( power_power @ A @ B @ ( plus_plus @ nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2601,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) )
= ( power_power @ A @ B @ ( plus_plus @ nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(84,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( dvd_dvd @ A @ C @ ( times_times @ A @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_dvd__mult2) ).
thf(825,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( dvd_dvd @ A @ C @ ( times_times @ A @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__eq__int__code_I14_J) ).
thf(1255,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(583,axiom,
dvd @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Odvd) ).
thf(2528,plain,
dvd @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(440,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__imp__0__less) ).
thf(2015,plain,
! [A: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(397,axiom,
( ( ti @ int @ s1 )
= s1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_s1_____res) ).
thf(1883,plain,
( ( ti @ int @ s1 )
= s1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ( ord_less @ int @ A @ C )
=> ( ( ord_less_eq @ int @ B @ A )
| ( ord_less_eq @ int @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_Euler_Oaux2) ).
thf(1021,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ( ord_less @ int @ A @ C )
=> ( ( ord_less_eq @ int @ B @ A )
| ( ord_less_eq @ int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(59,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(778,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(151,axiom,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( times_times @ A @ B @ C ) @ ( zero_zero @ A ) )
<=> ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
& ( ord_less_eq @ A @ C @ ( zero_zero @ A ) ) )
| ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
& ( ord_less_eq @ A @ ( zero_zero @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_mult__le__0__iff) ).
thf(1042,plain,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less_eq @ A @ ( times_times @ A @ B @ C ) @ ( zero_zero @ A ) )
=> ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
& ( ord_less_eq @ A @ C @ ( zero_zero @ A ) ) )
| ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
& ( ord_less_eq @ A @ ( zero_zero @ A ) @ C ) ) ) )
& ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
& ( ord_less_eq @ A @ C @ ( zero_zero @ A ) ) )
| ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
& ( ord_less_eq @ A @ ( zero_zero @ A ) @ C ) ) )
=> ( ord_less_eq @ A @ ( times_times @ A @ B @ C ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ A @ B ) @ ( plus_plus @ int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zadd__left__mono) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ A @ B ) @ ( plus_plus @ int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ C @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_zcong__not) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ C @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(81,axiom,
comm_semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(820,plain,
comm_semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ord_less @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) )
<=> ( ord_less @ real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_real__mult__less__iff1) ).
thf(2150,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ( ord_less @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) )
=> ( ord_less @ real @ A @ B ) )
& ( ( ord_less @ real @ A @ B )
=> ( ord_less @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ord_less @ int @ C @ D )
=> ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less @ int @ ( plus_plus @ int @ C @ A ) @ ( plus_plus @ int @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_zadd__zless__mono) ).
thf(1370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ord_less @ int @ C @ D )
=> ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less @ int @ ( plus_plus @ int @ C @ A ) @ ( plus_plus @ int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_zcong__zmult) ).
thf(2414,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
thf(729,plain,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C )
= ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) )
=> ( ( ord_less @ int @ F @ D )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ D )
=> ( ( ord_less_eq @ int @ D @ A )
=> ( ord_less_eq @ int @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_zdiv__mono2__lemma) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C )
= ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) )
=> ( ( ord_less @ int @ F @ D )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ D )
=> ( ( ord_less_eq @ int @ D @ A )
=> ( ord_less_eq @ int @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(424,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ord_less @ A @ ( plus_plus @ A @ B @ B ) @ ( zero_zero @ A ) )
<=> ( ord_less @ A @ B @ ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_even__less__0__iff) ).
thf(1968,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( plus_plus @ A @ B @ B ) @ ( zero_zero @ A ) )
=> ( ord_less @ A @ B @ ( zero_zero @ A ) ) )
& ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less @ A @ ( plus_plus @ A @ B @ B ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) @ ( plus_plus @ int @ ( times_times @ int @ A @ D ) @ E ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ C @ A )
=> ( ( ord_less @ int @ E @ A )
=> ( ord_less_eq @ int @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_unique__quotient__lemma) ).
thf(1888,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) @ ( plus_plus @ int @ ( times_times @ int @ A @ D ) @ E ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ C @ A )
=> ( ( ord_less @ int @ E @ A )
=> ( ord_less_eq @ int @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(107,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_zero__le__power2) ).
thf(889,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(530,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) )
<=> ( ord_less @ int @ B @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_less__special_I3_J) ).
thf(2345,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) )
=> ( ord_less @ int @ B @ pls ) )
& ( ( ord_less @ int @ B @ pls )
=> ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(255,axiom,
! [A: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I5_J) ).
thf(1407,plain,
! [A: $i] :
( ( ( ord_less @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__eq__int__code_I15_J) ).
thf(1281,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(406,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ int @ pls @ C )
=> ( ( ord_less_eq @ int @ pls @ B )
=> ( ( times_times @ A @ ( number_number_of @ A @ C ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( times_times @ int @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_semiring__mult__number__of) ).
thf(1910,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ int @ pls @ C )
=> ( ( ord_less_eq @ int @ pls @ B )
=> ( ( times_times @ A @ ( number_number_of @ A @ C ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( times_times @ int @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(127,axiom,
ordere453448008miring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).
thf(974,plain,
ordere453448008miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(138,axiom,
! [A: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_odd__less__0) ).
thf(1012,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(337,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ B @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ C @ ( plus_plus @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1687,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ B @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ C @ ( plus_plus @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(270,axiom,
( ( ti @ int @ t )
= t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(1457,plain,
( ( ti @ int @ t )
= t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(380,axiom,
ord_less_eq @ int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_rel__simps_I23_J) ).
thf(1836,plain,
ord_less_eq @ int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(366,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) )
<=> ( ord_less_eq @ int @ pls @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_le__special_I1_J) ).
thf(1787,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) )
=> ( ord_less_eq @ int @ pls @ B ) )
& ( ( ord_less_eq @ int @ pls @ B )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(524,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
<=> ( ord_less_eq @ int @ B @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_le__special_I4_J) ).
thf(2313,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
=> ( ord_less_eq @ int @ B @ ( bit1 @ pls ) ) )
& ( ( ord_less_eq @ int @ B @ ( bit1 @ pls ) )
=> ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(177,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
~ ( ord_less @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
thf(1128,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
~ ( ord_less @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(626,axiom,
! [A: $i] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_eq__0__number__of) ).
thf(2653,plain,
! [A: $i] :
( ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(1106,plain,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(415,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(1936,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(580,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ nat @ C @ D )
=> ( ( ord_less_eq @ A @ ( one_one @ A ) @ B )
=> ( ord_less_eq @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_power__increasing) ).
thf(2515,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ nat @ C @ D )
=> ( ( ord_less_eq @ A @ ( one_one @ A ) @ B )
=> ( ord_less_eq @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(539,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_less__special_I2_J) ).
thf(2377,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
=> ( ord_less @ int @ ( bit1 @ pls ) @ B ) )
& ( ( ord_less @ int @ ( bit1 @ pls ) @ B )
=> ( ord_less @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(244,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_semiring__one__add__one__is__two) ).
thf(1375,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(208,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_sum__power2__le__zero__iff) ).
thf(1227,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less_eq @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) )
=> ( ord_less_eq @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus @ real @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
<=> ( ( A
= ( zero_zero @ real ) )
& ( B
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_realpow__two__sum__zero__iff) ).
thf(980,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus @ real @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
=> ( ( A
= ( zero_zero @ real ) )
& ( B
= ( zero_zero @ real ) ) ) )
& ( ( ( A
= ( zero_zero @ real ) )
& ( B
= ( zero_zero @ real ) ) )
=> ( ( plus_plus @ real @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(578,axiom,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Bit0__def) ).
thf(2509,plain,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(136,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1006,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(62,axiom,
comm_monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) ).
thf(783,plain,
comm_monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( minus_minus @ nat @ ( power_power @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ nat @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_diff__square) ).
thf(2268,plain,
! [A: $i,B: $i] :
( ( minus_minus @ nat @ ( power_power @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ nat @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(130,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( power_power @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_zero__le__power) ).
thf(989,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( power_power @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(95,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
thf(857,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)],[95]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).
thf(697,plain,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(164,axiom,
dvd_dvd @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(1089,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)],[164]) ).
thf(294,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ min )
<=> ( ord_less_eq @ int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_rel__simps_I28_J) ).
thf(1541,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ min )
=> ( ord_less_eq @ int @ A @ min ) )
& ( ( ord_less_eq @ int @ A @ min )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ A @ ( times_times @ int @ B @ C ) ) @ D ) @ ( times_times @ int @ ( minus_minus @ int @ E @ ( times_times @ int @ B @ F ) ) @ G ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ D ) @ ( times_times @ int @ E @ G ) ) @ ( times_times @ int @ B @ ( plus_plus @ int @ ( times_times @ int @ C @ D ) @ ( times_times @ int @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_xzgcda__linear__aux1) ).
thf(874,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ A @ ( times_times @ int @ B @ C ) ) @ D ) @ ( times_times @ int @ ( minus_minus @ int @ E @ ( times_times @ int @ B @ F ) ) @ G ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ D ) @ ( times_times @ int @ E @ G ) ) @ ( times_times @ int @ B @ ( plus_plus @ int @ ( times_times @ int @ C @ D ) @ ( times_times @ int @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(183,axiom,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_zprime__2) ).
thf(1143,plain,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(217,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ ( one_one @ A ) @ B )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_power__one) ).
thf(1270,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ ( one_one @ A ) @ B )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power @ int @ B @ A ) @ ( power_power @ int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_zcong__zpower) ).
thf(1851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power @ int @ B @ A ) @ ( power_power @ int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(139,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ nat @ C @ D )
=> ( ( ord_less @ A @ ( one_one @ A ) @ B )
=> ( ord_less @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_power__strict__increasing) ).
thf(1017,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ nat @ C @ D )
=> ( ( ord_less @ A @ ( one_one @ A ) @ B )
=> ( ord_less @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(420,axiom,
! [A: $i] :
( ( semiring @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( plus_plus @ A @ ( times_times @ A @ D @ C ) @ E ) )
= ( plus_plus @ A @ ( times_times @ A @ ( plus_plus @ A @ B @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_combine__common__factor) ).
thf(1953,plain,
! [A: $i] :
( ( semiring @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( plus_plus @ A @ ( times_times @ A @ D @ C ) @ E ) )
= ( plus_plus @ A @ ( times_times @ A @ ( plus_plus @ A @ B @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of @ int @ min ) @ B )
=> ~ ( zcong @ A @ ( one_one @ int ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_zcong__neg__1__impl__ne__1) ).
thf(2685,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of @ int @ min ) @ B )
=> ~ ( zcong @ A @ ( one_one @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(649,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_number__of__Pls) ).
thf(2724,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(587,axiom,
ord_less @ int @ t @ ( one_one @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(2537,plain,
ord_less @ int @ t @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ int @ A @ ( minus_minus @ int @ B @ C ) )
=> ( ( dvd_dvd @ int @ A @ C )
=> ( dvd_dvd @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_zdvd__zdiffD) ).
thf(2561,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ int @ A @ ( minus_minus @ int @ B @ C ) )
=> ( ( dvd_dvd @ int @ A @ C )
=> ( dvd_dvd @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(194,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ min )
<=> ( ord_less @ int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_rel__simps_I13_J) ).
thf(1182,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ min )
=> ( ord_less @ int @ A @ min ) )
& ( ( ord_less @ int @ A @ min )
=> ( ord_less @ int @ ( bit1 @ A ) @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( B
= ( zero_zero @ nat ) )
| ( B = A )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_divides__cases) ).
thf(1739,plain,
! [A: $i,B: $i] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( B
= ( zero_zero @ nat ) )
| ( B = A )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( ti @ C @ ( minus_minus @ C @ A @ B ) )
= ( minus_minus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_0_res) ).
thf(669,plain,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( ti @ C @ ( minus_minus @ C @ A @ B ) )
= ( minus_minus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(159,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( number_number_of @ A @ ( bit1 @ pls ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_semiring__numeral__1__eq__1) ).
thf(1075,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( number_number_of @ A @ ( bit1 @ pls ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(560,axiom,
ordered_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring) ).
thf(2455,plain,
ordered_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(416,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(1937,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__number__of__int__code) ).
thf(1446,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(26,axiom,
comm_ring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__ring__1) ).
thf(706,plain,
comm_ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(144,axiom,
order @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
thf(1028,plain,
order @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(162,axiom,
~ ! [A: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__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(1082,plain,
~ ! [A: $i] :
( ( 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)],[162]) ).
thf(423,axiom,
! [A: $i] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_rel__simps_I42_J) ).
thf(1964,plain,
! [A: $i] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(418,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(1942,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(332,axiom,
ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(1659,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(453,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( times_times @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( times_times @ A @ ( number_number_of @ A @ ( times_times @ int @ B @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mult__number__of__left) ).
thf(2053,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( times_times @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( times_times @ A @ ( number_number_of @ A @ ( times_times @ int @ B @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(500,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_number__of__add) ).
thf(2240,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(565,axiom,
( ( number_number_of @ int @ pls )
!= ( number_number_of @ int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_eq__number__of__Pls__Min) ).
thf(2472,plain,
( ( number_number_of @ int @ pls )
!= ( number_number_of @ int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(14,axiom,
semiri456707255roduct @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) ).
thf(679,plain,
semiri456707255roduct @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(149,axiom,
( ( ti @ int @ s )
= s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_s_____res) ).
thf(1039,plain,
( ( ti @ int @ s )
= s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(224,axiom,
! [A: $i] :
( ( ( number @ A )
& ( semiring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( plus_plus @ A @ B @ C ) @ ( number_number_of @ A @ D ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ ( number_number_of @ A @ D ) ) @ ( times_times @ A @ C @ ( number_number_of @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_left__distrib__number__of) ).
thf(1297,plain,
! [A: $i] :
( ( ( number @ A )
& ( semiring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( plus_plus @ A @ B @ C ) @ ( number_number_of @ A @ D ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ ( number_number_of @ A @ D ) ) @ ( times_times @ A @ C @ ( number_number_of @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(268,axiom,
! [A: $i] :
( ( comm_monoid_mult @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_power__mult__distrib) ).
thf(1451,plain,
! [A: $i] :
( ( comm_monoid_mult @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(291,axiom,
! [A: $i] :
( ( ti @ int @ ( bit0 @ A ) )
= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
thf(1530,plain,
! [A: $i] :
( ( ti @ int @ ( bit0 @ A ) )
= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I15_J) ).
thf(2243,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(533,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(2355,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(603,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ nat @ C @ D )
=> ( dvd_dvd @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_le__imp__power__dvd) ).
thf(2581,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ nat @ C @ D )
=> ( dvd_dvd @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(576,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ C )
=> ( ord_less @ A @ ( one_one @ A ) @ ( times_times @ A @ C @ ( power_power @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_power__gt1__lemma) ).
thf(2505,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ C )
=> ( ord_less @ A @ ( one_one @ A ) @ ( times_times @ A @ C @ ( power_power @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(35,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ B @ ( times_times @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(721,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ B @ ( times_times @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(369,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( one_one @ A ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1799,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( one_one @ A ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(429,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(1984,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(135,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
| ( ( ti @ A @ B )
= ( one_one @ A ) ) )
=> ( dvd_dvd @ A @ B @ ( power_power @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_dvd__power) ).
thf(1002,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
| ( ( ti @ A @ B )
= ( one_one @ A ) ) )
=> ( dvd_dvd @ A @ B @ ( power_power @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( quadRes @ A @ B )
<=> ? [C: $i] : ( zcong @ ( power_power @ int @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_QuadRes__def) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( ( quadRes @ A @ B )
=> ? [C: $i] : ( zcong @ ( power_power @ int @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) )
& ( ? [C: $i] : ( 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)],[261]) ).
thf(376,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less @ A @ C @ ( one_one @ A ) )
=> ( ord_less @ A @ ( times_times @ A @ C @ ( power_power @ A @ C @ B ) ) @ ( power_power @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_power__Suc__less) ).
thf(1825,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less @ A @ C @ ( one_one @ A ) )
=> ( ord_less @ A @ ( times_times @ A @ C @ ( power_power @ A @ C @ B ) ) @ ( power_power @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( minus_minus @ nat @ A @ ( ti @ nat @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_arg2) ).
thf(1114,plain,
! [A: $i,B: $i] :
( ( minus_minus @ nat @ A @ ( ti @ nat @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times @ int @ C @ B ) @ E )
<=> ( zcong @ A @ ( times_times @ int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_zcong__zmult__prop1) ).
thf(2450,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( ( zcong @ A @ ( times_times @ int @ C @ B ) @ E )
=> ( zcong @ A @ ( times_times @ int @ D @ B ) @ E ) )
& ( ( zcong @ A @ ( times_times @ int @ D @ B ) @ E )
=> ( zcong @ A @ ( times_times @ int @ C @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(310,axiom,
! [A: $i] :
( ( mult_zero @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( zero_zero @ A ) @ B )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_mult__zero__left) ).
thf(1588,plain,
! [A: $i] :
( ( mult_zero @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( zero_zero @ A ) @ B )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) @ ( plus_plus @ int @ ( times_times @ int @ A @ D ) @ E ) )
=> ( ( ord_less_eq @ int @ E @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ A @ E )
=> ( ( ord_less @ int @ A @ C )
=> ( ord_less_eq @ int @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_unique__quotient__lemma__neg) ).
thf(2153,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) @ ( plus_plus @ int @ ( times_times @ int @ A @ D ) @ E ) )
=> ( ( ord_less_eq @ int @ E @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ A @ E )
=> ( ( ord_less @ int @ A @ C )
=> ( ord_less_eq @ int @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(379,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rel__simps_I12_J) ).
thf(1831,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(178,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ ( power_power @ A @ B @ C ) @ D )
= ( power_power @ A @ B @ ( times_times @ nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1131,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ ( power_power @ A @ B @ C ) @ D )
= ( power_power @ A @ B @ ( times_times @ nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ real @ A @ B )
=> ( ( ord_less_eq @ real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_real__le__antisym) ).
thf(654,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ real @ A @ B )
=> ( ( ord_less_eq @ real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(452,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(2052,plain,
no_zero_divisors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zadd__zmult__distrib2) ).
thf(2482,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_divides__mul__l) ).
thf(1979,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(60,axiom,
comm_semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring) ).
thf(779,plain,
comm_semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(210,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(1241,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(53,axiom,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(765,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(274,axiom,
! [A: $i] : ( ord_less_eq @ int @ A @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_power2__ge__self) ).
thf(1466,plain,
! [A: $i] : ( ord_less_eq @ int @ A @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_real__mult__order) ).
thf(2221,plain,
! [A: $i,B: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(616,axiom,
~ ( ord_less @ int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_rel__simps_I3_J) ).
thf(2617,plain,
~ ( ord_less @ int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(628,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ B @ ( plus_plus @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2662,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ B @ ( plus_plus @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( zero_zero @ nat ) )
=> ( ( dvd_dvd @ nat @ ( power_power @ nat @ A @ C ) @ B )
=> ( dvd_dvd @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_divides__exp2) ).
thf(2529,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( zero_zero @ nat ) )
=> ( ( dvd_dvd @ nat @ ( power_power @ nat @ A @ C ) @ B )
=> ( dvd_dvd @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(354,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( ( dvd_dvd @ A @ C @ B )
=> ( dvd_dvd @ A @ C @ ( plus_plus @ A @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_dvd__add) ).
thf(1732,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( ( dvd_dvd @ A @ C @ B )
=> ( dvd_dvd @ A @ C @ ( plus_plus @ A @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(622,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I27_J) ).
thf(2634,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ ( power_power @ int @ B @ C ) @ ( one_one @ int ) @ D )
=> ( zcong @ ( power_power @ int @ B @ ( times_times @ nat @ C @ A ) ) @ ( one_one @ int ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_zcong__zpower__zmult) ).
thf(1434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ ( power_power @ int @ B @ C ) @ ( one_one @ int ) @ D )
=> ( zcong @ ( power_power @ int @ B @ ( times_times @ nat @ C @ A ) ) @ ( one_one @ int ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(301,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( bit0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_double__number__of__Bit0) ).
thf(1563,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( minus_minus @ C @ ( ti @ C @ A ) @ B )
= ( minus_minus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_0_arg1) ).
thf(657,plain,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( minus_minus @ C @ ( ti @ C @ A ) @ B )
= ( minus_minus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(222,axiom,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ! [B: $i,C: $i] :
( ( ( power_power @ A @ B @ ( number_number_of @ nat @ C ) )
= ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( number_number_of @ nat @ C )
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_power__eq__0__iff__number__of) ).
thf(1286,plain,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ( power_power @ A @ B @ ( number_number_of @ nat @ C ) )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( number_number_of @ nat @ C )
!= ( zero_zero @ nat ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( number_number_of @ nat @ C )
!= ( zero_zero @ nat ) ) )
=> ( ( power_power @ A @ B @ ( number_number_of @ nat @ C ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ A @ C )
= ( times_times @ real @ B @ C ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_real__mult__right__cancel) ).
thf(2368,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( zero_zero @ real ) )
=> ( ( ( ( times_times @ real @ A @ C )
= ( times_times @ real @ B @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( times_times @ real @ A @ C )
= ( times_times @ real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(195,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ C )
=> ( ord_less @ A @ ( power_power @ A @ C @ B ) @ ( times_times @ A @ C @ ( power_power @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_power__less__power__Suc) ).
thf(1187,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ C )
=> ( ord_less @ A @ ( power_power @ A @ C @ B ) @ ( times_times @ A @ C @ ( power_power @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(12,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( dvd_dvd @ A @ C @ ( times_times @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_dvd__mult) ).
thf(674,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( dvd_dvd @ A @ C @ ( times_times @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) )
=> ( ( ( ti @ int @ A )
!= ( zero_zero @ int ) )
=> ( dvd_dvd @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_zdvd__mult__cancel) ).
thf(2645,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) )
=> ( ( ( ti @ int @ A )
!= ( zero_zero @ int ) )
=> ( dvd_dvd @ int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(322,axiom,
~ ! [A: $i] :
~ ( zcong @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(1616,plain,
~ ! [A: $i] :
~ ( 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)],[322]) ).
thf(56,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(773,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(68,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(794,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(529,axiom,
! [A: $i] :
( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_eq__number__of__0) ).
thf(2338,plain,
! [A: $i] :
( ( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(220,axiom,
! [A: $i] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_four__x__squared) ).
thf(1278,plain,
! [A: $i] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
<=> ( ( B
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_zero__less__power__nat__eq) ).
thf(1648,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
=> ( ( B
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(124,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ ( bit1 @ pls ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_numeral__1__eq__1) ).
thf(965,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ ( bit1 @ pls ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(633,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ B @ A ) )
=> ( ord_less @ int @ ( zero_zero @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pos__zmult__pos) ).
thf(2677,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ B @ A ) )
=> ( ord_less @ int @ ( zero_zero @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(543,axiom,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( ti @ A @ ( one_one @ A ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_0_res) ).
thf(2391,plain,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( ti @ A @ ( one_one @ A ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(83,axiom,
ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring) ).
thf(824,plain,
ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ord_less_eq @ real @ ( times_times @ real @ C @ A ) @ ( times_times @ real @ C @ B ) )
<=> ( ord_less_eq @ real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_real__mult__le__cancel__iff2) ).
thf(1273,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ( ord_less_eq @ real @ ( times_times @ real @ C @ A ) @ ( times_times @ real @ C @ B ) )
=> ( ord_less_eq @ real @ A @ B ) )
& ( ( ord_less_eq @ real @ A @ B )
=> ( ord_less_eq @ real @ ( times_times @ real @ C @ A ) @ ( times_times @ real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(600,axiom,
quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(2570,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)],[600]) ).
thf(18,axiom,
no_zero_divisors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(689,plain,
no_zero_divisors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( no_zero_divisors @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_arg1) ).
thf(733,plain,
! [A: $i,B: $i,C: $i] :
( ( no_zero_divisors @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rel__simps_I33_J) ).
thf(1959,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(594,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(2556,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( times_times @ int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_mult__nat__number__of) ).
thf(2028,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( times_times @ int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( times_times @ int @ ( plus_plus @ int @ A @ B ) @ ( minus_minus @ int @ A @ B ) )
= ( minus_minus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_zspecial__product) ).
thf(1301,plain,
! [A: $i,B: $i] :
( ( times_times @ int @ ( plus_plus @ int @ A @ B ) @ ( minus_minus @ int @ A @ B ) )
= ( minus_minus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(313,axiom,
ab_group_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
thf(1595,plain,
ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(80,axiom,
semiring_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__0) ).
thf(819,plain,
semiring_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(128,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ A )
<=> ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_int__one__le__iff__zero__less) ).
thf(975,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ ( one_one @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ A ) )
& ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(650,axiom,
! [A: $i] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Bit1__def) ).
thf(2727,plain,
! [A: $i] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(694,plain,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(39,axiom,
semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring) ).
thf(732,plain,
semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( power_power @ C @ ( ti @ C @ A ) @ B )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg1) ).
thf(1784,plain,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( power_power @ C @ ( ti @ C @ A ) @ B )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ( ( zcong @ B @ ( zero_zero @ int ) @ A )
=> ( ( ti @ int @ B )
= ( zero_zero @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_Int2_Ozcong__zero) ).
thf(1125,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ( ( zcong @ B @ ( zero_zero @ int ) @ A )
=> ( ( ti @ int @ B )
= ( zero_zero @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
| ( ( ti @ int @ A )
= ( ti @ int @ B ) )
| ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_zless__linear) ).
thf(2188,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
| ( ( ti @ int @ A )
= ( ti @ int @ B ) )
| ( ord_less @ int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( legendre @ A @ ( ti @ int @ B ) )
= ( legendre @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_arg2) ).
thf(1620,plain,
! [A: $i,B: $i] :
( ( legendre @ A @ ( ti @ int @ B ) )
= ( legendre @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(632,axiom,
! [A: $i] :
( ( no_zero_divisors @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_1_res) ).
thf(2674,plain,
! [A: $i] :
( ( no_zero_divisors @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ ( zero_zero @ int ) @ C )
=> ( ~ ( zcong @ A @ ( zero_zero @ int ) @ C )
=> ~ ( zcong @ ( times_times @ int @ B @ A ) @ ( zero_zero @ int ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_zcong__zmult__prop3) ).
thf(1388,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ ( zero_zero @ int ) @ C )
=> ( ~ ( zcong @ A @ ( zero_zero @ int ) @ C )
=> ~ ( zcong @ ( times_times @ int @ B @ A ) @ ( zero_zero @ int ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_arg1) ).
thf(743,plain,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( times_times @ C @ ( ti @ C @ A ) @ B )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(29,axiom,
order @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(711,plain,
order @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(368,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) ) @ ( zero_zero @ A ) )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_even__power__le__0__imp__0) ).
thf(1795,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) ) @ ( zero_zero @ A ) )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(646,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( zero_zero @ nat ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2716,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( zero_zero @ nat ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(282,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(1488,plain,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( 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 )
=> ( ( ti @ int @ B )
= ( ti @ int @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_zdvd__antisym__nonneg) ).
thf(1139,plain,
! [A: $i,B: $i] :
( ( 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 )
=> ( ( ti @ int @ B )
= ( ti @ int @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(116,axiom,
ord_less @ int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_rel__simps_I6_J) ).
thf(936,plain,
ord_less @ int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(493,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(2220,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(347,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(1707,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less @ nat @ ( power_power @ nat @ C @ A ) @ ( power_power @ nat @ C @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_nat__power__less__imp__less) ).
thf(2308,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less @ nat @ ( power_power @ nat @ C @ A ) @ ( power_power @ nat @ C @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg2) ).
thf(787,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(433,axiom,
! [A: $i] : ( ord_less_eq @ int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_zle__refl) ).
thf(1997,plain,
! [A: $i] : ( ord_less_eq @ int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(165,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ min @ ( bit0 @ A ) )
<=> ( ord_less @ int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_rel__simps_I25_J) ).
thf(1090,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ min @ ( bit0 @ A ) )
=> ( ord_less @ int @ min @ A ) )
& ( ( ord_less @ int @ min @ A )
=> ( ord_less_eq @ int @ min @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_rel__simps_I49_J) ).
thf(2557,plain,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(207,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( power_power @ A @ ( number_number_of @ A @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_power__m1__even) ).
thf(1224,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( power_power @ A @ ( number_number_of @ A @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ B @ A ) @ ( times_times @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_divides__mul__r) ).
thf(2148,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ B @ A ) @ ( times_times @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ real @ B @ C )
=> ( ( ord_less_eq @ real @ C @ A )
=> ( ord_less_eq @ real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_real__le__trans) ).
thf(672,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ real @ B @ C )
=> ( ( ord_less_eq @ real @ C @ A )
=> ( ord_less_eq @ real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
ordered_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oordered__ring) ).
thf(713,plain,
ordered_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( zcong @ A @ ( zero_zero @ int ) @ B )
<=> ( dvd_dvd @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_zcong__zero__equiv__div) ).
thf(1865,plain,
! [A: $i,B: $i] :
( ( ( zcong @ A @ ( zero_zero @ int ) @ B )
=> ( dvd_dvd @ int @ B @ A ) )
& ( ( dvd_dvd @ int @ B @ A )
=> ( zcong @ A @ ( zero_zero @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(199,axiom,
! [A: $i] :
( ( number @ A )
=> ! [B: $i,C: $i] :
( ( ( number_number_of @ A @ B )
= ( ti @ A @ C ) )
<=> ( ( ti @ A @ C )
= ( number_number_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_number__of__reorient) ).
thf(1194,plain,
! [A: $i] :
( ( number @ A )
=> ! [B: $i,C: $i] :
( ( ( ( number_number_of @ A @ B )
= ( ti @ A @ C ) )
=> ( ( ti @ A @ C )
= ( number_number_of @ A @ B ) ) )
& ( ( ( ti @ A @ C )
= ( number_number_of @ A @ B ) )
=> ( ( number_number_of @ A @ B )
= ( ti @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(470,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(2119,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(634,axiom,
! [A: $i] :
( ( linord626643107strict @ A )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ord_less @ A @ E @ F )
=> ( ( ord_less @ A @ D @ F )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ( plus_plus @ A @ C @ B )
= ( one_one @ A ) )
=> ( ord_less @ A @ ( plus_plus @ A @ ( times_times @ A @ C @ E ) @ ( times_times @ A @ B @ D ) ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_convex__bound__lt) ).
thf(2679,plain,
! [A: $i] :
( ( linord626643107strict @ A )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ord_less @ A @ E @ F )
=> ( ( ord_less @ A @ D @ F )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ( plus_plus @ A @ C @ B )
= ( one_one @ A ) )
=> ( ord_less @ A @ ( plus_plus @ A @ ( times_times @ A @ C @ E ) @ ( times_times @ A @ B @ D ) ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(88,axiom,
mult_zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(831,plain,
mult_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(567,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ord_less_eq @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_power__le__imp__le__exp) ).
thf(2478,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ D )
=> ( ( ord_less_eq @ A @ ( power_power @ A @ D @ B ) @ ( power_power @ A @ D @ C ) )
=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(497,axiom,
! [A: $i] :
( ( zprime @ A )
=> ( ( ( ti @ int @ A )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( ( ti @ int @ A )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_prime__g__5) ).
thf(2229,plain,
! [A: $i] :
( ( zprime @ A )
=> ( ( ( ti @ int @ A )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( ( ti @ int @ 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)],[497]) ).
thf(460,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( ring_char_0 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( number_number_of @ A @ B )
= ( number_number_of @ A @ C ) )
<=> ( ( ti @ int @ B )
= ( ti @ int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_eq__number__of) ).
thf(2084,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( ring_char_0 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ( number_number_of @ A @ B )
= ( number_number_of @ A @ C ) )
=> ( ( ti @ int @ B )
= ( ti @ int @ C ) ) )
& ( ( ( ti @ int @ B )
= ( ti @ int @ C ) )
=> ( ( number_number_of @ A @ B )
= ( number_number_of @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(305,axiom,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
thf(1574,plain,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(41,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(736,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_nat__zero__less__power__iff) ).
thf(1144,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) )
& ( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(469,axiom,
! [A: $i] :
( ( minus_minus @ int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus @ int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_diff__bin__simps_I5_J) ).
thf(2116,plain,
! [A: $i] :
( ( minus_minus @ int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus @ int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ord_less_eq @ C @ A @ ( ti @ C @ B ) )
<=> ( ord_less_eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_arg2) ).
thf(737,plain,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ( ord_less_eq @ C @ A @ ( ti @ C @ B ) )
=> ( ord_less_eq @ C @ A @ B ) )
& ( ( ord_less_eq @ C @ A @ B )
=> ( ord_less_eq @ C @ A @ ( ti @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ B @ ( zero_zero @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_q__neg__lemma) ).
thf(880,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C ) @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ B @ ( zero_zero @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(175,axiom,
! [A: $i] :
( ( power @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( zero_zero @ nat ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_power__0) ).
thf(1122,plain,
! [A: $i] :
( ( power @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( zero_zero @ nat ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(338,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(1690,plain,
mult_zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(304,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ ( minus_minus @ A @ B @ C ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ A @ ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_power2__diff) ).
thf(1571,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ ( minus_minus @ A @ B @ C ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ A @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ A @ ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(228,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( times_times @ int @ B @ C ) )
= ( times_times @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_number__of__mult) ).
thf(1307,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( times_times @ int @ B @ C ) )
= ( times_times @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(98,axiom,
! [A: $i] :
( ( no_zero_divisors @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ C )
!= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
=> ( ( times_times @ A @ C @ B )
!= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_no__zero__divisors) ).
thf(863,plain,
! [A: $i] :
( ( no_zero_divisors @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ C )
!= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
=> ( ( times_times @ A @ C @ B )
!= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(458,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_one__is__num__one) ).
thf(2079,plain,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus @ int @ C @ A ) @ ( minus_minus @ int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_zcong__zdiff) ).
thf(2361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus @ int @ C @ A ) @ ( minus_minus @ int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( zprime @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ B )
=> ( ( zcong @ ( times_times @ int @ A @ A ) @ ( one_one @ int ) @ B )
=> ( ( ( ti @ int @ A )
= ( one_one @ int ) )
| ( ( ti @ int @ A )
= ( minus_minus @ int @ B @ ( one_one @ int ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_zcong__square__zless) ).
thf(2538,plain,
! [A: $i,B: $i] :
( ( zprime @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ B )
=> ( ( zcong @ ( times_times @ int @ A @ A ) @ ( one_one @ int ) @ B )
=> ( ( ( ti @ int @ A )
= ( one_one @ int ) )
| ( ( ti @ int @ A )
= ( minus_minus @ int @ B @ ( one_one @ int ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(386,axiom,
! [A: $i] :
( ( linordered_ring @ A )
=> ! [B: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_zero__le__square) ).
thf(1853,plain,
! [A: $i] :
( ( linordered_ring @ A )
=> ! [B: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult_zero @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_res) ).
thf(784,plain,
! [A: $i,B: $i,C: $i] :
( ( mult_zero @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(173,axiom,
! [A: $i] :
( ( ring_1 @ A )
=> ! [B: $i] :
( ( minus_minus @ A @ ( times_times @ A @ B @ B ) @ ( one_one @ A ) )
= ( times_times @ A @ ( plus_plus @ A @ B @ ( one_one @ A ) ) @ ( minus_minus @ A @ B @ ( one_one @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_real__squared__diff__one__factored) ).
thf(1117,plain,
! [A: $i] :
( ( ring_1 @ A )
=> ! [B: $i] :
( ( minus_minus @ A @ ( times_times @ A @ B @ B ) @ ( one_one @ A ) )
= ( times_times @ A @ ( plus_plus @ A @ B @ ( one_one @ A ) ) @ ( minus_minus @ A @ B @ ( one_one @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(334,axiom,
! [A: $i] :
( ( zprime @ A )
<=> ( ( ord_less @ int @ ( one_one @ int ) @ A )
& ! [B: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( dvd_dvd @ int @ B @ A ) )
=> ( ( ( ti @ int @ B )
= ( one_one @ int ) )
| ( ( ti @ int @ B )
= ( ti @ int @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_zprime__def) ).
thf(1667,plain,
! [A: $i] :
( ( ( zprime @ A )
=> ( ( ord_less @ int @ ( one_one @ int ) @ A )
& ! [B: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( dvd_dvd @ int @ B @ A ) )
=> ( ( ( ti @ int @ B )
= ( one_one @ int ) )
| ( ( ti @ int @ B )
= ( ti @ int @ A ) ) ) ) ) )
& ( ( ( ord_less @ int @ ( one_one @ int ) @ A )
& ! [B: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( dvd_dvd @ int @ B @ A ) )
=> ( ( ( ti @ int @ B )
= ( one_one @ int ) )
| ( ( ti @ int @ B )
= ( ti @ int @ A ) ) ) ) )
=> ( zprime @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(326,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ B @ ( plus_plus @ nat @ C @ D ) )
= ( times_times @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_power__add) ).
thf(1630,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( power_power @ A @ B @ ( plus_plus @ nat @ C @ D ) )
= ( times_times @ A @ ( power_power @ A @ B @ C ) @ ( power_power @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(23,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( times_times @ A @ B @ C )
= ( times_times @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(700,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( times_times @ A @ B @ C )
= ( times_times @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(145,axiom,
linord581940658strict @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(1029,plain,
linord581940658strict @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ B )
= A )
& ! [D: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( power_power @ real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_realpow__pos__nth__unique) ).
thf(2252,plain,
! [A: $i,B: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ B )
= A )
& ! [D: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( power_power @ real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_zadd__power2) ).
thf(1381,plain,
! [A: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(171,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( one_one @ A ) @ C )
=> ( ord_less_eq @ A @ ( one_one @ A ) @ ( power_power @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_one__le__power) ).
thf(1112,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( one_one @ A ) @ C )
=> ( ord_less_eq @ A @ ( one_one @ A ) @ ( power_power @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(75,axiom,
ordere453448008miring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) ).
thf(811,plain,
ordere453448008miring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
thf(2182,plain,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(394,axiom,
! [A: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_one__not__neg__one__mod__m) ).
thf(1877,plain,
! [A: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( zcong @ A @ ( zero_zero @ int ) @ B )
<=> ( dvd_dvd @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_zcong__eq__zdvd__prop) ).
thf(1471,plain,
! [A: $i,B: $i] :
( ( ( zcong @ A @ ( zero_zero @ int ) @ B )
=> ( dvd_dvd @ int @ B @ A ) )
& ( ( dvd_dvd @ int @ B @ A )
=> ( zcong @ A @ ( zero_zero @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(444,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(2025,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(621,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( zcong @ ( times_times @ int @ B @ A ) @ ( zero_zero @ int ) @ C )
=> ( ( zcong @ B @ ( zero_zero @ int ) @ C )
| ( zcong @ A @ ( zero_zero @ int ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_zcong__zprime__prod__zero) ).
thf(2632,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( zcong @ ( times_times @ int @ B @ A ) @ ( zero_zero @ int ) @ C )
=> ( ( zcong @ B @ ( zero_zero @ int ) @ C )
| ( zcong @ A @ ( zero_zero @ int ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(96,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ B @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(858,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ B @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_rel__simps_I16_J) ).
thf(1557,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(513,axiom,
~ ( ord_less_eq @ int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_rel__simps_I20_J) ).
thf(2278,plain,
~ ( ord_less_eq @ int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(593,axiom,
! [A: $i] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
thf(2553,plain,
! [A: $i] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(643,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(2710,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( ( dvd_dvd @ nat @ B @ ( plus_plus @ nat @ C @ A ) )
=> ( dvd_dvd @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_divides__add__revr) ).
thf(1820,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ B @ C )
=> ( ( dvd_dvd @ nat @ B @ ( plus_plus @ nat @ C @ A ) )
=> ( dvd_dvd @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ~ ( zcong @ B @ ( zero_zero @ int ) @ C )
& ~ ( zcong @ A @ ( zero_zero @ int ) @ C ) )
=> ~ ( zcong @ ( times_times @ int @ B @ A ) @ ( zero_zero @ int ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_zcong__zprime__prod__zero__contra) ).
thf(1926,plain,
! [A: $i,B: $i,C: $i] :
( ( zprime @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ~ ( zcong @ B @ ( zero_zero @ int ) @ C )
& ~ ( zcong @ A @ ( zero_zero @ int ) @ C ) )
=> ~ ( zcong @ ( times_times @ int @ B @ A ) @ ( zero_zero @ int ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(531,axiom,
! [A: $i] :
( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ A )
= ( one_one @ int ) )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ A )
= ( number_number_of @ int @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_neg__one__power) ).
thf(2350,plain,
! [A: $i] :
( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ A )
= ( one_one @ int ) )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ A )
= ( number_number_of @ int @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(592,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__special_I3_J) ).
thf(2550,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(192,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ ( times_times @ A @ B @ D ) @ ( times_times @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1176,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ ( times_times @ A @ B @ D ) @ ( times_times @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(517,axiom,
! [A: $i] :
( ( linordered_ring @ A )
=> ! [B: $i,C: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_sum__squares__ge__zero) ).
thf(2288,plain,
! [A: $i] :
( ( linordered_ring @ A )
=> ! [B: $i,C: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ord_less @ int @ ( plus_plus @ int @ B @ A ) @ ( plus_plus @ int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_zadd__strict__right__mono) ).
thf(1000,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ord_less @ int @ ( plus_plus @ int @ B @ A ) @ ( plus_plus @ int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(443,axiom,
! [A: $i] :
( ( bit1 @ ( ti @ int @ A ) )
= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
thf(2022,plain,
! [A: $i] :
( ( bit1 @ ( ti @ int @ A ) )
= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(464,axiom,
! [A: $i] :
( ( ( number @ A )
& ( ring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( minus_minus @ A @ B @ C ) @ ( number_number_of @ A @ D ) )
= ( minus_minus @ A @ ( times_times @ A @ B @ ( number_number_of @ A @ D ) ) @ ( times_times @ A @ C @ ( number_number_of @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_left__diff__distrib__number__of) ).
thf(2101,plain,
! [A: $i] :
( ( ( number @ A )
& ( ring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( minus_minus @ A @ B @ C ) @ ( number_number_of @ A @ D ) )
= ( minus_minus @ A @ ( times_times @ A @ B @ ( number_number_of @ A @ D ) ) @ ( times_times @ A @ C @ ( number_number_of @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(352,axiom,
! [A: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_nat__mult__2) ).
thf(1726,plain,
! [A: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(3,axiom,
power @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(653,plain,
power @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(425,axiom,
! [A: $i] :
( ( minus_minus @ int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus @ int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_diff__bin__simps_I4_J) ).
thf(1973,plain,
! [A: $i] :
( ( minus_minus @ int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus @ int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(300,axiom,
ord_less @ int @ t @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_t__l__p) ).
thf(1562,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)],[300]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( power_power @ real @ ( plus_plus @ real @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ real @ ( plus_plus @ real @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_real__sum__squared__expand) ).
thf(1699,plain,
! [A: $i,B: $i] :
( ( power_power @ real @ ( plus_plus @ real @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ real @ ( plus_plus @ real @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power @ int @ ( power_power @ int @ A @ B ) @ C )
= ( power_power @ int @ A @ ( times_times @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_zpower__zpower) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power @ int @ ( power_power @ int @ A @ B ) @ C )
= ( power_power @ int @ A @ ( times_times @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(312,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(1594,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(491,axiom,
! [A: $i] :
( ( minus_minus @ int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus @ int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_diff__bin__simps_I6_J) ).
thf(2212,plain,
! [A: $i] :
( ( minus_minus @ int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus @ int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(480,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( plus_plus @ int @ ( bit1 @ pls ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__special_I2_J) ).
thf(2171,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( plus_plus @ int @ ( bit1 @ pls ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(204,axiom,
! [A: $i] :
( ( number_number_of @ int @ A )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
thf(1213,plain,
! [A: $i] :
( ( number_number_of @ int @ A )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( no_zero_divisors @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_res) ).
thf(768,plain,
! [A: $i,B: $i,C: $i] :
( ( no_zero_divisors @ C )
=> ( ( ti @ C @ ( times_times @ C @ A @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(85,axiom,
order @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
thf(827,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ord_less_eq @ C @ ( ti @ C @ A ) @ B )
<=> ( ord_less_eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_arg1) ).
thf(780,plain,
! [A: $i,B: $i,C: $i] :
( ( order @ C )
=> ( ( ( ord_less_eq @ C @ ( ti @ C @ A ) @ B )
=> ( ord_less_eq @ C @ A @ B ) )
& ( ( ord_less_eq @ C @ A @ B )
=> ( ord_less_eq @ C @ ( ti @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ti @ int @ ( legendre @ A @ B ) )
= ( legendre @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_res) ).
thf(1643,plain,
! [A: $i,B: $i] :
( ( ti @ int @ ( legendre @ A @ B ) )
= ( legendre @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(436,axiom,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( one_one @ A )
!= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_one__neq__zero) ).
thf(2005,plain,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( one_one @ A )
!= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ D )
=> ( ( ord_less @ nat @ D @ C )
=> ~ ( dvd_dvd @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_divides__div__not) ).
thf(1626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ D )
=> ( ( ord_less @ nat @ D @ C )
=> ~ ( dvd_dvd @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(615,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( zero_zero @ A ) @ B )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2614,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( zero_zero @ A ) @ B )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(227,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1304,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(7,axiom,
linordered_semidom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(663,plain,
linordered_semidom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(448,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ A @ ( times_times @ A @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_power3__eq__cube) ).
thf(2037,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ A @ ( times_times @ A @ B @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(179,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ B )
= ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(1134,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ B )
= ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(76,axiom,
! [A: $i,B: $i] : ( zcong @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_zcong__refl) ).
thf(812,plain,
! [A: $i,B: $i] : ( zcong @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( zcong @ A @ B @ ( zero_zero @ int ) )
<=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_IntPrimes_Ozcong__zero) ).
thf(1990,plain,
! [A: $i,B: $i] :
( ( ( zcong @ A @ B @ ( zero_zero @ int ) )
=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) )
& ( ( ( ti @ int @ A )
= ( ti @ int @ B ) )
=> ( zcong @ A @ B @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(598,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( dvd_dvd @ A @ ( zero_zero @ A ) @ B )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_dvd__0__left) ).
thf(2564,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( dvd_dvd @ A @ ( zero_zero @ A ) @ B )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(609,axiom,
( ( minus_minus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) )
= ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(2597,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)],[609]) ).
thf(48,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ ( times_times @ A @ B @ C ) @ D )
=> ( dvd_dvd @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_dvd__mult__right) ).
thf(754,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ ( times_times @ A @ B @ C ) @ D )
=> ( dvd_dvd @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ( ( ti @ int @ C )
= ( plus_plus @ int @ A @ ( times_times @ int @ C @ B ) ) )
=> ( ( ord_less @ int @ A @ C )
=> ( ord_less_eq @ int @ ( one_one @ int ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_self__quotient__aux1) ).
thf(968,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ( ( ti @ int @ 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)],[125]) ).
thf(297,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( power_power @ A @ B @ C )
= ( power_power @ A @ D @ C ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ D )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ti @ A @ B )
= ( ti @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_power__eq__imp__eq__base) ).
thf(1551,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( power_power @ A @ B @ C )
= ( power_power @ A @ D @ C ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ D )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ti @ A @ B )
= ( ti @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(361,axiom,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ ( times_times @ A @ D @ C ) ) )
<=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( ( ti @ A @ C )
= ( ti @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_crossproduct__eq) ).
thf(1758,plain,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ ( times_times @ A @ D @ C ) ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( ( ti @ A @ C )
= ( ti @ A @ E ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( ( ti @ A @ C )
= ( ti @ A @ E ) ) )
=> ( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ ( times_times @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(190,axiom,
! [A: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ A @ A ) )
<=> ( A
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_not__real__square__gt__zero) ).
thf(1166,plain,
! [A: $i] :
( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ A @ A ) )
=> ( A
= ( zero_zero @ real ) ) )
& ( ( A
= ( zero_zero @ real ) )
=> ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus @ int @ C @ A ) @ ( plus_plus @ int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_zcong__zadd) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus @ int @ C @ A ) @ ( plus_plus @ int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times @ int @ B @ A ) @ ( times_times @ int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_zcong__scalar) ).
thf(1203,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times @ int @ B @ A ) @ ( times_times @ int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__eq__int__code_I16_J) ).
thf(1208,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(119,axiom,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ti @ A @ D )
!= ( ti @ A @ E ) )
& ( ( ti @ A @ B )
!= ( ti @ A @ C ) ) )
<=> ( ( plus_plus @ A @ ( times_times @ A @ D @ B ) @ ( times_times @ A @ E @ C ) )
!= ( plus_plus @ A @ ( times_times @ A @ D @ C ) @ ( times_times @ A @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_crossproduct__noteq) ).
thf(944,plain,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( ti @ A @ D )
!= ( ti @ A @ E ) )
& ( ( ti @ A @ B )
!= ( ti @ A @ C ) ) )
=> ( ( plus_plus @ A @ ( times_times @ A @ D @ B ) @ ( times_times @ A @ E @ C ) )
!= ( plus_plus @ A @ ( times_times @ A @ D @ C ) @ ( times_times @ A @ E @ B ) ) ) )
& ( ( ( plus_plus @ A @ ( times_times @ A @ D @ B ) @ ( times_times @ A @ E @ C ) )
!= ( plus_plus @ A @ ( times_times @ A @ D @ C ) @ ( times_times @ A @ E @ B ) ) )
=> ( ( ( ti @ A @ D )
!= ( ti @ A @ E ) )
& ( ( ti @ A @ B )
!= ( ti @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(629,axiom,
! [A: $i] :
( ( ring @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( minus_minus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ ( minus_minus @ A @ C @ E ) ) @ ( times_times @ A @ ( minus_minus @ A @ B @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_mult__diff__mult) ).
thf(2665,plain,
! [A: $i] :
( ( ring @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( minus_minus @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( plus_plus @ A @ ( times_times @ A @ B @ ( minus_minus @ A @ C @ E ) ) @ ( times_times @ A @ ( minus_minus @ A @ B @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ A @ B @ C )
<=> ( zcong @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_zcong__sym) ).
thf(795,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ A @ B @ C )
=> ( zcong @ B @ A @ C ) )
& ( ( zcong @ B @ A @ C )
=> ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(525,axiom,
! [A: $i,B: $i] :
( ( ( power_power @ nat @ A @ B )
= ( one_one @ nat ) )
<=> ( ( A
= ( one_one @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_exp__eq__1) ).
thf(2318,plain,
! [A: $i,B: $i] :
( ( ( ( power_power @ nat @ A @ B )
= ( one_one @ nat ) )
=> ( ( A
= ( one_one @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) )
& ( ( ( A
= ( one_one @ nat ) )
| ( B
= ( zero_zero @ nat ) ) )
=> ( ( power_power @ nat @ A @ B )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_add__Bit0__Bit1) ).
thf(2271,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( dvd_dvd @ C @ ( ti @ C @ A ) @ B )
<=> ( dvd_dvd @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Rings_Odvd__class_Odvd_arg1) ).
thf(680,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd @ C )
=> ( ( ( dvd_dvd @ C @ ( ti @ C @ A ) @ B )
=> ( dvd_dvd @ C @ A @ B ) )
& ( ( dvd_dvd @ C @ A @ B )
=> ( dvd_dvd @ C @ ( ti @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(161,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(1081,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(46,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ ( times_times @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(749,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ D )
= ( times_times @ A @ ( times_times @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(620,axiom,
! [A: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ A )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zadd__0) ).
thf(2629,plain,
! [A: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ A )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(30,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(712,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(645,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(2715,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(19,axiom,
zero_neq_one @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(690,plain,
zero_neq_one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(100,axiom,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ord_less_eq @ A @ ( times_times @ A @ C @ B ) @ ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_mult__nonpos__nonneg) ).
thf(872,plain,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ord_less_eq @ A @ ( times_times @ A @ C @ B ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(27,axiom,
ab_group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__group__add) ).
thf(707,plain,
ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(126,axiom,
! [A: $i] :
( ( mult_zero @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_2_res) ).
thf(971,plain,
! [A: $i] :
( ( mult_zero @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(607,axiom,
! [A: $i] :
( ( ring_11004092258visors @ A )
=> ! [B: $i] :
( ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) )
<=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_zero__eq__power2) ).
thf(2588,plain,
! [A: $i] :
( ( ring_11004092258visors @ A )
=> ! [B: $i] :
( ( ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) )
& ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
=> ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_rel__simps_I50_J) ).
thf(1780,plain,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_zadd__power3) ).
thf(1098,plain,
! [A: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(599,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( minus_minus @ int @ B @ C ) )
= ( minus_minus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_number__of__diff) ).
thf(2567,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( minus_minus @ int @ B @ C ) )
= ( minus_minus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ C @ A )
= ( times_times @ real @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_real__mult__left__cancel) ).
thf(1845,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( zero_zero @ real ) )
=> ( ( ( ( times_times @ real @ C @ A )
= ( times_times @ real @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( times_times @ real @ C @ A )
= ( times_times @ real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(546,axiom,
! [A: $i] :
( ( ( number @ A )
& ( ring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( minus_minus @ A @ C @ D ) )
= ( minus_minus @ A @ ( times_times @ A @ ( number_number_of @ A @ B ) @ C ) @ ( times_times @ A @ ( number_number_of @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_right__diff__distrib__number__of) ).
thf(2397,plain,
! [A: $i] :
( ( ( number @ A )
& ( ring @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( number_number_of @ A @ B ) @ ( minus_minus @ A @ C @ D ) )
= ( minus_minus @ A @ ( times_times @ A @ ( number_number_of @ A @ B ) @ C ) @ ( times_times @ A @ ( number_number_of @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(143,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ pls ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__numeral__0) ).
thf(1025,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ pls ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(25,axiom,
linord626643107strict @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring__1__strict) ).
thf(705,plain,
linord626643107strict @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(320,axiom,
( ( ti @ int @ m )
= m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_m_res) ).
thf(1611,plain,
( ( ti @ int @ m )
= m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(186,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
<=> ( ord_less @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_less__number__of) ).
thf(1156,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
=> ( ord_less @ int @ B @ C ) )
& ( ( ord_less @ int @ B @ C )
=> ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_zdiff__power2) ).
thf(1566,plain,
! [A: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zle__add1__eq__le) ).
thf(2143,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( minus_minus @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_diff__bin__simps_I10_J) ).
thf(2012,plain,
! [A: $i,B: $i] :
( ( minus_minus @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( power_power @ C @ A @ ( ti @ nat @ B ) )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg2) ).
thf(954,plain,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( power_power @ C @ A @ ( ti @ nat @ B ) )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(212,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( one_one @ A ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1252,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( one_one @ A ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(360,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_bin__less__0__simps_I3_J) ).
thf(1753,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(216,axiom,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ A @ F )
!= ( zero_zero @ A ) )
=> ( ( ( ( ti @ A @ D )
= ( ti @ A @ E ) )
& ( ( ti @ A @ B )
!= ( ti @ A @ C ) ) )
=> ( ( plus_plus @ A @ D @ ( times_times @ A @ F @ B ) )
!= ( plus_plus @ A @ E @ ( times_times @ A @ F @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_add__scale__eq__noteq) ).
thf(1267,plain,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ A @ F )
!= ( zero_zero @ A ) )
=> ( ( ( ( ti @ A @ D )
= ( ti @ A @ E ) )
& ( ( ti @ A @ B )
!= ( ti @ A @ C ) ) )
=> ( ( plus_plus @ A @ D @ ( times_times @ A @ F @ B ) )
!= ( plus_plus @ A @ E @ ( times_times @ A @ F @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ( ( zcong @ B @ ( zero_zero @ int ) @ A )
=> ( ( ti @ int @ B )
= ( zero_zero @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_zcong__zless__0) ).
thf(1987,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ( ( zcong @ B @ ( zero_zero @ int ) @ A )
=> ( ( ti @ int @ B )
= ( zero_zero @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(66,axiom,
! [A: $i] :
( ( comm_ring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( ( dvd_dvd @ A @ C @ B )
=> ( dvd_dvd @ A @ C @ ( minus_minus @ A @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_dvd__diff) ).
thf(791,plain,
! [A: $i] :
( ( comm_ring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( ( dvd_dvd @ A @ C @ B )
=> ( dvd_dvd @ A @ C @ ( minus_minus @ A @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( times_times @ real @ A @ B )
= ( times_times @ real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_real__mult__commute) ).
thf(717,plain,
! [A: $i,B: $i] :
( ( times_times @ real @ A @ B )
= ( times_times @ real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus @ real @ ( times_times @ real @ A @ A ) @ ( times_times @ real @ B @ B ) )
= ( zero_zero @ real ) )
<=> ( ( A
= ( zero_zero @ real ) )
& ( B
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_real__two__squares__add__zero__iff) ).
thf(840,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus @ real @ ( times_times @ real @ A @ A ) @ ( times_times @ real @ B @ B ) )
= ( zero_zero @ real ) )
=> ( ( A
= ( zero_zero @ real ) )
& ( B
= ( zero_zero @ real ) ) ) )
& ( ( ( A
= ( zero_zero @ real ) )
& ( B
= ( zero_zero @ real ) ) )
=> ( ( plus_plus @ real @ ( times_times @ real @ A @ A ) @ ( times_times @ real @ B @ B ) )
= ( zero_zero @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(555,axiom,
! [A: $i] :
( ( power @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ B @ C )
= ( one_one @ A ) ) )
& ( ( C
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ B @ C )
= ( times_times @ A @ B @ ( power_power @ A @ B @ ( minus_minus @ nat @ C @ ( one_one @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_realpow__num__eq__if) ).
thf(2429,plain,
! [A: $i] :
( ( power @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ B @ C )
= ( one_one @ A ) ) )
& ( ( C
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ B @ C )
= ( times_times @ A @ B @ ( power_power @ A @ B @ ( minus_minus @ nat @ C @ ( one_one @ nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__eq__int__code_I13_J) ).
thf(1262,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(378,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(1830,plain,
no_zero_divisors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(403,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_int__0__less__1) ).
thf(1901,plain,
ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(307,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_one__add__one__is__two) ).
thf(1579,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ~ ( zcong @ B @ ( zero_zero @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_zcong__not__zero) ).
thf(1813,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ~ ( zcong @ B @ ( zero_zero @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(225,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(1300,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(512,axiom,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_mult__nonneg__nonneg) ).
thf(2276,plain,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(473,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( ( ti @ A @ B )
!= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__power2) ).
thf(2128,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ti @ A @ B )
!= ( zero_zero @ A ) ) )
& ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 )
=> ( ( ti @ int @ C )
= ( ti @ int @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_zcong__less__eq) ).
thf(1538,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 )
=> ( ( ti @ int @ C )
= ( ti @ int @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(73,axiom,
! [A: $i] : ( ord_less_eq @ real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_real__le__refl) ).
thf(808,plain,
! [A: $i] : ( ord_less_eq @ real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ real @ A @ B )
<=> ( ord_less_eq @ real @ ( minus_minus @ real @ A @ B ) @ ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_real__le__eq__diff) ).
thf(2545,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ real @ A @ B )
=> ( ord_less_eq @ real @ ( minus_minus @ real @ A @ B ) @ ( zero_zero @ real ) ) )
& ( ( ord_less_eq @ real @ ( minus_minus @ real @ A @ B ) @ ( zero_zero @ real ) )
=> ( ord_less_eq @ real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(610,axiom,
comm_ring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring__1) ).
thf(2599,plain,
comm_ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(414,axiom,
( ( ti @ int @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(1934,plain,
( ( ti @ int @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(402,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_mult__2__right) ).
thf(1898,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_zcong__trans) ).
thf(703,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(428,axiom,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_3_res) ).
thf(1981,plain,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( legendre @ ( ti @ int @ A ) @ B )
= ( legendre @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_arg1) ).
thf(1702,plain,
! [A: $i,B: $i] :
( ( legendre @ ( ti @ int @ A ) @ B )
= ( legendre @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(590,axiom,
! [A: $i] :
( ( ordered_ring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
=> ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_mult__nonpos__nonpos) ).
thf(2543,plain,
! [A: $i] :
( ( ordered_ring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
=> ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ A @ B ) @ C )
= ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zadd__assoc) ).
thf(1221,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ A @ B ) @ C )
= ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( plus_plus @ real @ A @ B ) @ ( plus_plus @ real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_real__add__left__mono) ).
thf(1749,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( plus_plus @ real @ A @ B ) @ ( plus_plus @ real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(37,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] : ( dvd_dvd @ A @ B @ ( times_times @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_dvd__triv__left) ).
thf(727,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] : ( dvd_dvd @ A @ B @ ( times_times @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_add__Bit0__Bit0) ).
thf(1585,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ A @ B )
| ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zle__linear) ).
thf(2722,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ A @ B )
| ( ord_less_eq @ int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ C @ B ) )
=> ( ( B
!= ( zero_zero @ nat ) )
=> ( dvd_dvd @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_divides__rev) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ C @ B ) )
=> ( ( B
!= ( zero_zero @ nat ) )
=> ( dvd_dvd @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(508,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_zero__le__even__power_H) ).
thf(2266,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(605,axiom,
! [A: $i] :
( ( plus_plus @ int @ A @ pls )
= ( ti @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add__Pls__right) ).
thf(2584,plain,
! [A: $i] :
( ( plus_plus @ int @ A @ pls )
= ( ti @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(131,axiom,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_rel__simps_I39_J) ).
thf(991,plain,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I31_J) ).
thf(2056,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(254,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) )
= ( power_power @ A @ ( power_power @ A @ B @ C ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_power__even__eq) ).
thf(1404,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i] :
( ( power_power @ A @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ C ) )
= ( power_power @ A @ ( power_power @ A @ B @ C ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(370,axiom,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) )
= ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_sum__squares__eq__zero__iff) ).
thf(1802,plain,
! [A: $i] :
( ( linord581940658strict @ A )
=> ! [B: $i,C: $i] :
( ( ( ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) )
=> ( ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ A @ ( one_one @ int ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zless__imp__add1__zle) ).
thf(1023,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ A @ ( one_one @ int ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(281,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
= ( plus_plus @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_mult__2) ).
thf(1485,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
= ( plus_plus @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(152,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_rel__simps_I10_J) ).
thf(1052,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(644,axiom,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ s )
& ( ord_less @ int @ s @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ s @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_s0p) ).
thf(2711,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)],[644]) ).
thf(259,axiom,
ord_less_eq @ int @ min @ min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_rel__simps_I24_J) ).
thf(1421,plain,
ord_less_eq @ int @ min @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(639,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( number_number_of @ A @ ( bit1 @ pls ) ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mult__numeral__1) ).
thf(2696,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ ( number_number_of @ A @ ( bit1 @ pls ) ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(407,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Bit1__Min) ).
thf(1913,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(487,axiom,
! [A: $i] :
( ( min
= ( bit1 @ A ) )
<=> ( min
= ( ti @ int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_rel__simps_I43_J) ).
thf(2194,plain,
! [A: $i] :
( ( ( min
= ( bit1 @ A ) )
=> ( min
= ( ti @ int @ A ) ) )
& ( ( min
= ( ti @ int @ A ) )
=> ( min
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(256,axiom,
! [A: $i] :
( ( power @ A )
=> ( ( ti @ A @ ( one_one @ A ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_1_res) ).
thf(1412,plain,
! [A: $i] :
( ( power @ A )
=> ( ( ti @ A @ ( one_one @ A ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(492,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) )
<=> ( ord_less @ int @ pls @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_less__special_I1_J) ).
thf(2215,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) )
=> ( ord_less @ int @ pls @ B ) )
& ( ( ord_less @ int @ pls @ B )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(196,axiom,
! [A: $i] : ( zcong @ A @ ( zero_zero @ int ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_zcong__id) ).
thf(1189,plain,
! [A: $i] : ( zcong @ A @ ( zero_zero @ int ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(496,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ ( number_number_of @ A @ pls ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add__numeral__0__right) ).
thf(2226,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ ( number_number_of @ A @ pls ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(456,axiom,
! [A: $i] :
( ( ring_11004092258visors @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ C )
!= ( zero_zero @ A ) )
=> ( ( power_power @ A @ C @ B )
!= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_field__power__not__zero) ).
thf(2071,plain,
! [A: $i] :
( ( ring_11004092258visors @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ C )
!= ( zero_zero @ A ) )
=> ( ( power_power @ A @ C @ B )
!= ( zero_zero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(619,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/sandbox2/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
thf(2626,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)],[619]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( times_times @ int @ A @ B )
= ( times_times @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
thf(1918,plain,
! [A: $i,B: $i] :
( ( times_times @ int @ A @ B )
= ( times_times @ int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(271,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1459,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ord_less @ real @ A @ B )
=> ( ord_less @ real @ ( times_times @ real @ C @ A ) @ ( times_times @ real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_real__mult__less__mono2) ).
thf(2045,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ord_less @ real @ A @ B )
=> ( ord_less @ real @ ( times_times @ real @ C @ A ) @ ( times_times @ real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(115,axiom,
! [A: $i] :
( ( zprime @ ( ti @ int @ A ) )
<=> ( zprime @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozprime_arg1) ).
thf(931,plain,
! [A: $i] :
( ( ( zprime @ ( ti @ int @ A ) )
=> ( zprime @ A ) )
& ( ( zprime @ A )
=> ( zprime @ ( ti @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(336,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(1685,plain,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(523,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( one_one @ nat ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_power__one__right) ).
thf(2310,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( one_one @ nat ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(17,axiom,
number @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(688,plain,
number @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(111,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less_eq @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_le__special_I2_J) ).
thf(903,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less_eq @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ B ) )
& ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ B )
=> ( ord_less_eq @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( ti @ nat @ ( minus_minus @ nat @ A @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_res) ).
thf(2611,plain,
! [A: $i,B: $i] :
( ( ti @ nat @ ( minus_minus @ nat @ A @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(50,axiom,
number_semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(759,plain,
number_semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(205,axiom,
! [A: $i] :
( ( ( number @ A )
& ( linorder @ A ) )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
<=> ~ ( ord_less @ A @ ( number_number_of @ A @ C ) @ ( number_number_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(1216,plain,
! [A: $i] :
( ( ( number @ A )
& ( linorder @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
=> ~ ( ord_less @ A @ ( number_number_of @ A @ C ) @ ( number_number_of @ A @ B ) ) )
& ( ~ ( ord_less @ A @ ( number_number_of @ A @ C ) @ ( number_number_of @ A @ B ) )
=> ( ord_less_eq @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(108,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less_eq @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_power2__le__imp__le) ).
thf(891,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less_eq @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(490,axiom,
( ( zero_zero @ int )
!= ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_int__0__neq__1) ).
thf(2209,plain,
( ( zero_zero @ int )
!= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(250,axiom,
! [A: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rel__simps_I4_J) ).
thf(1390,plain,
! [A: $i] :
( ( ( ord_less @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(521,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_semiring__mult__2__right) ).
thf(2305,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
<=> ( ord_less @ int @ ( minus_minus @ int @ A @ B ) @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_less__bin__lemma) ).
thf(1734,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( minus_minus @ int @ A @ B ) @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ ( minus_minus @ int @ A @ B ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(55,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] : ( dvd_dvd @ A @ B @ ( times_times @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_dvd__triv__right) ).
thf(771,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] : ( dvd_dvd @ A @ B @ ( times_times @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(219,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ A @ ( power_power @ A @ C @ D ) @ E )
=> ( ( ord_less_eq @ nat @ B @ D )
=> ( dvd_dvd @ A @ ( power_power @ A @ C @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_power__le__dvd) ).
thf(1276,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ A @ ( power_power @ A @ C @ D ) @ E )
=> ( ( ord_less_eq @ nat @ B @ D )
=> ( dvd_dvd @ A @ ( power_power @ A @ C @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(329,axiom,
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
thf(1646,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)],[329]) ).
thf(232,axiom,
zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_s) ).
thf(1326,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)],[232]) ).
thf(641,axiom,
semiring_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(2707,plain,
semiring_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(248,axiom,
! [A: $i] :
( ( comm_semiring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ ( times_times @ A @ B @ D ) @ ( times_times @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_comm__semiring__class_Odistrib) ).
thf(1385,plain,
! [A: $i] :
( ( comm_semiring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( times_times @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ ( times_times @ A @ B @ D ) @ ( times_times @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(123,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] : ( dvd_dvd @ A @ ( one_one @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_one__dvd) ).
thf(963,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] : ( dvd_dvd @ A @ ( one_one @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_less__int__code_I15_J) ).
thf(1101,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
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/sandbox2/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(652,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(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_zmult__zless__mono2) ).
thf(2026,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( times_times @ int @ A @ B ) @ ( times_times @ int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less_eq @ int @ B @ A )
=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zle__antisym) ).
thf(1822,plain,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less_eq @ int @ B @ A )
=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(544,axiom,
ring_n68954251visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(2394,plain,
ring_n68954251visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(481,axiom,
! [A: $i] :
( ( times_times @ int @ A @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_cube__square) ).
thf(2174,plain,
! [A: $i] :
( ( times_times @ int @ A @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(278,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ B @ C )
=> ( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( ord_less @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_order__le__neq__implies__less) ).
thf(1476,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ B @ C )
=> ( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( ord_less @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_rel__simps_I14_J) ).
thf(2290,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(503,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(2251,plain,
semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(405,axiom,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i] :
( ( ( ti @ A @ B )
= ( plus_plus @ A @ B @ C ) )
<=> ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__0__iff) ).
thf(1903,plain,
! [A: $i] :
( ( semiri456707255roduct @ A )
=> ! [B: $i,C: $i] :
( ( ( ( ti @ A @ B )
= ( plus_plus @ A @ B @ C ) )
=> ( ( ti @ A @ C )
= ( zero_zero @ A ) ) )
& ( ( ( ti @ A @ C )
= ( zero_zero @ A ) )
=> ( ( ti @ A @ B )
= ( plus_plus @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) ) )
& ( ( B
!= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ B @ A )
= ( plus_plus @ nat @ A @ ( times_times @ nat @ ( minus_minus @ nat @ B @ ( one_one @ nat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_mult__eq__if) ).
thf(2135,plain,
! [A: $i,B: $i] :
( ( ( B
= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) ) )
& ( ( B
!= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ B @ A )
= ( plus_plus @ nat @ A @ ( times_times @ nat @ ( minus_minus @ nat @ B @ ( one_one @ nat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(155,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( one_one @ nat ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1062,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( power_power @ A @ B @ ( one_one @ nat ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(585,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_rel__simps_I2_J) ).
thf(2532,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(287,axiom,
! [A: $i] :
( ( twoSqu420862341sum2sq @ ( ti @ int @ A ) )
<=> ( twoSqu420862341sum2sq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__iprzenvtji_Ois__sum2sq_arg1) ).
thf(1508,plain,
! [A: $i] :
( ( ( twoSqu420862341sum2sq @ ( ti @ int @ A ) )
=> ( twoSqu420862341sum2sq @ A ) )
& ( ( twoSqu420862341sum2sq @ A )
=> ( twoSqu420862341sum2sq @ ( ti @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(582,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ nat @ C @ D )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less_eq @ A @ B @ ( one_one @ A ) )
=> ( ord_less_eq @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_power__decreasing) ).
thf(2526,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ord_less_eq @ nat @ C @ D )
=> ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
=> ( ( ord_less_eq @ A @ B @ ( one_one @ A ) )
=> ( ord_less_eq @ A @ ( power_power @ A @ B @ D ) @ ( power_power @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(552,axiom,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ B )
= ( one_one @ A ) ) )
& ( ( B
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ B )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_power__0__left) ).
thf(2416,plain,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ B )
= ( one_one @ A ) ) )
& ( ( B
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ B )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(132,axiom,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_0_res) ).
thf(995,plain,
! [A: $i] :
( ( zero_neq_one @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(506,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Pls__def) ).
thf(2262,plain,
( pls
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(557,axiom,
! [A: $i] :
( ( minus_minus @ int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_diff__bin__simps_I3_J) ).
thf(2447,plain,
! [A: $i] :
( ( minus_minus @ int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus @ int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(390,axiom,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i] :
( ( times_times @ A @ ( power_power @ A @ B @ C ) @ B )
= ( times_times @ A @ B @ ( power_power @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_power__commutes) ).
thf(1861,plain,
! [A: $i] :
( ( monoid_mult @ A )
=> ! [B: $i,C: $i] :
( ( times_times @ A @ ( power_power @ A @ B @ C ) @ B )
= ( times_times @ A @ B @ ( power_power @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(459,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_add__number__of__eq) ).
thf(2081,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(566,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ ( plus_plus @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2475,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ D )
= ( plus_plus @ A @ ( plus_plus @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ A @ ( one_one @ int ) ) @ B )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add1__zle__eq) ).
thf(2648,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ A @ ( one_one @ int ) ) @ B )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ A @ ( one_one @ int ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(9,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( ( dvd_dvd @ A @ D @ B )
=> ( dvd_dvd @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_dvd__trans) ).
thf(667,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( ( dvd_dvd @ A @ D @ B )
=> ( dvd_dvd @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(527,axiom,
! [A: $i,B: $i] :
( ( quadRes @ A @ ( ti @ int @ B ) )
<=> ( quadRes @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Residues_OQuadRes_arg2) ).
thf(2330,plain,
! [A: $i,B: $i] :
( ( ( quadRes @ A @ ( ti @ int @ B ) )
=> ( quadRes @ A @ B ) )
& ( ( quadRes @ A @ B )
=> ( quadRes @ A @ ( ti @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(198,axiom,
comm_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
thf(1193,plain,
comm_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(52,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] : ( dvd_dvd @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_dvd__refl) ).
thf(763,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] : ( dvd_dvd @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(288,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I29_J) ).
thf(1513,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(471,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ B )
= ( times_times @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2120,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ B )
= ( times_times @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( dvd_dvd @ int @ A @ B )
=> ( dvd_dvd @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_zpower__zdvd__prop1) ).
thf(832,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( dvd_dvd @ int @ A @ B )
=> ( dvd_dvd @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(618,axiom,
! [A: $i] :
( ( ab_group_add @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ ( plus_plus @ A @ D @ E ) )
= ( plus_plus @ A @ ( minus_minus @ A @ B @ D ) @ ( minus_minus @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_add__diff__add) ).
thf(2623,plain,
! [A: $i] :
( ( ab_group_add @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ ( plus_plus @ A @ D @ E ) )
= ( plus_plus @ A @ ( minus_minus @ A @ B @ D ) @ ( minus_minus @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(442,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ int @ pls @ C )
=> ( ( ord_less_eq @ int @ pls @ B )
=> ( ( plus_plus @ A @ ( number_number_of @ A @ C ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( plus_plus @ int @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring__add__number__of) ).
thf(2019,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ int @ pls @ C )
=> ( ( ord_less_eq @ int @ pls @ B )
=> ( ( plus_plus @ A @ ( number_number_of @ A @ C ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( plus_plus @ int @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(146,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( one_one @ A )
= ( number_number_of @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_semiring__norm_I110_J) ).
thf(1030,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( one_one @ A )
= ( number_number_of @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ord_less_eq @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) )
<=> ( ord_less_eq @ real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_real__mult__le__cancel__iff1) ).
thf(1491,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
=> ( ( ( ord_less_eq @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) )
=> ( ord_less_eq @ real @ A @ B ) )
& ( ( ord_less_eq @ real @ A @ B )
=> ( ord_less_eq @ real @ ( times_times @ real @ A @ C ) @ ( times_times @ real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(573,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] : ( dvd_dvd @ A @ B @ ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_dvd__0__right) ).
thf(2494,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] : ( dvd_dvd @ A @ B @ ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(265,axiom,
comm_monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(1442,plain,
comm_monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(187,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( dvd_dvd @ A @ ( power_power @ A @ C @ B ) @ ( power_power @ A @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_dvd__power__same) ).
thf(1161,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( dvd_dvd @ A @ C @ D )
=> ( dvd_dvd @ A @ ( power_power @ A @ C @ B ) @ ( power_power @ A @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_arg2) ).
thf(800,plain,
! [A: $i,B: $i,C: $i] :
( ( power @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ ( ti @ int @ A ) @ B @ C )
<=> ( zcong @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg1) ).
thf(2123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ ( ti @ int @ A ) @ B @ C )
=> ( zcong @ A @ B @ C ) )
& ( ( zcong @ A @ B @ C )
=> ( zcong @ ( ti @ int @ A ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(538,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ B @ ( times_times @ A @ C @ B ) )
= ( times_times @ A @ ( plus_plus @ A @ C @ ( one_one @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2374,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ B @ ( times_times @ A @ C @ B ) )
= ( times_times @ A @ ( plus_plus @ A @ C @ ( one_one @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(47,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ A @ D @ E )
=> ( ( dvd_dvd @ A @ B @ C )
=> ( dvd_dvd @ A @ ( times_times @ A @ D @ B ) @ ( times_times @ A @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_mult__dvd__mono) ).
thf(752,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( dvd_dvd @ A @ D @ E )
=> ( ( dvd_dvd @ A @ B @ C )
=> ( dvd_dvd @ A @ ( times_times @ A @ D @ B ) @ ( times_times @ A @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(351,axiom,
linordered_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
thf(1725,plain,
linordered_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(541,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ C )
= ( times_times @ A @ ( plus_plus @ A @ B @ ( one_one @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2385,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ ( times_times @ A @ B @ C ) @ C )
= ( times_times @ A @ ( plus_plus @ A @ B @ ( one_one @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(647,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ B @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2719,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ B @ ( plus_plus @ A @ C @ D ) )
= ( plus_plus @ A @ ( plus_plus @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(295,axiom,
! [A: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_odd__nonzero) ).
thf(1546,plain,
! [A: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( ti @ B @ ( number_number_of @ B @ A ) )
= ( number_number_of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
thf(1395,plain,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( ti @ B @ ( number_number_of @ B @ A ) )
= ( number_number_of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(79,axiom,
ring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1) ).
thf(818,plain,
ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ( times_times @ int @ B @ A )
= ( one_one @ int ) )
<=> ( ( ( ti @ int @ B )
= ( one_one @ int ) )
& ( ( ti @ int @ A )
= ( one_one @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_pos__zmult__eq__1__iff) ).
thf(2604,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ( ( times_times @ int @ B @ A )
= ( one_one @ int ) )
=> ( ( ( ti @ int @ B )
= ( one_one @ int ) )
& ( ( ti @ int @ A )
= ( one_one @ int ) ) ) )
& ( ( ( ( ti @ int @ B )
= ( one_one @ int ) )
& ( ( ti @ int @ A )
= ( one_one @ int ) ) )
=> ( ( times_times @ int @ B @ A )
= ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ A ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ B ) @ C )
=> ( ( power_power @ int @ ( number_number_of @ int @ min ) @ A )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_neg__one__power__eq__mod__m) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ A ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ B ) @ C )
=> ( ( power_power @ int @ ( number_number_of @ int @ min ) @ A )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(65,axiom,
linorder @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(790,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
<=> ( ( B
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_nat__mult__dvd__cancel__disj_H) ).
thf(2517,plain,
! [A: $i,B: $i,C: $i] :
( ( ( dvd_dvd @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
=> ( ( B
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ A @ C ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ A @ C ) )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(636,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Bit0__Pls) ).
thf(2683,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( ( times_times @ int @ A @ B )
= ( one_one @ int ) )
<=> ( ( ( ( ti @ int @ A )
= ( one_one @ int ) )
& ( ( ti @ int @ B )
= ( one_one @ int ) ) )
| ( ( ( ti @ int @ A )
= ( number_number_of @ int @ min ) )
& ( ( ti @ int @ B )
= ( number_number_of @ int @ min ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_zmult__eq__1__iff) ).
thf(2155,plain,
! [A: $i,B: $i] :
( ( ( ( times_times @ int @ A @ B )
= ( one_one @ int ) )
=> ( ( ( ( ti @ int @ A )
= ( one_one @ int ) )
& ( ( ti @ int @ B )
= ( one_one @ int ) ) )
| ( ( ( ti @ int @ A )
= ( number_number_of @ int @ min ) )
& ( ( ti @ int @ B )
= ( number_number_of @ int @ min ) ) ) ) )
& ( ( ( ( ( ti @ int @ A )
= ( one_one @ int ) )
& ( ( ti @ int @ B )
= ( one_one @ int ) ) )
| ( ( ( ti @ int @ A )
= ( number_number_of @ int @ min ) )
& ( ( ti @ int @ B )
= ( number_number_of @ int @ min ) ) ) )
=> ( ( times_times @ int @ A @ B )
= ( one_one @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ( ( ( ti @ int @ B )
!= ( minus_minus @ int @ A @ ( one_one @ int ) ) )
=> ( ord_less @ int @ B @ ( minus_minus @ int @ A @ ( one_one @ int ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_Euler_Oaux1) ).
thf(2534,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A )
=> ( ( ( ti @ int @ 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)],[586]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I32_J) ).
thf(835,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq @ int @ A @ B ) )
& ( ( ord_less_eq @ int @ A @ B )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(606,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(2587,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( times_times @ int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__Bit0) ).
thf(854,plain,
! [A: $i,B: $i] :
( ( times_times @ int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(437,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( number_number_of @ A @ ( bit1 @ pls ) ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_mult__numeral__1__right) ).
thf(2008,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( times_times @ A @ B @ ( number_number_of @ A @ ( bit1 @ pls ) ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(263,axiom,
! [A: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I21_J) ).
thf(1436,plain,
! [A: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(488,axiom,
! [A: $i] :
( ( ord_less @ int @ min @ ( bit0 @ A ) )
<=> ( ord_less @ int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_rel__simps_I8_J) ).
thf(2201,plain,
! [A: $i] :
( ( ( ord_less @ int @ min @ ( bit0 @ A ) )
=> ( ord_less @ int @ min @ A ) )
& ( ( ord_less @ int @ min @ A )
=> ( ord_less @ int @ min @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd @ int @ A @ B )
=> ( ( ord_less_eq @ int @ B @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_zdvd__bounds) ).
thf(1657,plain,
! [A: $i,B: $i] :
( ( dvd_dvd @ int @ A @ B )
=> ( ( ord_less_eq @ int @ B @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(341,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( plus_plus @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( plus_plus @ A @ ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add__number__of__left) ).
thf(1693,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( plus_plus @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( plus_plus @ A @ ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg2) ).
thf(664,plain,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power @ int @ A @ ( plus_plus @ nat @ B @ C ) )
= ( times_times @ int @ ( power_power @ int @ A @ B ) @ ( power_power @ int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zpower__zadd__distrib) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power @ int @ A @ ( plus_plus @ nat @ B @ C ) )
= ( times_times @ int @ ( power_power @ int @ A @ B ) @ ( power_power @ int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_rel__simps_I51_J) ).
thf(1891,plain,
! [A: $i,B: $i] :
( ( ( ( bit1 @ A )
= ( bit1 @ B ) )
=> ( ( ti @ int @ A )
= ( ti @ int @ B ) ) )
& ( ( ( ti @ int @ A )
= ( ti @ int @ B ) )
=> ( ( bit1 @ A )
= ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(86,axiom,
ring_n68954251visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) ).
thf(828,plain,
ring_n68954251visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( B
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_divides__ge) ).
thf(2223,plain,
! [A: $i,B: $i] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( B
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( zcong @ ( times_times @ int @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ B )
<=> ( zcong @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_inv__not__p__minus__1__aux) ).
thf(2040,plain,
! [A: $i,B: $i] :
( ( ( zcong @ ( times_times @ int @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ B )
=> ( zcong @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) @ B ) )
& ( ( zcong @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) @ B )
=> ( zcong @ ( times_times @ int @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(235,axiom,
dvd_dvd @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( minus_minus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(1346,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)],[235]) ).
thf(461,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ ( zero_zero @ A ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2091,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ ( zero_zero @ A ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(549,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ A @ B )
= ( one_one @ nat ) ) )
& ( ( B
!= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ A @ B )
= ( times_times @ nat @ A @ ( power_power @ nat @ A @ ( minus_minus @ nat @ B @ ( one_one @ nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_power__eq__if) ).
thf(2404,plain,
! [A: $i,B: $i] :
( ( ( B
= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ A @ B )
= ( one_one @ nat ) ) )
& ( ( B
!= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ A @ B )
= ( times_times @ nat @ A @ ( power_power @ nat @ A @ ( minus_minus @ nat @ B @ ( one_one @ nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( ( times_times @ int @ A @ B )
= ( one_one @ int ) )
=> ( ( ( ti @ int @ A )
= ( one_one @ int ) )
| ( ( ti @ int @ A )
= ( number_number_of @ int @ min ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_pos__zmult__eq__1__iff__lemma) ).
thf(2619,plain,
! [A: $i,B: $i] :
( ( ( times_times @ int @ A @ B )
= ( one_one @ int ) )
=> ( ( ( ti @ int @ A )
= ( one_one @ int ) )
| ( ( ti @ int @ A )
= ( number_number_of @ int @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(156,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
~ ( ord_less @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__less__0) ).
thf(1065,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
~ ( ord_less @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(34,axiom,
number_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(720,plain,
number_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 )
=> ( ( ti @ int @ C )
= ( ti @ int @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_zcong__zless__imp__eq) ).
thf(2668,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 )
=> ( ( ti @ int @ C )
= ( ti @ int @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(106,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( number_number_of @ A @ ( bit1 @ B ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) ) @ ( number_number_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_number__of__Bit1) ).
thf(886,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( number_number_of @ A @ ( bit1 @ B ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) ) @ ( number_number_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( zcong @ A @ B @ C )
<=> ? [D: $i] :
( ( ti @ int @ B )
= ( plus_plus @ int @ A @ ( times_times @ int @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_zcong__iff__lin) ).
thf(1742,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zcong @ A @ B @ C )
=> ? [D: $i] :
( ( ti @ int @ B )
= ( plus_plus @ int @ A @ ( times_times @ int @ C @ D ) ) ) )
& ( ? [D: $i] :
( ( ti @ int @ B )
= ( plus_plus @ int @ A @ ( times_times @ int @ C @ D ) ) )
=> ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ord_less_eq @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_power__dvd__imp__le) ).
thf(2353,plain,
! [A: $i,B: $i,C: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ord_less_eq @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times @ real @ ( times_times @ real @ A @ B ) @ C )
= ( times_times @ real @ A @ ( times_times @ real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_real__mult__assoc) ).
thf(740,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times @ real @ ( times_times @ real @ A @ B ) @ C )
= ( times_times @ real @ A @ ( times_times @ real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(209,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
<=> ( ord_less @ int @ B @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_less__special_I4_J) ).
thf(1236,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
=> ( ord_less @ int @ B @ ( bit1 @ pls ) ) )
& ( ( ord_less @ int @ B @ ( bit1 @ pls ) )
=> ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
= ( number_number_of @ int @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_plus__numeral__code_I9_J) ).
thf(1827,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
= ( number_number_of @ int @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( minus_minus @ int @ A @ B )
= ( ti @ int @ C ) )
=> ( ( ti @ int @ A )
= ( plus_plus @ int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_Int2_Oaux1) ).
thf(1378,plain,
! [A: $i,B: $i,C: $i] :
( ( ( minus_minus @ int @ A @ B )
= ( ti @ int @ C ) )
=> ( ( ti @ int @ A )
= ( plus_plus @ int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ A @ B )
| ( ( ti @ int @ A )
= ( ti @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_zless__add1__eq) ).
thf(908,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) )
=> ( ( ord_less @ int @ A @ B )
| ( ( ti @ int @ A )
= ( ti @ int @ B ) ) ) )
& ( ( ( ord_less @ int @ A @ B )
| ( ( ti @ int @ A )
= ( ti @ int @ B ) ) )
=> ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(577,axiom,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less_eq @ A @ ( times_times @ A @ C @ B ) @ ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_mult__nonneg__nonpos) ).
thf(2507,plain,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less_eq @ A @ ( times_times @ A @ C @ B ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_rel__simps_I17_J) ).
thf(1713,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(174,axiom,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less_eq @ A @ ( times_times @ A @ B @ C ) @ ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_mult__nonneg__nonpos2) ).
thf(1120,plain,
! [A: $i] :
( ( ordere453448008miring @ A )
=> ! [B: $i,C: $i] :
( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
=> ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less_eq @ A @ ( times_times @ A @ B @ C ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(611,axiom,
semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(2600,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(247,axiom,
ordere453448008miring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__cancel__semiring) ).
thf(1384,plain,
ordere453448008miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( minus_minus @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_diff__bin__simps_I9_J) ).
thf(2485,plain,
! [A: $i,B: $i] :
( ( minus_minus @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ ( minus_minus @ int @ A @ B ) @ C )
= ( minus_minus @ int @ ( times_times @ int @ A @ C ) @ ( times_times @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_zdiff__zmult__distrib) ).
thf(1582,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ ( minus_minus @ int @ A @ B ) @ C )
= ( minus_minus @ int @ ( times_times @ int @ A @ C ) @ ( times_times @ int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(140,axiom,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_zero__less__power) ).
thf(1019,plain,
! [A: $i] :
( ( linordered_semidom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ C )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C )
= ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) )
=> ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ C @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ F )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ D )
=> ( ( ord_less_eq @ int @ D @ A )
=> ( ord_less_eq @ int @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_zdiv__mono2__neg__lemma) ).
thf(1976,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ A @ B ) @ C )
= ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) )
=> ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ D @ E ) @ F ) @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ C @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ F )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ D )
=> ( ( ord_less_eq @ int @ D @ A )
=> ( ord_less_eq @ int @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(296,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(1550,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( zprime @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( zcong @ ( times_times @ int @ A @ A ) @ ( one_one @ int ) @ B )
=> ( ( zcong @ A @ ( one_one @ int ) @ B )
| ( zcong @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_zcong__square) ).
thf(1357,plain,
! [A: $i,B: $i] :
( ( zprime @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( zcong @ ( times_times @ int @ A @ A ) @ ( one_one @ int ) @ B )
=> ( ( zcong @ A @ ( one_one @ int ) @ B )
| ( zcong @ A @ ( minus_minus @ int @ B @ ( one_one @ int ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(604,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(2583,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(315,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_rel__simps_I37_J) ).
thf(1597,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( ord_less @ real @ A @ B )
<=> ( ( ord_less_eq @ real @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_real__less__def) ).
thf(2687,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ real @ A @ B )
=> ( ( ord_less_eq @ real @ A @ B )
& ( A != B ) ) )
& ( ( ( ord_less_eq @ real @ A @ B )
& ( A != B ) )
=> ( ord_less @ real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(404,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(1902,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( no_zero_divisors @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_arg2) ).
thf(691,plain,
! [A: $i,B: $i,C: $i] :
( ( no_zero_divisors @ C )
=> ( ( times_times @ C @ A @ ( ti @ C @ B ) )
= ( times_times @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(398,axiom,
! [A: $i] :
( ( no_zero_divisors @ A )
=> ! [B: $i,C: $i] :
( ( ( times_times @ A @ B @ C )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_divisors__zero) ).
thf(1885,plain,
! [A: $i] :
( ( no_zero_divisors @ A )
=> ! [B: $i,C: $i] :
( ( ( times_times @ A @ B @ C )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( ord_less @ nat @ ( number_number_of @ nat @ A ) @ ( number_number_of @ nat @ B ) )
<=> ( ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ pls @ B ) )
& ( ord_less @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__nat__number__of) ).
thf(2699,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ nat @ ( number_number_of @ nat @ A ) @ ( number_number_of @ nat @ B ) )
=> ( ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ pls @ B ) )
& ( ord_less @ int @ A @ B ) ) )
& ( ( ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ pls @ B ) )
& ( ord_less @ int @ A @ B ) )
=> ( ord_less @ nat @ ( number_number_of @ nat @ A ) @ ( number_number_of @ nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( minus_minus @ C @ A @ ( ti @ C @ B ) )
= ( minus_minus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_0_arg2) ).
thf(803,plain,
! [A: $i,B: $i,C: $i] :
( ( ab_group_add @ C )
=> ( ( minus_minus @ C @ A @ ( ti @ C @ B ) )
= ( minus_minus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(597,axiom,
linord626643107strict @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1__strict) ).
thf(2563,plain,
linord626643107strict @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ int @ B @ ( plus_plus @ int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__left__commute) ).
thf(1009,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ int @ B @ ( plus_plus @ int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(489,axiom,
( ~ ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(2206,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)],[489]) ).
thf(457,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_bin__less__0__simps_I4_J) ).
thf(2074,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(283,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/sandbox2/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(1490,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)],[283]) ).
thf(13,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( times_times @ A @ D @ ( times_times @ A @ ( times_times @ A @ B @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(676,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( times_times @ A @ D @ ( times_times @ A @ ( times_times @ A @ B @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(559,axiom,
( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(2453,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)],[559]) ).
thf(486,axiom,
! [A: $i] :
( ( linordered_ring @ A )
=> ! [B: $i,C: $i] :
~ ( ord_less @ A @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) @ ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_not__sum__squares__lt__zero) ).
thf(2191,plain,
! [A: $i] :
( ( linordered_ring @ A )
=> ! [B: $i,C: $i] :
~ ( ord_less @ A @ ( plus_plus @ A @ ( times_times @ A @ B @ B ) @ ( times_times @ A @ C @ C ) ) @ ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd @ int @ D @ C )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ ( times_times @ int @ C @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_zprime__power__zdvd__cancel__left) ).
thf(1468,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd @ int @ D @ C )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ ( times_times @ int @ C @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(28,axiom,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( times_times @ A @ ( times_times @ A @ B @ D ) @ ( times_times @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(708,plain,
! [A: $i] :
( ( comm_semiring_1 @ A )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( times_times @ A @ ( times_times @ A @ B @ C ) @ ( times_times @ A @ D @ E ) )
= ( times_times @ A @ ( times_times @ A @ B @ D ) @ ( times_times @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(393,axiom,
! [A: $i] :
( ( ( bit1 @ A )
= min )
<=> ( ( ti @ int @ A )
= min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_rel__simps_I47_J) ).
thf(1870,plain,
! [A: $i] :
( ( ( ( bit1 @ A )
= min )
=> ( ( ti @ int @ A )
= min ) )
& ( ( ( ti @ int @ A )
= min )
=> ( ( bit1 @ A )
= min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ ( plus_plus @ int @ A @ B ) @ C )
= ( plus_plus @ int @ ( times_times @ int @ A @ C ) @ ( times_times @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_zadd__zmult__distrib) ).
thf(1367,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times @ int @ ( plus_plus @ int @ A @ B ) @ C )
= ( plus_plus @ int @ ( times_times @ int @ A @ C ) @ ( times_times @ int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(118,axiom,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_rel__simps_I46_J) ).
thf(940,plain,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(882,plain,
! [A: $i,B: $i,C: $i] :
( ( semiring @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_less__int__code_I16_J) ).
thf(2177,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(2735,plain,
$false,
inference(e,[status(thm)],[1036,1501,2094,1633,1729,2412,2595,1179,777,1295,1956,1879,1337,1718,2295,760,2109,1454,893,1840,962,2427,2480,2280,1554,2512,683,1882,1068,2395,1443,1401,1073,2671,1205,1533,1692,1173,2363,1855,1596,2104,1422,1569,1939,2248,2099,1591,2114,1142,1041,861,1705,1078,1137,1310,2035,1260,2459,2580,1354,1164,1999,814,1327,2491,1576,1441,885,1613,1921,1359,1601,2400,1518,829,1095,1623,1482,724,2328,1792,1985,1660,2708,2501,1860,1323,2682,1313,2185,2488,1191,2466,2274,917,1462,1059,2571,2356,1087,1890,1347,1398,1931,2730,1362,1778,2388,817,902,1479,1609,1815,1494,2456,1465,756,1811,2259,1418,937,806,2335,821,2017,2237,1415,1109,2469,1682,834,1858,1864,1843,2281,877,866,660,1600,1696,2437,1928,2424,774,2002,998,2286,2639,1943,1201,1697,1242,849,1604,2011,1691,793,925,1153,810,2047,2496,2061,1470,1915,1708,2232,2296,2660,1768,714,2382,1057,1163,2264,957,746,2601,825,1255,2528,2015,1883,1021,778,1042,2541,1751,820,2150,1370,2414,729,1837,1968,1888,889,2345,1407,1281,1910,974,1012,1687,1457,1836,1787,2313,1128,2653,1106,1936,2515,2377,1375,1227,980,2509,1006,783,2268,989,857,697,1089,1541,874,1143,1270,1851,1017,1953,2685,2724,2537,2561,1182,1739,669,1075,2455,1937,1446,706,1028,1082,1964,1942,1659,2053,2240,2472,679,1039,1297,1451,1530,2243,2355,2581,2505,721,1799,1984,1002,1429,1825,1114,2450,1588,2153,1831,1131,654,2052,2482,1979,779,1241,765,1466,2221,2617,2662,2529,1732,2634,1434,1563,657,1286,2368,1187,674,2645,1616,773,794,2338,1278,1648,965,2677,2391,824,1273,2570,689,733,1959,2556,2028,1301,1595,819,975,2727,694,732,1784,1125,2188,1620,2674,1388,743,711,1795,2716,1488,1139,936,2220,1707,2308,787,1997,1090,2557,1224,2148,672,713,1865,1194,2119,2679,831,2478,2229,2084,1574,736,1144,2116,737,880,1122,1690,1571,1307,863,2079,2361,2538,1853,784,1117,1667,1630,700,1029,2252,1381,1112,811,2182,1877,1471,2025,2632,858,1557,2278,2553,2710,1820,1926,2350,2550,1176,2288,1000,2022,2101,1726,653,1973,1562,1699,2401,1594,2212,2171,1213,768,827,780,1643,2005,1626,2614,1304,663,2037,1134,812,1990,2564,2597,754,968,1551,1758,1166,2107,1203,1208,944,2665,795,2318,2271,680,1081,749,2629,712,2715,690,872,707,971,2588,1780,1098,2567,1845,2397,1025,705,1611,1156,1566,2143,2012,954,1252,1753,1267,1987,791,717,840,2429,1262,1830,1901,1579,1813,1300,2276,2128,1538,808,2545,2599,1934,1898,703,1981,1702,2543,1221,1749,727,1585,2722,1372,2266,2584,991,2056,1404,1802,1023,1485,1052,2711,1421,2696,1913,2194,1412,2215,1189,2226,2071,2626,1918,1459,2045,931,1685,2310,688,903,2611,759,1216,891,2209,1390,2305,1734,771,1276,1646,1326,2707,1385,963,1101,652,2026,1822,2394,2174,1476,2290,2251,1903,2135,1062,2532,1508,2526,2416,995,2262,2447,1861,2081,2475,2648,667,2330,1193,763,1513,2120,832,2623,2019,1030,1491,2494,1442,1161,800,2123,2374,752,1725,2385,2719,1546,1395,818,2604,1527,790,2517,2683,2155,2534,835,2587,854,2008,1436,2201,1657,1693,664,1033,1891,828,2223,2040,1346,2091,2404,2619,1065,720,2668,886,1742,2353,740,1236,1827,1378,908,2507,1713,1120,2600,1384,2485,1582,1019,1976,1550,1357,2583,1597,2687,1902,691,1885,2699,803,2563,1009,2206,2074,1490,676,2453,2191,1468,708,1870,1367,940,882,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 16:51:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.07 % [INFO] Parsing done (237ms).
% 1.86/1.08 % [INFO] Running in sequential loop mode.
% 2.28/1.28 % [INFO] eprover registered as external prover.
% 2.28/1.28 % [INFO] cvc4 registered as external prover.
% 2.28/1.29 % [INFO] Scanning for conjecture ...
% 2.83/1.40 % [INFO] Found a conjecture and 649 axioms. Running axiom selection ...
% 3.35/1.52 % [INFO] Axiom selection finished. Selected 649 axioms (removed 0 axioms).
% 4.00/1.75 % [INFO] Problem is first-order (TPTP FOF).
% 4.00/1.77 % [INFO] Type checking passed.
% 4.00/1.77 % [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 ...
% 13.64/4.01 % External prover 'e' found a proof!
% 13.64/4.01 % [INFO] Killing All external provers ...
% 13.64/4.01 % Time passed: 3494ms (effective reasoning time: 2925ms)
% 13.64/4.01 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.64/4.01 % Axioms used in derivation (649): fact_320__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_78_nat__numeral__1__eq__1, fact_102_power2__less__imp__less, fact_316_zcong__zless__0, fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_17_t__l__p, fact_458_divides__add__revr, fact_144_semiring__norm_I112_J, fact_142_semiring__numeral__0__eq__0, fact_205_zprime__2, fact_278_rel__simps_I40_J, fact_410_power__strict__mono, fact_313_zcong__not, arity_HOL_Obool___Orderings_Oorder, arity_Nat_Onat___Groups_Omonoid__mult, fact_414_real__le__antisym, fact_185_power2__ge__self, fact_417_power__commutes, fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_54_rel__simps_I27_J, fact_276_rel__simps_I43_J, fact_388_real__mult__assoc, fact_192__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_309_zcong__scalar2, fact_330_zdiff__zmult__distrib, tsy_c_Groups_Oplus__class_Oplus_0_arg2, arity_Int_Oint___Rings_Olinordered__ring__strict, fact_301_zcong__refl, fact_164_zless__add1__eq, fact_42_mult__number__of__left, fact_263_zdiv__mono2__lemma, fact_210_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, arity_Nat_Onat___Rings_Osemiring__1, fact_31_zpower__zadd__distrib, arity_RealDef_Oreal___Rings_Olinordered__ring__strict, tsy_v_s_____res, tsy_c_Int_OPls_res, fact_337_diff__bin__simps_I9_J, fact_355_zcong__zmult__prop2, arity_Int_Oint___Rings_Oordered__cancel__semiring, fact_35_less__eq__int__code_I13_J, fact_145_add__numeral__0, arity_Int_Oint___Rings_Olinordered__idom, fact_50_le__number__of__eq__not__less, fact_25_times__numeral__code_I5_J, fact_130_Bit0__def, arity_Int_Oint___Orderings_Oorder, fact_465_divides__div__not, fact_470_no__zero__divisors, tsy_c_Groups_Oplus__class_Oplus_1_arg2, fact_59_le__special_I4_J, fact_13_zero__power2, arity_Int_Oint___Int_Oring__char__0, fact_85_le__imp__0__less, fact_81_add1__zle__eq, fact_206_zdvd__imp__le, fact_401_real__mult__less__mono2, fact_268_s, fact_398_mult__diff__mult, tsy_c_Groups_Otimes__class_Otimes_3_arg1, fact_58_semiring__norm_I113_J, fact_466_power__dvd__imp__le, fact_161_int__0__less__1, fact_334_number__of__diff, fact_69_zadd__zmult__distrib2, fact_352_zcong__square, fact_199_zpower__zpower, fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_327_zcong__zdiff, fact_165_power2__eq__square__number__of, fact_193_s1, fact_63_mult__Bit0, fact_223_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_33_rel__simps_I34_J, fact_460_divides__rev, arity_Int_Oint___Rings_Olinordered__ring, fact_446_power__decreasing, fact_224_zero__less__power__nat__eq__number__of, fact_442_power__increasing, fact_217_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, tsy_c_Groups_Oplus__class_Oplus_0_res, fact_324__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, tsy_c_Groups_Ominus__class_Ominus_0_arg1, fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, tsy_c_Groups_Otimes__class_Otimes_0_res, arity_RealDef_Oreal___Rings_Osemiring__0, fact_432_le__imp__power__dvd, tsy_c_Groups_Oone__class_Oone_0_res, fact_129_add__Bit0__Bit0, fact_450_dvd__power, fact_182_int__pos__lt__two__imp__zero__or__one, fact_261_q__neg__lemma, fact_269_Euler_Oaux____1, arity_Nat_Onat___Int_Onumber__semiring, fact_28_zmult__assoc, arity_Int_Oint___Rings_Oordered__ring, fact_389_real__mult__commute, fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_463_dvd__trans, fact_202_zdvd__mult__cancel, arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp, fact_331_diff__bin__simps_I7_J, fact_302_zcong__trans, fact_247_zero__le__even__power_H, fact_201_zdvd__antisym__nonneg, fact_168_number__of__Bit1, tsy_c_Groups_Ominus__class_Ominus_1_arg2, arity_RealDef_Oreal___Int_Onumber__semiring, arity_Nat_Onat___Power_Opower, arity_RealDef_Oreal___Groups_Ocomm__monoid__mult, tsy_c_Groups_Otimes__class_Otimes_0_arg2, fact_453_dvd__0__right, fact_11_zero__less__power2, fact_39_eq__number__of__0, arity_RealDef_Oreal___Rings_Oring__no__zero__divisors, fact_148_add__number__of__left, arity_Int_Oint___Rings_Ono__zero__divisors, fact_111_pos__zmult__eq__1__iff, fact_37_zless__le, tsy_c_Int_OMin_res, fact_374_zpower__zdvd__prop2, fact_310_zcong__zmult, fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_405_exp__eq__1, fact_322_neg__one__power__eq__mod__m, fact_252_power__eq__0__iff__number__of, arity_Int_Oint___Rings_Oring, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, fact_264_unique__quotient__lemma__neg, arity_RealDef_Oreal___Rings_Odvd, tsy_c_Int_Onumber__class_Onumber__of_res, fact_390_real__mult__1, fact_284_rel__simps_I13_J, fact_346_diff__bin__simps_I4_J, fact_138_semiring__mult__2__right, fact_335_right__diff__distrib__number__of, fact_237_crossproduct__noteq, fact_447_power__le__imp__le__exp, fact_329_zdiff__zmult__distrib2, tsy_c_TwoSquares__Mirabelle__iprzenvtji_Ois__sum2sq_arg1, fact_473_zero__neq__one, fact_179__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096, tsy_c_Groups_Oplus__class_Oplus_1_res, arity_Int_Oint___Groups_Oab__group__add, fact_74_less__int__code_I14_J, fact_61_nat__1__add__1, tsy_c_Groups_Oplus__class_Oplus_1_arg1, fact_275_Bit1__Min, arity_Int_Oint___Int_Onumber__semiring, tsy_c_Groups_Ozero__class_Ozero_1_res, fact_340_less__bin__lemma, fact_235_add__0__iff, fact_155_rel__simps_I10_J, fact_377_Legendre__def, fact_21_zle__refl, tsy_c_Groups_Otimes__class_Otimes_4_arg2, fact_403_real__mult__less__iff1, fact_345_zle__diff1__eq, arity_Int_Oint___Rings_Ocomm__semiring, fact_227_mult__nat__number__of, fact_83_semiring__add__number__of, fact_428_power__0, fact_486_one__dvd, tsy_v_s1_____res, fact_373_zcong__zprime__prod__zero, fact_339_diff__bin__simps_I3_J, fact_370_neg__one__power, arity_Int_Oint___Int_Onumber__ring, fact_72_less__eq__int__code_I15_J, tsy_c_Orderings_Oord__class_Oless__eq_arg1, fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_356_zcong__zmult__prop1, fact_220_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_73_rel__simps_I33_J, fact_298_zmult__eq__1__iff, fact_266_quartic__square__square, fact_14_zero__eq__power2, arity_Int_Oint___Rings_Osemiring__1, fact_4_calculation_I2_J, fact_147_less__number__of, fact_300_zcong__sym, fact_0__096t_A_060_A0_096, fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, tsy_c_Groups_Ozero__class_Ozero_0_res, fact_89_rel__simps_I48_J, fact_429_power__add, fact_467_mult__zero__left, fact_51_rel__simps_I22_J, fact_127_add__Pls__right, fact_76_less__nat__number__of, fact_47_le__special_I3_J, arity_Nat_Onat___Rings_Omult__zero, fact_318_zcong__zpower__zmult, fact_225_nat__mult__2__right, fact_175_semiring__one__add__one__is__two, arity_RealDef_Oreal___Rings_Olinordered__ring, fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_82_zle__add1__eq__le, fact_256_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_52_less__eq__int__code_I14_J, fact_99_power2__eq__imp__eq, fact_323_zcong__neg__1__impl__ne__1, tsy_c_Residues_OLegendre_arg2, fact_384_real__zero__not__eq__one, fact_187_self__quotient__aux2, fact_437_power__gt1__lemma, fact_372_zcong__zprime__prod__zero__contra, fact_321__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_203_zdvd__reduce, fact_156_rel__simps_I4_J, fact_292_rel__simps_I23_J, fact_18__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_158_bin__less__0__simps_I3_J, fact_172_odd__less__0, fact_448_power__increasing__iff, fact_19_p, fact_319_zprime__zdvd__zmult, fact_91_sum__squares__eq__zero__iff, fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_170_numeral__1__eq__1, tsy_c_Groups_Otimes__class_Otimes_1_res, fact_226_nat__mult__2, fact_433_nat__power__less__imp__less, fact_107_mult__numeral__1, fact_478_dvd__mult__left, tsy_c_Groups_Oone__class_Oone_1_res, fact_494_mult__nonneg__nonpos2, fact_282_rel__simps_I7_J, fact_328_zdvd__zdiffD, fact_371_zcong__zmult__prop3, fact_493_mult__nonneg__nonpos, fact_357_zcong__shift, fact_455_divides__exp, fact_49_less__0__number__of, fact_274__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_386_real__less__def, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, fact_419_dvd__power__same, fact_250_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_34_rel__simps_I19_J, fact_196_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, arity_Int_Oint___Rings_Oring__1, fact_425_one__le__power, fact_445_power__eq__imp__eq__base, tsy_c_Groups_Otimes__class_Otimes_4_res, fact_77_int__one__le__iff__zero__less, fact_416_power__mult__distrib, tsy_c_Groups_Otimes__class_Otimes_2_res, fact_160_add__Bit0__Bit1, fact_481_dvd__mult, fact_180_zadd__power3, fact_154_bin__less__0__simps_I4_J, fact_64_less__number__of__int__code, fact_286_rel__simps_I3_J, tsy_c_Groups_Oplus__class_Oplus_0_arg1, fact_444_power__strict__decreasing, fact_128_add__Pls, fact_38_zadd__left__mono, fact_368_Int2_Ozcong__zero, fact_92_left__distrib__number__of, fact_104_sum__power2__ge__zero, tsy_c_Groups_Otimes__class_Otimes_0_arg1, arity_Nat_Onat___Orderings_Olinorder, arity_RealDef_Oreal___Rings_Osemiring__1, fact_40_eq__0__number__of, fact_430_power__le__dvd, fact_208_le__nat__number__of, arity_RealDef_Oreal___Rings_Ocomm__semiring, fact_87_number__of__reorient, fact_358_zcong__zpower, fact_75_rel__simps_I15_J, tsy_c_Groups_Ominus__class_Ominus_0_res, fact_3_t, fact_10_power2__less__0, arity_Nat_Onat___Rings_Osemiring__0, fact_219_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_215_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_479_dvdI, tsy_c_Groups_Ominus__class_Ominus_1_arg1, fact_307_zcong__zmult__self, fact_338_diff__bin__simps_I10_J, fact_56_zadd__zless__mono, fact_421_power__one__right, fact_471_divisors__zero, fact_366_zcong__eq__zdvd__prop, tsy_v_m_res, fact_303_order__le__neq__implies__less, tsy_c_Groups_Otimes__class_Otimes_1_arg1, fact_246_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_395_nat__mult__eq__one, arity_RealDef_Oreal___Int_Onumber__ring, fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_434_nat__zero__less__power__iff, arity_Int_Oint___Groups_Omonoid__mult, fact_415_field__power__not__zero, fact_254_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_369_zpower__zdvd__prop1, fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_406_real__squared__diff__one__factored, tsy_c_Int_OBit1_res, fact_364_zdvd__bounds, fact_207_is__mult__sum2sq, fact_5__096_126_A1_A_060_061_At_096, fact_462_linorder__neqE__linordered__idom, tsy_c_IntPrimes_Ozcong_arg2, fact_141_even__less__0__iff, arity_RealDef_Oreal___Rings_Oring, fact_326_not__real__square__gt__zero, fact_108_mult__numeral__1__right, arity_Int_Oint___Rings_Oring__no__zero__divisors, fact_449_one__less__power, fact_150_number__of__add, tsy_c_HOL_Oundefined_res, fact_177_less__special_I4_J, tsy_c_Residues_OLegendre_res, fact_281_rel__simps_I45_J, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_134_double__number__of__Bit0, fact_137_mult__2, fact_393_real__mult__left__cancel, fact_115_rel__simps_I50_J, arity_RealDef_Oreal___Rings_Oring__1, fact_422_power__mono, arity_Int_Oint___Orderings_Olinorder, fact_476_dvd__0__left, fact_98_zmult__zless__mono2, fact_461_divides__exp2, fact_306_zcong__1, help_ti_idem, fact_472_one__neq__zero, arity_Nat_Onat___Rings_Olinordered__semidom, fact_48_le__special_I1_J, fact_188_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_259_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_272_pos2, arity_Nat_Onat___Rings_Ocomm__semiring, fact_103_sum__power2__le__zero__iff, fact_7_not__sum__power2__lt__zero, fact_67_plus__numeral__code_I9_J, fact_376_one__not__neg__one__mod__m, fact_360_zdiff__power2, tsy_c_Orderings_Oord__class_Oless_arg2, fact_79_Numeral1__eq1__nat, fact_496_mult__nonpos__nonpos, fact_125_rel__simps_I14_J, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_109_one__is__num__one, fact_311_zcong__zadd, fact_176_one__add__one__is__two, tsy_c_IntPrimes_Ozprime_arg1, fact_314_zcong__iff__lin, arity_Int_Oint___Rings_Osemiring, fact_80_zless__imp__add1__zle, fact_251_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, arity_Nat_Onat___Rings_Oordered__cancel__semiring, fact_117_rel__simps_I44_J, fact_474_comm__semiring__class_Odistrib, fact_90_zless__linear, fact_139_mult__2__right, fact_459_nat__mult__dvd__cancel__disj_H, fact_136_semiring__mult__2, fact_27_le__number__of, fact_173_less__special_I3_J, fact_483_dvd__triv__right, fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_475_combine__common__factor, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_184_cube__square, fact_394_real__mult__right__cancel, arity_RealDef_Oreal___Groups_Oab__group__add, fact_211_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_348_diff__bin__simps_I5_J, 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_290_rel__simps_I26_J, fact_143_number__of__Pls, fact_296_rel__simps_I11_J, arity_RealDef_Oreal___Int_Oring__char__0, fact_451_convex__bound__lt, fact_6_p0, fact_440_power__less__imp__less__exp, fact_297_rel__simps_I25_J, fact_399_real__mult__le__cancel__iff1, fact_487_dvd__diff, fact_396_real__add__mult__distrib, fact_424_zero__less__power, fact_157_bin__less__0__simps_I1_J, fact_20_qf1pt, fact_112_double__eq__0__iff, tsy_c_Residues_OLegendre_arg1, fact_229_power__even__eq, tsy_c_Residues_OQuadRes_arg1, fact_113_rel__simps_I46_J, fact_408_two__realpow__ge__one, arity_RealDef_Oreal___Rings_Omult__zero, fact_118_rel__simps_I38_J, fact_120_Pls__def, arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_70_rel__simps_I29_J, fact_400_real__mult__le__cancel__iff2, fact_257_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, tsy_c_Power_Opower__class_Opower_arg1, fact_260_q__pos__lemma, fact_378_QuadRes__def, arity_RealDef_Oreal___Rings_Osemiring, fact_267_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_283_rel__simps_I24_J, fact_359_power2__diff, fact_71_rel__simps_I5_J, fact_407_realpow__minus__mult, fact_68_zadd__zmult__distrib, fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_29_zle__trans, fact_197_zprime__power__zdvd__cancel__right, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc, tsy_c_Power_Opower__class_Opower_res, tsy_c_Groups_Ozero__class_Ozero_3_res, arity_RealDef_Oreal___Rings_Ocomm__ring__1, arity_RealDef_Oreal___Rings_Ono__zero__divisors, tsy_c_Groups_Otimes__class_Otimes_4_arg1, fact_336_left__diff__distrib__number__of, fact_353_zspecial__product, arity_RealDef_Oreal___Orderings_Oorder, fact_464_dvd__refl, fact_30_zle__antisym, fact_383_realpow__two__sum__zero__iff, fact_295_eq__number__of__Pls__Min, arity_RealDef_Oreal___Rings_Olinordered__semiring__1__strict, arity_Int_Oint___Power_Opower, fact_9_sum__power2__eq__zero__iff, arity_RealDef_Oreal___Orderings_Olinorder, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, fact_270_zprime__def, fact_8_sum__power2__gt__zero__iff, arity_Int_Oint___Rings_Osemiring__0, fact_380_mult__eq__if, fact_41_semiring__mult__number__of, fact_317_zcong__zless__imp__eq, fact_488_divides__cases, fact_456_divides__mul__l, fact_391_real__add__left__mono, fact_341_xzgcda__linear__aux1, fact_121_less__int__code_I16_J, fact_32_less__eq__int__code_I16_J, fact_183_s0p, fact_413_real__le__trans, fact_178_less__special_I2_J, fact_194_zero__less__power__nat__eq, fact_265_zdiv__mono2__neg__lemma, fact_159_add__Bit1__Bit0, fact_94_zadd__assoc, fact_240_crossproduct__eq, fact_454_divides__ge, fact_93_right__distrib__number__of, fact_308_zcong__scalar, fact_191__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_468_mult__zero__right, fact_131_zadd__0__right, tsy_c_Groups_Ominus__class_Ominus_1_res, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_86_eq__number__of, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_347_diff__bin__simps_I6_J, fact_375_Legendre__1mod4, arity_RealDef_Oreal___Rings_Oordered__cancel__semiring, fact_382_diff__square, fact_248_add__scale__eq__noteq, fact_84_add__nat__number__of, fact_262_unique__quotient__lemma, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_255_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_228_nat__number__of__mult__left, fact_26_less__eq__number__of__int__code, fact_1_calculation_I1_J, fact_186_self__quotient__aux1, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc, fact_404_real__two__squares__add__zero__iff, arity_Nat_Onat___Int_Onumber, fact_119_Bit0__Pls, fact_12_one__power2, tsy_c_IntPrimes_Ozcong_arg3, fact_88_rel__simps_I51_J, fact_490_zero__le__mult__iff, fact_482_dvd__mult2, fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_287_rel__simps_I6_J, tsy_c_Groups_Ozero__class_Ozero_2_res, fact_387_less__eq__real__def, fact_60_le__special_I2_J, fact_420_power__mult, fact_277_rel__simps_I47_J, fact_96_zadd__commute, fact_46_sum__squares__ge__zero, fact_280_rel__simps_I42_J, fact_153_rel__simps_I16_J, fact_36_rel__simps_I31_J, fact_469_mult__eq__0__iff, fact_333_Int2_Oaux1, fact_443_power__Suc__less, fact_106_not__sum__squares__lt__zero, tsy_c_IntPrimes_Ozcong_arg1, arity_Int_Oint___Rings_Ozero__neq__one, fact_105_sum__squares__gt__zero__iff, fact_397_nat__power__eq__0__iff, fact_344_Euler_Oaux1, tsy_c_Groups_Otimes__class_Otimes_3_res, fact_22_number__of__is__id, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_271_prime__g__5, fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_279_rel__simps_I37_J, tsy_c_Int_Onumber__class_Onumber__of_arg1, fact_100_power2__le__imp__le, fact_402_real__mult__order, fact_65_zmult__1__right, fact_418_power__one, tsy_c_Residues_OQuadRes_arg2, fact_385_real__le__eq__diff, fact_452_realpow__pos__nth__unique, tsy_c_Int_OBit0_res, fact_230_even__power__le__0__imp__0, fact_23_zmult__commute, tsy_c_Groups_Otimes__class_Otimes_1_arg2, fact_381_power__eq__if, fact_342_zcong__def, fact_116_rel__simps_I49_J, fact_392_add__diff__add, fact_169_semiring__numeral__1__eq__1, arity_Nat_Onat___Orderings_Oorder, tsy_c_Rings_Odvd__class_Odvd_arg2, fact_492_mult__nonneg__nonneg, fact_44_number__of__mult, fact_426_power__inject__exp, arity_RealDef_Oreal___Power_Opower, fact_140_power2__eq__square, fact_181_zadd__power2, fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, arity_Int_Oint___Rings_Ocomm__ring__1, fact_135_power3__eq__cube, arity_Nat_Onat___Rings_Osemiring, tsy_c_Groups_Otimes__class_Otimes_3_arg2, fact_351_zcong__square__zless, tsy_c_Groups_Otimes__class_Otimes_2_arg1, fact_441_power__strict__increasing__iff, fact_123_rel__simps_I2_J, fact_151_rel__simps_I12_J, fact_485_dvd__add, fact_495_mult__nonpos__nonneg, tsy_c_Power_Opower__class_Opower_arg2, fact_146_add__numeral__0__right, fact_477_dvd__mult__right, fact_57_nat__number__of__Pls, fact_174_less__special_I1_J, fact_411_real__le__refl, fact_132_zadd__0, arity_Nat_Onat___Rings_Ono__zero__divisors, arity_Nat_Onat___Rings_Odvd, fact_166_power2__sum, fact_126_int__0__neq__1, fact_332_diff__bin__simps_I1_J, fact_379_real__sum__squared__expand, fact_484_dvd__triv__left, fact_431_dvd__power__le, fact_258_power__0__left__number__of, fact_114_rel__simps_I39_J, fact_293_rel__simps_I20_J, fact_363_zcong__not__zero, fact_204_zdvd__period, tsy_v_t_____res, fact_133_zadd__strict__right__mono, fact_367_zprime__zdvd__zmult__better, fact_15_add__special_I2_J, fact_124_less__int__code_I13_J, fact_62_mult__Pls, fact_101_zero__le__power2, fact_190__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096, fact_149_add__number__of__eq, fact_55_rel__simps_I21_J, fact_97_zero__is__num__zero, fact_253_pos__zmult__pos, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, tsy_c_Groups_Otimes__class_Otimes_2_arg2, fact_435_power__less__imp__less__base, fact_299_pos__zmult__eq__1__iff__lemma, fact_198_zprime__power__zdvd__cancel__left, arity_RealDef_Oreal___Rings_Oordered__ring, fact_491_mult__le__0__iff, fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, tsy_c_Rings_Odvd__class_Odvd_arg1, arity_RealDef_Oreal___Int_Onumber, tsy_c_Int_OBit0_arg1, fact_24_zle__linear, fact_365_zcong__zero__equiv__div, fact_171_semiring__norm_I110_J, fact_195_zprime__zdvd__power, fact_457_divides__mul__r, fact_349_inv__not__p__minus__1__aux, fact_200_zdvd__not__zless, tsy_c_Int_OBit1_arg1, arity_Int_Oint___Rings_Omult__zero, fact_362_zcong__less__eq, fact_152_less__int__code_I15_J, fact_285_rel__simps_I9_J, fact_273__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_95_zadd__left__commute, fact_304_Euler_Oaux2, fact_438_power__0__left, fact_354_zcong__id, fact_122_rel__simps_I17_J, fact_343_add__number__of__diff1, fact_480_mult__dvd__mono, fact_45_sum__squares__le__zero__iff, fact_66_zmult__1, tsy_c_Orderings_Oord__class_Oless_arg1, fact_436_power__less__power__Suc, arity_Int_Oint___Rings_Odvd, fact_209_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, arity_Int_Oint___Rings_Olinordered__semidom, fact_423_zero__le__power, fact_361_zdiff__power3, fact_439_power__strict__increasing, fact_409_realpow__num__eq__if, fact_43_arith__simps_I32_J, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Int_Oint___Rings_Olinordered__semiring__1__strict, fact_305_IntPrimes_Ozcong__zero, fact_167_number__of__Bit0, fact_325__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_427_power__eq__0__iff, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_294_rel__simps_I28_J, tsy_c_Groups_Ominus__class_Ominus_0_arg2, fact_110_mult__Bit1, fact_489_zero__le__square, fact_315_four__x__squared, fact_162_Bit1__def, fact_53_rel__simps_I32_J, fact_350_zcong__eq__trans, fact_291_rel__simps_I30_J, fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, tsy_c_Orderings_Oord__class_Oless__eq_arg2, fact_412_real__le__linear, fact_312_power__m1__even, fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_163_odd__nonzero, fact_16_add__special_I3_J, fact_288_rel__simps_I8_J, fact_289_bin__less__0__simps_I2_J
% 13.64/4.02 % No. of inferences in proof: 1302
% 13.64/4.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3494 ms resp. 2925 ms w/o parsing
% 14.54/4.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.54/4.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------