TSTP Solution File: ITP097^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP097^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 : Tue May 7 07:47:47 EDT 2024
% Result : Theorem 10.42s 3.32s
% Output : Refutation 10.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 390
% Syntax : Number of formulae : 741 ( 552 unt; 41 typ; 0 def)
% Number of atoms : 1538 ( 942 equ; 2 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3729 ( 98 ~; 26 |; 26 &;3317 @)
% ( 0 <=>; 262 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 13 con; 0-3 aty)
% Number of variables : 1150 ( 14 ^1110 !; 26 ?;1150 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_real_type,type,
set_real: $tType ).
thf(real_type,type,
real: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(archim1371465213g_real_type,type,
archim1371465213g_real: real > int ).
thf(one_one_int_type,type,
one_one_int: int ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(one_one_real_type,type,
one_one_real: real ).
thf(zero_zero_int_type,type,
zero_zero_int: int ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(zero_zero_real_type,type,
zero_zero_real: real ).
thf(if_nat_type,type,
if_nat: $o > nat > nat > nat ).
thf(nat2_type,type,
nat2: int > nat ).
thf(ring_1_of_int_int_type,type,
ring_1_of_int_int: int > int ).
thf(ring_1_of_int_real_type,type,
ring_1_of_int_real: int > real ).
thf(suc_type,type,
suc: nat > nat ).
thf(semiri2019852685at_int_type,type,
semiri2019852685at_int: nat > int ).
thf(semiri1382578993at_nat_type,type,
semiri1382578993at_nat: nat > nat ).
thf(semiri2110766477t_real_type,type,
semiri2110766477t_real: nat > real ).
thf(neg_numeral_dbl_int_type,type,
neg_numeral_dbl_int: int > int ).
thf(neg_numeral_dbl_real_type,type,
neg_numeral_dbl_real: real > real ).
thf(bit0_type,type,
bit0: num > num ).
thf(one_type,type,
one: num ).
thf(numeral_numeral_int_type,type,
numeral_numeral_int: num > int ).
thf(numeral_numeral_nat_type,type,
numeral_numeral_nat: num > nat ).
thf(numeral_numeral_real_type,type,
numeral_numeral_real: num > real ).
thf(pow_type,type,
pow: num > num > num ).
thf(ord_less_int_type,type,
ord_less_int: int > int > $o ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_num_type,type,
ord_less_eq_num: num > num > $o ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: real > real > $o ).
thf(power_power_int_type,type,
power_power_int: int > nat > int ).
thf(power_power_nat_type,type,
power_power_nat: nat > nat > nat ).
thf(power_power_real_type,type,
power_power_real: real > nat > real ).
thf(log_type,type,
log: real > real > real ).
thf(powr_real_type,type,
powr_real: real > real > real ).
thf(member_real_type,type,
member_real: real > set_real > $o ).
thf(d_type,type,
d: int ).
thf(n_type,type,
n: nat ).
thf(313,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( semiri2019852685at_int @ A )
= ( power_power_int @ ( semiri2019852685at_int @ B ) @ C ) )
= ( A
= ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_of__nat__power__eq__of__nat__cancel__iff) ).
thf(1322,plain,
! [A: nat,B: nat,C: nat] :
( ( ( semiri2019852685at_int @ A )
= ( power_power_int @ ( semiri2019852685at_int @ B ) @ C ) )
= ( A
= ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(344,axiom,
! [A: real,B: int] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B )
= ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_ceiling__le__iff) ).
thf(1411,plain,
! [A: real,B: int] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B )
= ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(85,axiom,
! [A: num,B: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_numeral__le__iff) ).
thf(629,plain,
! [A: num,B: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(269,axiom,
! [A: num] :
( ( archim1371465213g_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_ceiling__numeral) ).
thf(1190,plain,
! [A: num] :
( ( archim1371465213g_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(151,axiom,
( ( ring_1_of_int_int @ one_one_int )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_of__int__1) ).
thf(846,plain,
( ( ring_1_of_int_int @ one_one_int )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(212,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_power2__less__eq__zero__iff) ).
thf(1031,plain,
! [A: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(164,axiom,
( ( suc @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Suc__1) ).
thf(893,plain,
( ( suc @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_le__SucI) ).
thf(518,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(3,axiom,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_of__nat__0) ).
thf(352,plain,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(342,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_of__int__power__le__of__int__cancel__iff) ).
thf(1406,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(303,axiom,
( ( '?' @ nat )
= ( ^ [A: nat > $o] :
? [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( A @ ( nat2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_ex__nat) ).
thf(1290,plain,
( ( '?' @ nat )
= ( ^ [A: nat > $o] :
? [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( A @ ( nat2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(226,axiom,
! [A: real] : ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_of__nat__ceiling) ).
thf(1068,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(198,axiom,
! [A: nat] :
( ( ring_1_of_int_real @ ( semiri2019852685at_int @ A ) )
= ( semiri2110766477t_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_of__int__of__nat__eq) ).
thf(994,plain,
! [A: nat] :
( ( ring_1_of_int_real @ ( semiri2019852685at_int @ A ) )
= ( semiri2110766477t_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(228,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_zle__int) ).
thf(1073,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(157,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( powr_real @ B @ A ) @ ( powr_real @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_powr__mono2) ).
thf(873,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( powr_real @ B @ A ) @ ( powr_real @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(296,axiom,
! [A: num,B: num] :
( ( ord_less_eq_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_semiring__norm_I71_J) ).
thf(1269,plain,
! [A: num,B: num] :
( ( ord_less_eq_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(91,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_power__one__right) ).
thf(655,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_not__less__eq__eq) ).
thf(614,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(307,axiom,
! [A: int,B: nat,C: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ A ) @ B )
= ( ring_1_of_int_real @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_of__int__eq__of__int__power__cancel__iff) ).
thf(1305,plain,
! [A: int,B: nat,C: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ A ) @ B )
= ( ring_1_of_int_real @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(216,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] : ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_nat__int__comparison_I3_J) ).
thf(1041,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] : ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(49,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_bot__nat__0_Oextremum__uniqueI) ).
thf(523,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ( semiri2019852685at_int @ A )
= ( semiri2019852685at_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_of__nat__eq__iff) ).
thf(582,plain,
! [A: nat,B: nat] :
( ( ( semiri2019852685at_int @ A )
= ( semiri2019852685at_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(350,axiom,
ord_less_int @ zero_zero_int @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_d_I2_J) ).
thf(1426,plain,
ord_less_int @ zero_zero_int @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(15,axiom,
! [A: int] :
( ( zero_zero_int
= ( ring_1_of_int_int @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_of__int__0__eq__iff) ).
thf(385,plain,
! [A: int] :
( ( zero_zero_int
= ( ring_1_of_int_int @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(309,axiom,
! [A: num] :
( zero_zero_real
!= ( numeral_numeral_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_zero__neq__numeral) ).
thf(1310,plain,
! [A: num] :
( zero_zero_real
!= ( numeral_numeral_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(298,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( power_power_nat @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_power2__eq__iff__nonneg) ).
thf(1275,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( power_power_nat @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(180,axiom,
! [A: nat] :
( ( nat2 @ ( semiri2019852685at_int @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_nat__int) ).
thf(945,plain,
! [A: nat] :
( ( nat2 @ ( semiri2019852685at_int @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(293,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_of__nat__power__le__of__nat__cancel__iff) ).
thf(1260,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(104,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_nat_Odistinct_I1_J) ).
thf(698,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_eq__imp__le) ).
thf(538,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(325,axiom,
! [A: num] :
( ( ring_1_of_int_int @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_of__int__numeral) ).
thf(1354,plain,
! [A: num] :
( ( ring_1_of_int_int @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(144,axiom,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_le__numeral__extra_I3_J) ).
thf(829,plain,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(271,axiom,
( ( ring_1_of_int_real @ d )
= ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062) ).
thf(1196,plain,
( ( ring_1_of_int_real @ d )
= ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(166,axiom,
! [A: int] :
( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_zero__eq__power2) ).
thf(898,plain,
! [A: int] :
( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(107,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_One__nat__def) ).
thf(709,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(149,axiom,
! [A: real] :
( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_power__Suc0__right) ).
thf(841,plain,
! [A: real] :
( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(218,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_int @ ( semiri2019852685at_int @ A ) @ B )
= ( semiri2019852685at_int @ C ) )
= ( ( power_power_nat @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_of__nat__eq__of__nat__power__cancel__iff) ).
thf(1046,plain,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_int @ ( semiri2019852685at_int @ A ) @ B )
= ( semiri2019852685at_int @ C ) )
= ( ( power_power_nat @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(295,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_power2__eq__iff__nonneg) ).
thf(1265,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(291,axiom,
! [A: num] :
( ( semiri2019852685at_int @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_of__nat__numeral) ).
thf(1254,plain,
! [A: num] :
( ( semiri2019852685at_int @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(302,axiom,
! [A: num] :
( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ A ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_power__zero__numeral) ).
thf(1287,plain,
! [A: num] :
( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ A ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(10,axiom,
( ( semiri1382578993at_nat @ one_one_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_of__nat__1) ).
thf(372,plain,
( ( semiri1382578993at_nat @ one_one_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_le__Suc__eq) ).
thf(504,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_verit__la__disequality) ).
thf(838,plain,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(105,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_le__0__eq) ).
thf(702,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(299,axiom,
! [A: num,B: num] :
( ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_numeral__le__iff) ).
thf(1279,plain,
! [A: num,B: num] :
( ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( semiri1382578993at_nat @ ( power_power_nat @ A @ B ) )
= ( power_power_nat @ ( semiri1382578993at_nat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_of__nat__power) ).
thf(357,plain,
! [A: nat,B: nat] :
( ( semiri1382578993at_nat @ ( power_power_nat @ A @ B ) )
= ( power_power_nat @ ( semiri1382578993at_nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(249,axiom,
! [A: num] :
( ( ( numeral_numeral_real @ A )
= one_one_real )
= ( A = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_numeral__eq__one__iff) ).
thf(1132,plain,
! [A: num] :
( ( ( numeral_numeral_real @ A )
= one_one_real )
= ( A = one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(55,axiom,
! [A: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ A )
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_power__Suc__0) ).
thf(542,plain,
! [A: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ A )
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(112,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_diff__induct) ).
thf(724,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(221,axiom,
! [A: int,B: int] :
( ( A = B )
| ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_verit__la__disequality) ).
thf(1055,plain,
! [A: int,B: int] :
( ( A = B )
| ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(343,axiom,
( ( numeral_numeral_real @ one )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_numeral__One) ).
thf(1409,plain,
( ( numeral_numeral_real @ one )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(333,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_nat__0__le) ).
thf(1379,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(233,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_of__int__le__0__iff) ).
thf(1087,plain,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(289,axiom,
! [A: nat,B: num,C: nat] :
( ( ( semiri2019852685at_int @ A )
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( A
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_real__of__nat__eq__numeral__power__cancel__iff) ).
thf(1247,plain,
! [A: nat,B: num,C: nat] :
( ( ( semiri2019852685at_int @ A )
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( A
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(126,axiom,
! [A: int,B: int] :
( ( ( ring_1_of_int_int @ A )
= ( ring_1_of_int_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_of__int__eq__iff) ).
thf(770,plain,
! [A: int,B: int] :
( ( ( ring_1_of_int_int @ A )
= ( ring_1_of_int_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(284,axiom,
! [A: num,B: nat,C: int] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( nat2 @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_numeral__power__le__nat__cancel__iff) ).
thf(1232,plain,
! [A: num,B: nat,C: int] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( nat2 @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(77,axiom,
! [A: num] : ( ord_less_eq_num @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_order__refl) ).
thf(606,plain,
! [A: num] : ( ord_less_eq_num @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(322,axiom,
! [A: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( nat2 @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_nat__le__0) ).
thf(1347,plain,
! [A: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( nat2 @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(160,axiom,
! [A: num,B: nat,C: nat] :
( ( ( power_power_real @ ( numeral_numeral_real @ A ) @ B )
= ( semiri2110766477t_real @ C ) )
= ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_numeral__power__eq__of__nat__cancel__iff) ).
thf(881,plain,
! [A: num,B: nat,C: nat] :
( ( ( power_power_real @ ( numeral_numeral_real @ A ) @ B )
= ( semiri2110766477t_real @ C ) )
= ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_le__SucE) ).
thf(416,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(346,axiom,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_int @ A )
= ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_of__int__power__eq__of__int__cancel__iff) ).
thf(1415,plain,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_int @ A )
= ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(39,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_le__numeral__extra_I3_J) ).
thf(492,plain,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(131,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_le__numeral__extra_I4_J) ).
thf(789,plain,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(72,axiom,
( ( neg_numeral_dbl_int @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_dbl__simps_I2_J) ).
thf(591,plain,
( ( neg_numeral_dbl_int @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(242,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_nat @ B @ ( nat2 @ A ) )
= ( ord_less_eq_int @ ( semiri2019852685at_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_le__nat__iff) ).
thf(1109,plain,
! [A: int,B: nat] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_nat @ B @ ( nat2 @ A ) )
= ( ord_less_eq_int @ ( semiri2019852685at_int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(317,axiom,
( ( ring_1_of_int_real @ one_one_int )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_of__int__1) ).
thf(1334,plain,
( ( ring_1_of_int_real @ one_one_int )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(66,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ one_one_real @ C )
=> ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_power__increasing) ).
thf(574,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ one_one_real @ C )
=> ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(267,axiom,
! [A: num] :
( one
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_semiring__norm_I83_J) ).
thf(1183,plain,
! [A: num] :
( one
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(220,axiom,
! [A: num] :
( ( bit0 @ A )
!= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_semiring__norm_I85_J) ).
thf(1051,plain,
! [A: num] :
( ( bit0 @ A )
!= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(306,axiom,
! [A: int,B: num,C: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_of__int__le__numeral__power__cancel__iff) ).
thf(1302,plain,
! [A: int,B: num,C: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(121,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Suc__leD) ).
thf(756,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(331,axiom,
! [A: real] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ one_one_int )
= ( ord_less_eq_real @ A @ one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ceiling__le__one) ).
thf(1373,plain,
! [A: real] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ one_one_int )
= ( ord_less_eq_real @ A @ one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(29,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( powr_real @ A @ one_one_real )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_powr__one) ).
thf(443,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( powr_real @ A @ one_one_real )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(347,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ ( archim1371465213g_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_ceiling__mono) ).
thf(1418,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ ( archim1371465213g_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(83,axiom,
! [A: num,B: num] :
( ( ( numeral_numeral_nat @ A )
= ( numeral_numeral_nat @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_numeral__eq__iff) ).
thf(623,plain,
! [A: num,B: num] :
( ( ( numeral_numeral_nat @ A )
= ( numeral_numeral_nat @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(262,axiom,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= zero_zero_real )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_of__int__eq__0__iff) ).
thf(1169,plain,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= zero_zero_real )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(278,axiom,
! [A: num] :
( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_dbl__simps_I5_J) ).
thf(1215,plain,
! [A: num] :
( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ( semiri2110766477t_real @ A )
= ( semiri2110766477t_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_of__nat__eq__iff) ).
thf(692,plain,
! [A: nat,B: nat] :
( ( ( semiri2110766477t_real @ A )
= ( semiri2110766477t_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_transitive__stepwise__le) ).
thf(453,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(19,axiom,
( ( semiri2110766477t_real @ one_one_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_of__nat__1) ).
thf(396,plain,
( ( semiri2110766477t_real @ one_one_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(273,axiom,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_numerals_I1_J) ).
thf(1201,plain,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(240,axiom,
! [A: num,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_numeral__power__le__of__int__cancel__iff) ).
thf(1104,plain,
! [A: num,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(45,axiom,
! [A: nat] :
( ( ( semiri2019852685at_int @ A )
= one_one_int )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_of__nat__eq__1__iff) ).
thf(507,plain,
! [A: nat] :
( ( ( semiri2019852685at_int @ A )
= one_one_int )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(275,axiom,
! [A: num,B: num] :
( ( power_power_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_int @ ( pow @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_power__numeral) ).
thf(1206,plain,
! [A: num,B: num] :
( ( power_power_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_int @ ( pow @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(13,axiom,
! [A: nat] :
( ( ( semiri1382578993at_nat @ A )
= one_one_nat )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_of__nat__eq__1__iff) ).
thf(380,plain,
! [A: nat] :
( ( ( semiri1382578993at_nat @ A )
= one_one_nat )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(179,axiom,
! [A: num] :
( ( semiri2019852685at_int @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_int__ops_I3_J) ).
thf(942,plain,
! [A: num] :
( ( semiri2019852685at_int @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_nat__le__linear) ).
thf(678,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(133,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_int__ops_I1_J) ).
thf(793,plain,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(175,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_power__0__left) ).
thf(925,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(123,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ one_one_real @ C )
=> ( ord_less_eq_real @ ( powr_real @ C @ A ) @ ( powr_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_powr__mono) ).
thf(761,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ one_one_real @ C )
=> ( ord_less_eq_real @ ( powr_real @ C @ A ) @ ( powr_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(139,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiri2019852685at_int @ A )
= ( semiri2019852685at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_nat__int__comparison_I1_J) ).
thf(810,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiri2019852685at_int @ A )
= ( semiri2019852685at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(319,axiom,
! [A: int,B: nat] :
( ( ring_1_of_int_int @ ( power_power_int @ A @ B ) )
= ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_of__int__power) ).
thf(1338,plain,
! [A: int,B: nat] :
( ( ring_1_of_int_int @ ( power_power_int @ A @ B ) )
= ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(8,axiom,
! [A: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ A ) )
= ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_of__nat__0__eq__iff) ).
thf(366,plain,
! [A: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ A ) )
= ( zero_zero_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Suc__inject) ).
thf(714,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_one__le__power) ).
thf(798,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(260,axiom,
! [A: num,B: nat,C: nat] :
( ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= ( semiri2019852685at_int @ C ) )
= ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_numeral__power__eq__of__nat__cancel__iff) ).
thf(1163,plain,
! [A: num,B: nat,C: nat] :
( ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= ( semiri2019852685at_int @ C ) )
= ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_power__not__zero) ).
thf(746,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(183,axiom,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_of__int__0__le__iff) ).
thf(952,plain,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(246,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_semiring__norm_I87_J) ).
thf(1123,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B )
=> ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_le__log2__of__power) ).
thf(1174,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B )
=> ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(21,axiom,
! [A: nat > num,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_num @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_num @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_lift__Suc__mono__le) ).
thf(407,plain,
! [A: nat > num,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_num @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_num @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: num,B: num] :
( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_nat @ ( pow @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_power__numeral) ).
thf(429,plain,
! [A: num,B: num] :
( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_nat @ ( pow @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(330,axiom,
! [A: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
= ( ord_less_eq_num @ A @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_numeral__le__one__iff) ).
thf(1370,plain,
! [A: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
= ( ord_less_eq_num @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(286,axiom,
! [A: int,B: num] :
( ( ( ring_1_of_int_real @ A )
= ( numeral_numeral_real @ B ) )
= ( A
= ( numeral_numeral_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_of__int__eq__numeral__iff) ).
thf(1238,plain,
! [A: int,B: num] :
( ( ( ring_1_of_int_real @ A )
= ( numeral_numeral_real @ B ) )
= ( A
= ( numeral_numeral_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(336,axiom,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_real @ A )
= ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_of__int__power__eq__of__int__cancel__iff) ).
thf(1387,plain,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_real @ A )
= ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(170,axiom,
( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) )
= ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062) ).
thf(910,plain,
( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) )
= ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(349,axiom,
! [A: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ zero_zero_int )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_of__nat__le__0__iff) ).
thf(1423,plain,
! [A: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ zero_zero_int )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(33,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_lift__Suc__antimono__le) ).
thf(467,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(63,axiom,
! [A: num] :
( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ A ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_power__zero__numeral) ).
thf(566,plain,
! [A: num] :
( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ A ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(159,axiom,
( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_one__power2) ).
thf(879,plain,
( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(145,axiom,
! [A: real] :
? [B: nat] : ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_real__arch__simple) ).
thf(830,plain,
! [A: real] :
? [B: nat] : ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(40,axiom,
( ( ring_1_of_int_int @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_of__int__0) ).
thf(493,plain,
( ( ring_1_of_int_int @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(230,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_of__int__le__of__int__power__cancel__iff) ).
thf(1079,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(58,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_power__one__right) ).
thf(551,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(341,axiom,
! [A: num] :
( zero_zero_int
!= ( numeral_numeral_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_zero__neq__numeral) ).
thf(1402,plain,
! [A: num] :
( zero_zero_int
!= ( numeral_numeral_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(323,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_nat @ ( nat2 @ A ) @ B )
= ( ord_less_eq_int @ A @ ( semiri2019852685at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_nat__le__iff) ).
thf(1350,plain,
! [A: int,B: nat] :
( ( ord_less_eq_nat @ ( nat2 @ A ) @ B )
= ( ord_less_eq_int @ A @ ( semiri2019852685at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(253,axiom,
! [A: int,B: num,C: nat] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_of__int__le__numeral__power__cancel__iff) ).
thf(1143,plain,
! [A: int,B: num,C: nat] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(315,axiom,
! [A: num] :
( ( semiri2110766477t_real @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_of__nat__numeral) ).
thf(1328,plain,
! [A: num] :
( ( semiri2110766477t_real @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(224,axiom,
! [A: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_one__le__numeral) ).
thf(1064,plain,
! [A: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(282,axiom,
( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_of__int__0) ).
thf(1227,plain,
( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(193,axiom,
! [A: int,B: num,C: nat] :
( ( ( ring_1_of_int_real @ A )
= ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( A
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_of__int__eq__numeral__power__cancel__iff) ).
thf(980,plain,
! [A: int,B: num,C: nat] :
( ( ( ring_1_of_int_real @ A )
= ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( A
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(202,axiom,
! [A: int] :
( ( archim1371465213g_real @ ( ring_1_of_int_real @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_ceiling__of__int) ).
thf(1006,plain,
! [A: int] :
( ( archim1371465213g_real @ ( ring_1_of_int_real @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(16,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_le__refl) ).
thf(388,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(251,axiom,
( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_one__power2) ).
thf(1138,plain,
( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(73,axiom,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_zero__reorient) ).
thf(593,plain,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(196,axiom,
! [A: nat,B: nat] :
( ( semiri2019852685at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri2019852685at_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_of__nat__power) ).
thf(989,plain,
! [A: nat,B: nat] :
( ( semiri2019852685at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri2019852685at_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_nat_OdiscI) ).
thf(650,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(181,axiom,
( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_one__power2) ).
thf(948,plain,
( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(161,axiom,
! [A: num] :
( ( ( numeral_numeral_int @ A )
= one_one_int )
= ( A = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_numeral__eq__one__iff) ).
thf(884,plain,
! [A: num] :
( ( ( numeral_numeral_int @ A )
= one_one_int )
= ( A = one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(259,axiom,
! [A: num] :
( ( nat2 @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_nat__numeral) ).
thf(1160,plain,
! [A: num] :
( ( nat2 @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(327,axiom,
! [A: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_of__int__0__eq__iff) ).
thf(1361,plain,
! [A: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(167,axiom,
( ( neg_numeral_dbl_int @ one_one_int )
= ( numeral_numeral_int @ ( bit0 @ one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_dbl__simps_I3_J) ).
thf(901,plain,
( ( neg_numeral_dbl_int @ one_one_int )
= ( numeral_numeral_int @ ( bit0 @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(88,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_nat__induct) ).
thf(637,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(38,axiom,
! [A: nat] :
( ( power_power_real @ zero_zero_real @ ( suc @ A ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_power__0__Suc) ).
thf(489,plain,
! [A: nat] :
( ( power_power_real @ zero_zero_real @ ( suc @ A ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(257,axiom,
( ( '!' @ nat )
= ( ^ [A: nat > $o] :
! [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A @ ( nat2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_all__nat) ).
thf(1155,plain,
( ( '!' @ nat )
= ( ^ [A: nat > $o] :
! [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A @ ( nat2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(211,axiom,
! [A: num,B: nat,C: int] :
( ( ( power_power_real @ ( numeral_numeral_real @ A ) @ B )
= ( ring_1_of_int_real @ C ) )
= ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_numeral__power__eq__of__int__cancel__iff) ).
thf(1028,plain,
! [A: num,B: nat,C: int] :
( ( ( power_power_real @ ( numeral_numeral_real @ A ) @ B )
= ( ring_1_of_int_real @ C ) )
= ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(231,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ? [B: nat] :
( A
= ( semiri2019852685at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_zero__le__imp__eq__int) ).
thf(1082,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ? [B: nat] :
( A
= ( semiri2019852685at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(304,axiom,
! [A: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= A ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_int__nat__eq) ).
thf(1292,plain,
! [A: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= A ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(176,axiom,
! [A: int] :
( ( ( nat2 @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_nat__0__iff) ).
thf(933,plain,
! [A: int] :
( ( ( nat2 @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( semiri2110766477t_real @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_of__nat__le__iff) ).
thf(554,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( semiri2110766477t_real @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_nat_Oinject) ).
thf(753,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(345,axiom,
ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062) ).
thf(1414,plain,
ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(50,axiom,
! [A: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_one__le__numeral) ).
thf(526,plain,
! [A: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(215,axiom,
! [A: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_one__le__numeral) ).
thf(1039,plain,
! [A: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(189,axiom,
( numeral_numeral_nat
= ( ^ [A: num] : ( nat2 @ ( numeral_numeral_int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_nat__numeral__as__int) ).
thf(970,plain,
( numeral_numeral_nat
= ( ^ [A: num] : ( nat2 @ ( numeral_numeral_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ A ) @ B ) @ ( semiri1382578993at_nat @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_of__nat__le__of__nat__power__cancel__iff) ).
thf(393,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ A ) @ B ) @ ( semiri1382578993at_nat @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(334,axiom,
! [A: num,B: int] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_of__int__numeral__le__iff) ).
thf(1382,plain,
! [A: num,B: int] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(64,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_zero__le) ).
thf(569,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(129,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_power__0__left) ).
thf(779,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(338,axiom,
! [A: num] :
( ( ( numeral_numeral_nat @ A )
= one_one_nat )
= ( A = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_numeral__eq__one__iff) ).
thf(1393,plain,
! [A: num] :
( ( ( numeral_numeral_nat @ A )
= one_one_nat )
= ( A = one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(89,axiom,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_verit__la__disequality) ).
thf(647,plain,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(294,axiom,
( ( archim1371465213g_real @ zero_zero_real )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_ceiling__zero) ).
thf(1263,plain,
( ( archim1371465213g_real @ zero_zero_real )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(199,axiom,
! [A: int,B: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ A @ B ) )
= ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_of__int__power) ).
thf(997,plain,
! [A: int,B: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ A @ B ) )
= ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(287,axiom,
! [A: nat,B: num] :
( ( ( semiri2019852685at_int @ A )
= ( numeral_numeral_int @ B ) )
= ( A
= ( numeral_numeral_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_int__eq__iff__numeral) ).
thf(1241,plain,
! [A: nat,B: num] :
( ( ( semiri2019852685at_int @ A )
= ( numeral_numeral_int @ B ) )
= ( A
= ( numeral_numeral_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( semiri1382578993at_nat @ A )
= ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ C ) )
= ( A
= ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_of__nat__power__eq__of__nat__cancel__iff) ).
thf(360,plain,
! [A: nat,B: nat,C: nat] :
( ( ( semiri1382578993at_nat @ A )
= ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ C ) )
= ( A
= ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: set_real] :
( ? [B: real] : ( member_real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member_real @ D @ A )
=> ( ord_less_eq_real @ D @ C ) )
=> ( ord_less_eq_real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_complete__real) ).
thf(398,plain,
! [A: set_real] :
( ? [B: real] : ( member_real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member_real @ D @ A )
=> ( ord_less_eq_real @ D @ C ) )
=> ( ord_less_eq_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(268,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_one__le__power) ).
thf(1187,plain,
! [A: int,B: nat] :
( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(127,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( B = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_nat__power__eq__Suc__0__iff) ).
thf(773,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( B = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(94,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_zero__induct) ).
thf(662,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(110,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_Zero__not__Suc) ).
thf(718,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(169,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ( nat2 @ A )
= ( nat2 @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_eq__nat__nat__iff) ).
thf(906,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ( nat2 @ A )
= ( nat2 @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(250,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2110766477t_real @ ( nat2 @ A ) )
= ( ring_1_of_int_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_of__nat__nat) ).
thf(1135,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2110766477t_real @ ( nat2 @ A ) )
= ( ring_1_of_int_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(119,axiom,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= one_one_int )
= ( A = one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_of__int__eq__1__iff) ).
thf(750,plain,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= one_one_int )
= ( A = one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(254,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_lift__Suc__antimono__le) ).
thf(1146,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(155,axiom,
! [A: nat,B: num,C: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_of__nat__le__numeral__power__cancel__iff) ).
thf(856,plain,
! [A: nat,B: num,C: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(115,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_bot__nat__0_Oextremum) ).
thf(733,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(191,axiom,
! [A: real] :
( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) )
= A )
= ( ? [B: int] :
( A
= ( ring_1_of_int_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_of__int__ceiling__cancel) ).
thf(975,plain,
! [A: real] :
( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) )
= A )
= ( ? [B: int] :
( A
= ( ring_1_of_int_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(117,axiom,
! [A: real] :
( ( ( powr_real @ A @ one_one_real )
= A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_powr__one__gt__zero__iff) ).
thf(743,plain,
! [A: real] :
( ( ( powr_real @ A @ one_one_real )
= A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(185,axiom,
! [A: nat,B: int] :
( ( A
= ( nat2 @ B ) )
= ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( B
= ( semiri2019852685at_int @ A ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_nat__eq__iff2) ).
thf(958,plain,
! [A: nat,B: int] :
( ( A
= ( nat2 @ B ) )
= ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( B
= ( semiri2019852685at_int @ A ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(56,axiom,
! [A: nat,B: num,C: nat] :
( ( ( semiri1382578993at_nat @ A )
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( A
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_real__of__nat__eq__numeral__power__cancel__iff) ).
thf(545,plain,
! [A: nat,B: num,C: nat] :
( ( ( semiri1382578993at_nat @ A )
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( A
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(23,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ one_one_nat @ C )
=> ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_power__increasing) ).
thf(413,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ one_one_nat @ C )
=> ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(143,axiom,
! [A: num,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( semiri1382578993at_nat @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_numeral__power__le__of__nat__cancel__iff) ).
thf(826,plain,
! [A: num,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( semiri1382578993at_nat @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(67,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_real @ ( power_power_real @ ( semiri2110766477t_real @ A ) @ B ) @ ( semiri2110766477t_real @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_of__nat__le__of__nat__power__cancel__iff) ).
thf(577,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_real @ ( power_power_real @ ( semiri2110766477t_real @ A ) @ B ) @ ( semiri2110766477t_real @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(108,axiom,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_power__one) ).
thf(711,plain,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(177,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_of__int__0__le__iff) ).
thf(936,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(130,axiom,
( ( neg_numeral_dbl_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_dbl__simps_I2_J) ).
thf(787,plain,
( ( neg_numeral_dbl_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(42,axiom,
! [A: real,B: real] :
( ( ( powr_real @ A @ B )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_powr__eq__0__iff) ).
thf(498,plain,
! [A: real,B: real] :
( ( ( powr_real @ A @ B )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(235,axiom,
( zero_zero_nat
= ( nat2 @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_nat__zero__as__int) ).
thf(1092,plain,
( zero_zero_nat
= ( nat2 @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(234,axiom,
( ( archim1371465213g_real @ one_one_real )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_ceiling__one) ).
thf(1090,plain,
( ( archim1371465213g_real @ one_one_real )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(281,axiom,
! [A: int] :
( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_power__Suc0__right) ).
thf(1224,plain,
! [A: int] :
( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(95,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_of__nat__power__le__of__nat__cancel__iff) ).
thf(672,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(222,axiom,
! [A: nat,B: int] :
( ( ( semiri2019852685at_int @ A )
= B )
= ( ( A
= ( nat2 @ B ) )
& ( ord_less_eq_int @ zero_zero_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_int__eq__iff) ).
thf(1058,plain,
! [A: nat,B: int] :
( ( ( semiri2019852685at_int @ A )
= B )
= ( ( A
= ( nat2 @ B ) )
& ( ord_less_eq_int @ zero_zero_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(241,axiom,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_two__realpow__ge__one) ).
thf(1107,plain,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(173,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_power__one__right) ).
thf(919,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(137,axiom,
! [A: num,B: num] :
( ( A = B )
| ~ ( ord_less_eq_num @ A @ B )
| ~ ( ord_less_eq_num @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_verit__la__disequality) ).
thf(804,plain,
! [A: num,B: num] :
( ( A = B )
| ~ ( ord_less_eq_num @ A @ B )
| ~ ( ord_less_eq_num @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(124,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_lift__Suc__mono__le) ).
thf(764,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(276,axiom,
! [A: real,B: num] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ ( numeral_numeral_int @ B ) )
= ( ord_less_eq_real @ A @ ( numeral_numeral_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_ceiling__le__numeral) ).
thf(1209,plain,
! [A: real,B: num] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ ( numeral_numeral_int @ B ) )
= ( ord_less_eq_real @ A @ ( numeral_numeral_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(300,axiom,
! [A: real] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_le__of__int__ceiling) ).
thf(1282,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(244,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_power2__nat__le__eq__le) ).
thf(1117,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(12,axiom,
! [A: num] :
( ( semiri1382578993at_nat @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_of__nat__numeral) ).
thf(377,plain,
! [A: num] :
( ( semiri1382578993at_nat @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(332,axiom,
! [A: int,B: num] :
( ( ( ring_1_of_int_int @ A )
= ( numeral_numeral_int @ B ) )
= ( A
= ( numeral_numeral_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_of__int__eq__numeral__iff) ).
thf(1376,plain,
! [A: int,B: num] :
( ( ( ring_1_of_int_int @ A )
= ( numeral_numeral_int @ B ) )
= ( A
= ( numeral_numeral_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(204,axiom,
! [A: nat,B: num,C: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_of__nat__le__numeral__power__cancel__iff) ).
thf(1011,plain,
! [A: nat,B: num,C: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(25,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_old_Onat_Oinducts) ).
thf(419,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(217,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__int__le__iff) ).
thf(1043,plain,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(28,axiom,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_exists__least__lemma) ).
thf(434,plain,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(163,axiom,
! [A: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ one_one_real )
= ( ord_less_eq_num @ A @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_numeral__le__one__iff) ).
thf(890,plain,
! [A: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ one_one_real )
= ( ord_less_eq_num @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(122,axiom,
! [A: nat] :
( ( ring_1_of_int_int @ ( semiri2019852685at_int @ A ) )
= ( semiri2019852685at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_of__int__of__nat__eq) ).
thf(758,plain,
! [A: nat] :
( ( ring_1_of_int_int @ ( semiri2019852685at_int @ A ) )
= ( semiri2019852685at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(53,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_of__nat__le__0__iff) ).
thf(535,plain,
! [A: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(314,axiom,
! [A: int,B: num] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( numeral_numeral_int @ B ) )
= ( ord_less_eq_int @ A @ ( numeral_numeral_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_of__int__le__numeral__iff) ).
thf(1325,plain,
! [A: int,B: num] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( numeral_numeral_int @ B ) )
= ( ord_less_eq_int @ A @ ( numeral_numeral_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(165,axiom,
! [A: int,B: num,C: nat] :
( ( ( nat2 @ A )
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( A
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_nat__eq__numeral__power__cancel__iff) ).
thf(895,plain,
! [A: int,B: num,C: nat] :
( ( ( nat2 @ A )
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( A
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(321,axiom,
! [A: nat,B: num,C: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_of__nat__le__numeral__power__cancel__iff) ).
thf(1344,plain,
! [A: nat,B: num,C: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(209,axiom,
! [A: num] :
~ ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_semiring__norm_I69_J) ).
thf(1022,plain,
! [A: num] :
~ ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(223,axiom,
! [A: num,B: nat] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( semiri2110766477t_real @ B ) )
= ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_numeral__le__real__of__nat__iff) ).
thf(1061,plain,
! [A: num,B: nat] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( semiri2110766477t_real @ B ) )
= ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( semiri2110766477t_real @ ( power_power_nat @ A @ B ) )
= ( power_power_real @ ( semiri2110766477t_real @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_of__nat__power) ).
thf(848,plain,
! [A: nat,B: nat] :
( ( semiri2110766477t_real @ ( power_power_nat @ A @ B ) )
= ( power_power_real @ ( semiri2110766477t_real @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ( semiri2019852685at_int @ A )
= ( semiri2019852685at_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_int__int__eq) ).
thf(520,plain,
! [A: nat,B: nat] :
( ( ( semiri2019852685at_int @ A )
= ( semiri2019852685at_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(255,axiom,
! [A: int,B: num] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( ord_less_eq_int @ A @ ( numeral_numeral_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_of__int__le__numeral__iff) ).
thf(1149,plain,
! [A: int,B: num] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( ord_less_eq_int @ A @ ( numeral_numeral_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_of__nat__le__iff) ).
thf(964,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(84,axiom,
! [A: real,B: real,C: real] :
( ( powr_real @ ( powr_real @ A @ B ) @ C )
= ( powr_real @ ( powr_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_powr__powr__swap) ).
thf(626,plain,
! [A: real,B: real,C: real] :
( ( powr_real @ ( powr_real @ A @ B ) @ C )
= ( powr_real @ ( powr_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( A
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
=> ( ( semiri2110766477t_real @ B )
= ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_log2__of__power__eq) ).
thf(915,plain,
! [A: nat,B: nat] :
( ( A
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
=> ( ( semiri2110766477t_real @ B )
= ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(171,axiom,
! [A: num] :
( ( one_one_int
= ( numeral_numeral_int @ A ) )
= ( one = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_one__eq__numeral__iff) ).
thf(912,plain,
! [A: num] :
( ( one_one_int
= ( numeral_numeral_int @ A ) )
= ( one = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(194,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= ( ring_1_of_int_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_of__nat__nat) ).
thf(983,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri2019852685at_int @ ( nat2 @ A ) )
= ( ring_1_of_int_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(103,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( powr_real @ A @ B ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_powr__nonneg__iff) ).
thf(695,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( powr_real @ A @ B ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(225,axiom,
( ( nat2 @ one_one_int )
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_nat__1) ).
thf(1066,plain,
( ( nat2 @ one_one_int )
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(206,axiom,
! [A: real,B: nat] :
( ( ord_less_eq_nat @ ( nat2 @ ( archim1371465213g_real @ A ) ) @ B )
= ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_nat__ceiling__le__eq) ).
thf(1015,plain,
! [A: real,B: nat] :
( ( ord_less_eq_nat @ ( nat2 @ ( archim1371465213g_real @ A ) ) @ B )
= ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(195,axiom,
! [A: num,B: int] :
( ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_of__int__numeral__le__iff) ).
thf(986,plain,
! [A: num,B: int] :
( ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(200,axiom,
! [A: real] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ zero_zero_int )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_ceiling__le__zero) ).
thf(1000,plain,
! [A: real] :
( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ zero_zero_int )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(174,axiom,
! [A: nat] :
( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_zero__eq__power2) ).
thf(922,plain,
! [A: nat] :
( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(92,axiom,
ord_less_eq_real @ one_one_real @ one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_le__numeral__extra_I4_J) ).
thf(658,plain,
ord_less_eq_real @ one_one_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(272,axiom,
! [A: num] :
( ( one_one_nat
= ( numeral_numeral_nat @ A ) )
= ( one = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_one__eq__numeral__iff) ).
thf(1198,plain,
! [A: num] :
( ( one_one_nat
= ( numeral_numeral_nat @ A ) )
= ( one = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(339,axiom,
! [A: nat] :
( ( archim1371465213g_real @ ( semiri2110766477t_real @ A ) )
= ( semiri2019852685at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_ceiling__of__nat) ).
thf(1396,plain,
! [A: nat] :
( ( archim1371465213g_real @ ( semiri2110766477t_real @ A ) )
= ( semiri2019852685at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(265,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( power_power_int @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_power2__eq__iff__nonneg) ).
thf(1176,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( power_power_int @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(78,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_Zero__neq__Suc) ).
thf(608,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(243,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ~ ! [B: nat] :
( A
!= ( semiri2019852685at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_nonneg__int__cases) ).
thf(1113,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ~ ! [B: nat] :
( A
!= ( semiri2019852685at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(62,axiom,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_power__one) ).
thf(563,plain,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(328,axiom,
! [A: num] :
( ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ one_one_int )
= ( ord_less_eq_num @ A @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_numeral__le__one__iff) ).
thf(1364,plain,
! [A: num] :
( ( ord_less_eq_int @ ( numeral_numeral_int @ A ) @ one_one_int )
= ( ord_less_eq_num @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(290,axiom,
! [A: real,B: num] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( powr_real @ A @ ( numeral_numeral_real @ B ) )
= ( power_power_real @ A @ ( numeral_numeral_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_powr__numeral) ).
thf(1250,plain,
! [A: real,B: num] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( powr_real @ A @ ( numeral_numeral_real @ B ) )
= ( power_power_real @ A @ ( numeral_numeral_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(153,axiom,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_of__int__eq__0__iff) ).
thf(851,plain,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(239,axiom,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_numeral__One) ).
thf(1102,plain,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(111,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_powr__ge__pzero) ).
thf(722,plain,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(213,axiom,
! [A: num] :
( ( ring_1_of_int_real @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_of__int__numeral) ).
thf(1034,plain,
! [A: num] :
( ( ring_1_of_int_real @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_le__antisym) ).
thf(675,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(261,axiom,
! [A: nat] :
( ( power_power_int @ zero_zero_int @ ( suc @ A ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_power__0__Suc) ).
thf(1166,plain,
! [A: nat] :
( ( power_power_int @ zero_zero_int @ ( suc @ A ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(274,axiom,
! [A: int,B: num,C: nat] :
( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_nat__le__numeral__power__cancel__iff) ).
thf(1203,plain,
! [A: int,B: num,C: nat] :
( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(52,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_old_Onat_Odistinct_I1_J) ).
thf(531,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(57,axiom,
! [A: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ zero_zero_real )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_of__nat__le__0__iff) ).
thf(548,plain,
! [A: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ zero_zero_real )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(348,axiom,
! [A: num,B: num] :
( ( ( numeral_numeral_int @ A )
= ( numeral_numeral_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_numeral__eq__iff) ).
thf(1420,plain,
! [A: num,B: num] :
( ( ( numeral_numeral_int @ A )
= ( numeral_numeral_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ ( semiri1382578993at_nat @ A ) @ B )
= ( semiri1382578993at_nat @ C ) )
= ( ( power_power_nat @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_of__nat__eq__of__nat__power__cancel__iff) ).
thf(374,plain,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ ( semiri1382578993at_nat @ A ) @ B )
= ( semiri1382578993at_nat @ C ) )
= ( ( power_power_nat @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(140,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Nat_Oex__has__greatest__nat) ).
thf(812,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(81,axiom,
! [A: nat] :
( ( ( semiri2019852685at_int @ A )
= zero_zero_int )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_of__nat__eq__0__iff) ).
thf(617,plain,
! [A: nat] :
( ( ( semiri2019852685at_int @ A )
= zero_zero_int )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(178,axiom,
! [A: num,B: nat,C: nat] :
( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ ( semiri2019852685at_int @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_numeral__power__le__of__nat__cancel__iff) ).
thf(939,plain,
! [A: num,B: nat,C: nat] :
( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ ( semiri2019852685at_int @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(207,axiom,
ord_less_eq_int @ one_one_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_le__numeral__extra_I4_J) ).
thf(1018,plain,
ord_less_eq_int @ one_one_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(142,axiom,
! [A: nat] :
( ( zero_zero_real
= ( semiri2110766477t_real @ A ) )
= ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_of__nat__0__eq__iff) ).
thf(823,plain,
! [A: nat] :
( ( zero_zero_real
= ( semiri2110766477t_real @ A ) )
= ( zero_zero_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(219,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_order__refl) ).
thf(1049,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(35,axiom,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiri2019852685at_int @ ( if_nat @ A @ B @ C ) )
= ( semiri2019852685at_int @ B ) ) )
& ( ~ A
=> ( ( semiri2019852685at_int @ ( if_nat @ A @ B @ C ) )
= ( semiri2019852685at_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_int__if) ).
thf(473,plain,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiri2019852685at_int @ ( if_nat @ A @ B @ C ) )
= ( semiri2019852685at_int @ B ) ) )
& ( ~ A
=> ( ( semiri2019852685at_int @ ( if_nat @ A @ B @ C ) )
= ( semiri2019852685at_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(229,axiom,
! [A: num,B: num] :
( ( ( numeral_numeral_real @ A )
= ( numeral_numeral_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_numeral__eq__iff) ).
thf(1076,plain,
! [A: num,B: num] :
( ( ( numeral_numeral_real @ A )
= ( numeral_numeral_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(134,axiom,
! [A: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ A ) )
= ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_of__nat__0__eq__iff) ).
thf(795,plain,
! [A: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ A ) )
= ( zero_zero_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(98,axiom,
! [A: num] :
( zero_zero_nat
!= ( numeral_numeral_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_zero__neq__numeral) ).
thf(680,plain,
! [A: num] :
( zero_zero_nat
!= ( numeral_numeral_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(128,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_power__Suc0__right) ).
thf(776,plain,
! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(68,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_le0) ).
thf(580,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(101,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( semiri2110766477t_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_of__nat__mono) ).
thf(690,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( semiri2110766477t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(210,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__int__le__of__int__power__cancel__iff) ).
thf(1025,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(227,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_of__int__le__1__iff) ).
thf(1070,plain,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(106,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_n__not__Suc__n) ).
thf(705,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(162,axiom,
! [A: num,B: nat] :
( ( archim1371465213g_real @ ( power_power_real @ ( numeral_numeral_real @ A ) @ B ) )
= ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ceiling__numeral__power) ).
thf(887,plain,
! [A: num,B: nat] :
( ( archim1371465213g_real @ ( power_power_real @ ( numeral_numeral_real @ A ) @ B ) )
= ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(60,axiom,
! [A: real,B: nat] :
( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_one__le__power) ).
thf(557,plain,
! [A: real,B: nat] :
( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(201,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__int__power__le__of__int__cancel__iff) ).
thf(1003,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( semiri2110766477t_real @ A )
= ( power_power_real @ ( semiri2110766477t_real @ B ) @ C ) )
= ( A
= ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_of__nat__power__eq__of__nat__cancel__iff) ).
thf(585,plain,
! [A: nat,B: nat,C: nat] :
( ( ( semiri2110766477t_real @ A )
= ( power_power_real @ ( semiri2110766477t_real @ B ) @ C ) )
= ( A
= ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(285,axiom,
! [A: num,B: nat,C: int] :
( ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= ( ring_1_of_int_int @ C ) )
= ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_numeral__power__eq__of__int__cancel__iff) ).
thf(1235,plain,
! [A: num,B: nat,C: int] :
( ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= ( ring_1_of_int_int @ C ) )
= ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(311,axiom,
! [A: num] :
( ( one_one_real
= ( numeral_numeral_real @ A ) )
= ( one = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_one__eq__numeral__iff) ).
thf(1317,plain,
! [A: num] :
( ( one_one_real
= ( numeral_numeral_real @ A ) )
= ( one = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(279,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_of__int__le__iff) ).
thf(1218,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(318,axiom,
! [A: real,B: int] :
( ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) )
=> ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_ceiling__le) ).
thf(1336,plain,
! [A: real,B: int] :
( ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) )
=> ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_of__nat__mono) ).
thf(1085,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(34,axiom,
! [A: nat] :
( ( ( semiri2110766477t_real @ A )
= one_one_real )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_of__nat__eq__1__iff) ).
thf(470,plain,
! [A: nat] :
( ( ( semiri2110766477t_real @ A )
= one_one_real )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(292,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_power2__less__eq__zero__iff) ).
thf(1257,plain,
! [A: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(158,axiom,
! [A: real] :
( ( powr_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_powr__one__eq__one) ).
thf(876,plain,
! [A: real] :
( ( powr_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_nat__induct__at__least) ).
thf(859,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(280,axiom,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ ( ring_1_of_int_int @ A ) @ B )
= ( ring_1_of_int_int @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_of__int__eq__of__int__power__cancel__iff) ).
thf(1221,plain,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ ( ring_1_of_int_int @ A ) @ B )
= ( ring_1_of_int_int @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(301,axiom,
! [A: num] :
( ( pow @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_pow_Osimps_I1_J) ).
thf(1284,plain,
! [A: num] :
( ( pow @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(324,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_less__eq__int__code_I1_J) ).
thf(1353,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(75,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_Suc__n__not__le__n) ).
thf(600,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(236,axiom,
! [A: num,B: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_numeral__le__iff) ).
thf(1094,plain,
! [A: num,B: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(192,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_power2__nat__le__imp__le) ).
thf(978,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(252,axiom,
! [A: int,B: nat] :
( ( ( nat2 @ A )
= B )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( A
= ( semiri2019852685at_int @ B ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( B = zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_nat__eq__iff) ).
thf(1140,plain,
! [A: int,B: nat] :
( ( ( nat2 @ A )
= B )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( A
= ( semiri2019852685at_int @ B ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(30,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_old_Onat_Oexhaust) ).
thf(446,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_of__nat__power__le__of__nat__cancel__iff) ).
thf(571,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_real @ ( semiri2110766477t_real @ A ) @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ C ) )
= ( ord_less_eq_nat @ A @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(297,axiom,
! [A: num,B: nat,C: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_numeral__power__le__of__int__cancel__iff) ).
thf(1272,plain,
! [A: num,B: nat,C: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(79,axiom,
( ( semiri2019852685at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_int__ops_I2_J) ).
thf(612,plain,
( ( semiri2019852685at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(31,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_le__zero__eq) ).
thf(450,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(266,axiom,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= one_one_real )
= ( A = one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_of__int__eq__1__iff) ).
thf(1180,plain,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= one_one_real )
= ( A = one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(7,axiom,
! [A: nat] :
( ( one_one_nat
= ( semiri1382578993at_nat @ A ) )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_of__nat__1__eq__iff) ).
thf(363,plain,
! [A: nat] :
( ( one_one_nat
= ( semiri1382578993at_nat @ A ) )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
! [A: real,B: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ B )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_power__not__zero) ).
thf(482,plain,
! [A: real,B: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ B )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(258,axiom,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_of__int__1__le__iff) ).
thf(1157,plain,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(41,axiom,
! [A: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ A ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_power__0__Suc) ).
thf(495,plain,
! [A: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ A ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(247,axiom,
! [A: num] :
( ( ord_less_eq_num @ A @ one )
= ( A = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_le__num__One__iff) ).
thf(1126,plain,
! [A: num] :
( ( ord_less_eq_num @ A @ one )
= ( A = one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(337,axiom,
! [A: real] :
( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_zero__eq__power2) ).
thf(1390,plain,
! [A: real] :
( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(150,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_order__refl) ).
thf(844,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(100,axiom,
( ( semiri2110766477t_real @ zero_zero_nat )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_of__nat__0) ).
thf(688,plain,
( ( semiri2110766477t_real @ zero_zero_nat )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(168,axiom,
! [A: num,B: nat,C: int] :
( ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= ( nat2 @ C ) )
= ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_numeral__power__eq__nat__cancel__iff) ).
thf(903,plain,
! [A: num,B: nat,C: int] :
( ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= ( nat2 @ C ) )
= ( ( power_power_int @ ( numeral_numeral_int @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(71,axiom,
! [A: nat] :
( ( one_one_int
= ( semiri2019852685at_int @ A ) )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_of__nat__1__eq__iff) ).
thf(588,plain,
! [A: nat] :
( ( one_one_int
= ( semiri2019852685at_int @ A ) )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(320,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_of__int__le__1__iff) ).
thf(1341,plain,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(238,axiom,
ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ one_one_real ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46__092_060open_062log_A2_A1_A_092_060le_062_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062) ).
thf(1101,plain,
ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ one_one_real ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1,conjecture,
ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(351,plain,
~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_not0__implies__Suc) ).
thf(390,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_real @ ( semiri2110766477t_real @ A ) @ B )
= ( semiri2110766477t_real @ C ) )
= ( ( power_power_nat @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_of__nat__eq__of__nat__power__cancel__iff) ).
thf(632,plain,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_real @ ( semiri2110766477t_real @ A ) @ B )
= ( semiri2110766477t_real @ C ) )
= ( ( power_power_nat @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(288,axiom,
! [A: num] :
( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_int @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_dbl__simps_I5_J) ).
thf(1244,plain,
! [A: num] :
( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ A ) )
= ( numeral_numeral_int @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(114,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_less__eq__nat_Osimps_I1_J) ).
thf(731,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(186,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_int @ ( power_power_int @ ( semiri2019852685at_int @ A ) @ B ) @ ( semiri2019852685at_int @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_of__nat__le__of__nat__power__cancel__iff) ).
thf(961,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_int @ ( power_power_int @ ( semiri2019852685at_int @ A ) @ B ) @ ( semiri2019852685at_int @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(335,axiom,
( ( neg_numeral_dbl_real @ one_one_real )
= ( numeral_numeral_real @ ( bit0 @ one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_dbl__simps_I3_J) ).
thf(1385,plain,
( ( neg_numeral_dbl_real @ one_one_real )
= ( numeral_numeral_real @ ( bit0 @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(46,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_power__0__left) ).
thf(510,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(308,axiom,
( ( numeral_numeral_int @ one )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_numeral__One) ).
thf(1308,plain,
( ( numeral_numeral_int @ one )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(270,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_of__int__le__0__iff) ).
thf(1193,plain,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(277,axiom,
! [A: real] :
( ( log @ A @ one_one_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_log__one) ).
thf(1212,plain,
! [A: real] :
( ( log @ A @ one_one_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_of__nat__mono) ).
thf(383,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(146,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_zero__reorient) ).
thf(832,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(99,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_old_Onat_Odistinct_I2_J) ).
thf(684,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(82,axiom,
! [A: num,B: nat,C: nat] :
( ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= ( semiri1382578993at_nat @ C ) )
= ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_numeral__power__eq__of__nat__cancel__iff) ).
thf(620,plain,
! [A: num,B: nat,C: nat] :
( ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= ( semiri1382578993at_nat @ C ) )
= ( ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(27,axiom,
( ( semiri2019852685at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_of__nat__1) ).
thf(432,plain,
( ( semiri2019852685at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(283,axiom,
! [A: int,B: num,C: nat] :
( ( ( ring_1_of_int_int @ A )
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( A
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_of__int__eq__numeral__power__cancel__iff) ).
thf(1229,plain,
! [A: int,B: num,C: nat] :
( ( ( ring_1_of_int_int @ A )
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) )
= ( A
= ( power_power_int @ ( numeral_numeral_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(141,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq_nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_full__nat__induct) ).
thf(818,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq_nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(154,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_order__refl) ).
thf(854,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Suc__le__mono) ).
thf(790,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(76,axiom,
! [A: num] :
( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ A ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_power__zero__numeral) ).
thf(603,plain,
! [A: num] :
( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ A ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(116,axiom,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( powr_real @ A @ zero_zero_real )
= zero_zero_real ) )
& ( ( A != zero_zero_real )
=> ( ( powr_real @ A @ zero_zero_real )
= one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_powr__zero__eq__one) ).
thf(735,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( powr_real @ A @ zero_zero_real )
= zero_zero_real ) )
& ( ( A != zero_zero_real )
=> ( ( powr_real @ A @ zero_zero_real )
= one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(22,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_lift__Suc__mono__le) ).
thf(410,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(188,axiom,
! [A: num,B: num] :
( ( powr_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( power_power_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_numeral__powr__numeral__real) ).
thf(967,plain,
! [A: num,B: num] :
( ( powr_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( power_power_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(182,axiom,
! [A: real] :
? [B: int] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_ex__le__of__int) ).
thf(950,plain,
! [A: real] :
? [B: int] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(237,axiom,
! [A: int,B: nat] :
( ( A != zero_zero_int )
=> ( ( power_power_int @ A @ B )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_power__not__zero) ).
thf(1097,plain,
! [A: int,B: nat] :
( ( A != zero_zero_int )
=> ( ( power_power_int @ A @ B )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(147,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_le__trans) ).
thf(835,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(136,axiom,
! [A: nat > num,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_num @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_num @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_lift__Suc__antimono__le) ).
thf(801,plain,
! [A: nat > num,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_num @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_num @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(310,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
=> ( ord_less_eq_nat @ B @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_self__le__ge2__pow) ).
thf(1314,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
=> ( ord_less_eq_nat @ B @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(138,axiom,
! [A: real] :
( ( powr_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_powr__0) ).
thf(807,plain,
! [A: real] :
( ( powr_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(87,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_of__nat__0) ).
thf(635,plain,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(184,axiom,
! [A: int,B: int] :
( ( ( ring_1_of_int_real @ A )
= ( ring_1_of_int_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_of__int__eq__iff) ).
thf(955,plain,
! [A: int,B: int] :
( ( ( ring_1_of_int_real @ A )
= ( ring_1_of_int_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(263,axiom,
( n
= ( suc @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_n__def) ).
thf(1172,plain,
( n
= ( suc @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(125,axiom,
! [A: nat] :
( ( ( semiri2110766477t_real @ A )
= zero_zero_real )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_of__nat__eq__0__iff) ).
thf(767,plain,
! [A: nat] :
( ( ( semiri2110766477t_real @ A )
= zero_zero_real )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(113,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_bot__nat__0_Oextremum__unique) ).
thf(728,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(248,axiom,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_power__one) ).
thf(1129,plain,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(256,axiom,
! [A: num,B: nat,C: nat] :
( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ A ) @ B ) @ ( semiri2110766477t_real @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_numeral__power__le__of__nat__cancel__iff) ).
thf(1152,plain,
! [A: num,B: nat,C: nat] :
( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ A ) @ B ) @ ( semiri2110766477t_real @ C ) )
= ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(74,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_Suc__neq__Zero) ).
thf(596,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(208,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_of__int__1__le__iff) ).
thf(1019,plain,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Suc__le__D) ).
thf(528,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(326,axiom,
! [A: num] :
( one
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_verit__eq__simplify_I10_J) ).
thf(1357,plain,
! [A: num] :
( one
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(197,axiom,
! [A: num] : ( ord_less_eq_num @ one @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_semiring__norm_I68_J) ).
thf(992,plain,
! [A: num] : ( ord_less_eq_num @ one @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(305,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_verit__eq__simplify_I8_J) ).
thf(1299,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(340,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( A = B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_verit__la__generic) ).
thf(1399,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( A = B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(245,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_int @ one_one_int @ C )
=> ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_power__increasing) ).
thf(1120,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_int @ one_one_int @ C )
=> ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(43,axiom,
! [A: nat] :
( ( one_one_real
= ( semiri2110766477t_real @ A ) )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_of__nat__1__eq__iff) ).
thf(501,plain,
! [A: nat] :
( ( one_one_real
= ( semiri2110766477t_real @ A ) )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_of__nat__le__iff) ).
thf(369,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(316,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_lift__Suc__mono__le) ).
thf(1331,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(37,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_zero__reorient) ).
thf(486,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(312,axiom,
( one_one_nat
= ( nat2 @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_nat__one__as__int) ).
thf(1320,plain,
( one_one_nat
= ( nat2 @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(329,axiom,
! [A: nat,B: num,C: nat] :
( ( ( semiri2110766477t_real @ A )
= ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( A
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_real__of__nat__eq__numeral__power__cancel__iff) ).
thf(1367,plain,
! [A: nat,B: num,C: nat] :
( ( ( semiri2110766477t_real @ A )
= ( power_power_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( A
= ( power_power_nat @ ( numeral_numeral_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(4,axiom,
! [A: nat] :
( ( ( semiri1382578993at_nat @ A )
= zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_of__nat__eq__0__iff) ).
thf(354,plain,
! [A: nat] :
( ( ( semiri1382578993at_nat @ A )
= zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(203,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_nat @ ( nat2 @ A ) @ ( nat2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_nat__mono) ).
thf(1009,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_nat @ ( nat2 @ A ) @ ( nat2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(93,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_lift__Suc__antimono__le) ).
thf(659,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(214,axiom,
! [A: real] : ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_real__nat__ceiling__ge) ).
thf(1037,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_old_Onat_Oinject) ).
thf(560,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(205,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_le__numeral__extra_I3_J) ).
thf(1014,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(190,axiom,
! [A: num,B: num] :
( ( power_power_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_real @ ( pow @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_power__numeral) ).
thf(972,plain,
! [A: num,B: num] :
( ( power_power_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_real @ ( pow @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1427,plain,
$false,
inference(e,[status(thm)],[1322,1411,629,1190,846,1031,893,518,352,1406,1290,1068,994,1073,873,1269,655,614,1305,1041,523,582,1426,385,1310,1275,945,1260,698,538,1354,829,1196,898,709,841,1046,1265,1254,1287,372,504,838,702,1279,357,1132,542,724,1055,1409,1379,1087,1247,770,1232,606,1347,881,416,1415,492,789,591,1109,1334,574,1183,1051,1302,756,1373,443,1418,623,1169,1215,692,453,396,1201,1104,507,1206,380,942,678,793,925,761,810,1338,366,714,798,1163,746,952,1123,1174,407,429,1370,1238,1387,910,1423,467,566,879,830,493,1079,551,1402,1350,1143,1328,1064,1227,980,1006,388,1138,593,989,650,948,884,1160,1361,901,637,489,1155,1028,1082,1292,933,554,753,1414,526,1039,970,393,1382,569,779,1393,647,1263,997,1241,360,398,1187,773,662,718,906,1135,750,1146,856,733,975,743,958,545,413,826,577,711,936,787,498,1092,1090,1224,672,1058,1107,919,804,764,1209,1282,1117,377,1376,1011,419,1043,434,890,758,535,1325,895,1344,1022,1061,848,520,1149,964,626,915,912,983,695,1066,1015,986,1000,922,658,1198,1396,1176,608,1113,563,1364,1250,851,1102,722,1034,675,1166,1203,531,548,1420,374,812,617,939,1018,823,1049,473,1076,795,680,776,580,690,1025,1070,705,887,557,1003,585,1235,1317,1218,1336,1085,470,1257,876,859,1221,1284,1353,600,1094,978,1140,446,571,1272,612,450,1180,363,482,1157,495,1126,1390,844,688,903,588,1341,1101,351,390,632,1244,731,961,1385,510,1308,1193,1212,383,832,684,620,432,1229,818,854,790,603,735,410,967,950,1097,835,801,1314,807,635,955,1172,767,728,1129,1152,596,1019,528,1357,992,1299,1399,1120,501,369,1331,486,1320,1367,354,1009,659,1037,560,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ITP097^1 : TPTP v8.1.2. Released v7.5.0.
% 0.08/0.17 % Command : run_Leo-III %s %d
% 0.18/0.39 % Computer : n021.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Mon May 6 14:24:24 EDT 2024
% 0.18/0.39 % CPUTime :
% 1.09/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.97/1.19 % [INFO] Parsing done (257ms).
% 2.06/1.20 % [INFO] Running in sequential loop mode.
% 2.58/1.42 % [INFO] eprover registered as external prover.
% 2.58/1.42 % [INFO] cvc4 registered as external prover.
% 2.58/1.43 % [INFO] Scanning for conjecture ...
% 2.86/1.51 % [INFO] Found a conjecture and 353 axioms. Running axiom selection ...
% 2.93/1.61 % [INFO] Axiom selection finished. Selected 348 axioms (removed 5 axioms).
% 3.68/1.77 % [INFO] Problem is higher-order (TPTP THF).
% 3.95/1.79 % [INFO] Type checking passed.
% 3.95/1.80 % [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 ...
% 10.40/3.31 % External prover 'e' found a proof!
% 10.42/3.31 % [INFO] Killing All external provers ...
% 10.42/3.31 % Time passed: 2764ms (effective reasoning time: 2105ms)
% 10.42/3.31 % 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)>
% 10.42/3.32 % Axioms used in derivation (348): fact_257_nat__int, fact_222_order__refl, fact_294_zero__le__imp__eq__int, fact_125_of__nat__1__eq__iff, fact_309_int__ops_I2_J, fact_345_eq__nat__nat__iff, fact_179_le__antisym, fact_280_of__int__le__0__iff, fact_71_numeral__eq__one__iff, fact_288_zero__eq__power2, fact_37_nat__eq__numeral__power__cancel__iff, fact_123_of__nat__1__eq__iff, fact_156_real__of__nat__eq__numeral__power__cancel__iff, fact_271_nat__1, fact_246_of__int__0__eq__iff, fact_108_power2__nat__le__imp__le, fact_81_numeral__le__one__iff, fact_5_numeral__power__eq__of__int__cancel__iff, fact_83_complete__real, fact_342_int__ops_I3_J, fact_326_diff__induct, fact_27_of__int__le__iff, fact_180_eq__imp__le, fact_38_numeral__power__le__nat__cancel__iff, fact_146_of__nat__power, fact_320_nat_Odistinct_I1_J, fact_256_nat__power__eq__Suc__0__iff, fact_2_of__int__le__numeral__power__cancel__iff, fact_234_of__nat__0, fact_161_nat__ceiling__le__eq, fact_325_One__nat__def, fact_197_one__le__power, fact_316_power__not__zero, fact_287_zero__eq__power2, fact_99_verit__la__generic, fact_149_of__nat__power__le__of__nat__cancel__iff, fact_145_of__nat__power, fact_304_power__0__left, fact_214_one__power2, fact_135_of__nat__numeral, fact_279_of__int__le__0__iff, fact_42_le__of__int__ceiling, fact_259_dbl__simps_I2_J, fact_129_of__int__of__nat__eq, fact_130_of__int__of__nat__eq, fact_228_le0, fact_231_le__zero__eq, fact_340_nat__int__comparison_I3_J, fact_143_of__nat__eq__of__nat__power__cancel__iff, fact_46__092_060open_062log_A2_A1_A_092_060le_062_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062, fact_302_zero__le, fact_199_one__le__power, fact_236_of__nat__0__eq__iff, fact_333_not0__implies__Suc, fact_164_of__nat__le__numeral__power__cancel__iff, fact_232_of__nat__0, fact_190_not__less__eq__eq, fact_13_ceiling__le__numeral, fact_195_le__SucE, fact_202_lift__Suc__antimono__le, fact_339_le__nat__iff, fact_57_semiring__norm_I87_J, fact_111_power__one__right, fact_343_ex__nat, fact_155_real__of__nat__eq__numeral__power__cancel__iff, fact_281_ceiling__le__zero, fact_162_of__nat__le__numeral__power__cancel__iff, fact_258_dbl__simps_I2_J, fact_298_nat__eq__iff, fact_137_of__nat__numeral, fact_49_semiring__norm_I85_J, fact_299_zero__reorient, fact_260_of__nat__le__0__iff, fact_310_le__numeral__extra_I3_J, fact_244_of__int__0, fact_163_of__nat__le__numeral__power__cancel__iff, fact_0_numeral__power__le__of__int__cancel__iff, fact_181_le__trans, fact_332_old_Onat_Oinducts, fact_66_of__int__1, fact_213_one__power2, fact_262_of__nat__le__0__iff, fact_47_semiring__norm_I69_J, fact_40_nat__mono, fact_107_power2__nat__le__eq__le, fact_263_power__0__Suc, fact_82_numeral__le__one__iff, fact_17_of__int__numeral__le__iff, fact_219_power__numeral, fact_208_powr__mono, fact_154_real__of__nat__eq__numeral__power__cancel__iff, fact_84_le__numeral__extra_I4_J, fact_75_of__int__1__le__iff, fact_86_le__numeral__extra_I4_J, fact_184_powr__powr__swap, fact_170_of__nat__mono, fact_221_order__refl, fact_63_of__int__eq__1__iff, fact_255_power__Suc__0, fact_87_one__le__numeral, fact_275_dbl__simps_I5_J, fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062, fact_92_numeral__One, fact_54_n__def, fact_25_ceiling__of__int, fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062, fact_311_le__numeral__extra_I3_J, fact_273_log__one, fact_11_of__int__power__le__of__int__cancel__iff, fact_330_Zero__not__Suc, fact_200_lift__Suc__antimono__le, fact_32_of__int__eq__numeral__iff, fact_113_nat_Oinject, fact_55_semiring__norm_I68_J, fact_201_lift__Suc__antimono__le, fact_73_one__eq__numeral__iff, fact_187_transitive__stepwise__le, fact_289_power2__less__eq__zero__iff, fact_238_of__nat__eq__0__iff, fact_141_of__nat__eq__of__nat__power__cancel__iff, fact_19_of__int__power, fact_192_le__Suc__eq, fact_115_of__nat__eq__iff, fact_301_zero__reorient, fact_319_exists__least__lemma, fact_152_of__nat__le__of__nat__power__cancel__iff, fact_20_of__int__eq__of__int__power__cancel__iff, fact_229_bot__nat__0_Oextremum, fact_203_lift__Suc__antimono__le, fact_78_of__int__le__1__iff, fact_85_le__numeral__extra_I4_J, fact_151_of__nat__le__of__nat__power__cancel__iff, fact_14_of__int__le__numeral__iff, fact_252_ceiling__zero, fact_296_int__int__eq, fact_100_verit__eq__simplify_I10_J, fact_76_of__int__1__le__iff, fact_205_lift__Suc__mono__le, fact_160_numeral__le__real__of__nat__iff, fact_158_numeral__power__eq__of__nat__cancel__iff, fact_28_of__int__le__iff, fact_277_of__int__0__le__iff, fact_303_nat__zero__as__int, fact_270_powr__nonneg__iff, fact_148_of__nat__power__le__of__nat__cancel__iff, fact_196_Suc__leD, fact_194_le__SucI, fact_126_of__nat__1, fact_274_int__nat__eq, fact_297_nat__eq__iff2, fact_134_of__nat__le__iff, fact_166_numeral__power__le__of__nat__cancel__iff, fact_313_zero__neq__numeral, fact_144_of__nat__power, fact_139_of__nat__power__eq__of__nat__cancel__iff, fact_218_power__numeral, fact_349_nat__le__iff, fact_282_powr__one, fact_245_of__int__0, fact_230_d_I2_J, fact_22_of__int__eq__iff, fact_307_nat__0__le, fact_171_of__nat__mono, fact_33_ceiling__numeral, fact_120_of__nat__eq__1__iff, fact_329_Zero__neq__Suc, fact_285_of__nat__nat, fact_48_semiring__norm_I83_J, fact_104_numeral__powr__numeral__real, fact_122_of__nat__eq__1__iff, fact_347_powr__ge__pzero, fact_131_ceiling__of__nat, fact_272_int__eq__iff__numeral, fact_110_power__one__right, fact_39_nat__le__numeral__power__cancel__iff, fact_305_power__0__left, fact_226_power2__eq__iff__nonneg, fact_306_power__0__left, fact_249_of__int__eq__0__iff, fact_317_power__not__zero, fact_167_numeral__power__le__of__nat__cancel__iff, fact_117_power__one, fact_215_dbl__simps_I3_J, fact_237_of__nat__0__eq__iff, fact_50_numeral__le__iff, fact_290_power2__less__eq__zero__iff, fact_7_of__int__eq__numeral__power__cancel__iff, fact_295_nonneg__int__cases, fact_106_self__le__ge2__pow, fact_276_dbl__simps_I5_J, fact_206_lift__Suc__mono__le, fact_250_powr__eq__0__iff, fact_109_Suc__le__mono, fact_136_of__nat__numeral, fact_116_of__nat__eq__iff, fact_1_numeral__power__le__of__int__cancel__iff, fact_334_bot__nat__0_Oextremum__uniqueI, fact_56_semiring__norm_I71_J, fact_186_le__log2__of__power, fact_124_of__nat__1__eq__iff, fact_300_zero__reorient, fact_225_power2__eq__iff__nonneg, fact_114_old_Onat_Oinject, fact_97_le__num__One__iff, fact_314_zero__neq__numeral, fact_210_power__increasing, fact_336_le__0__eq, fact_331_old_Onat_Oexhaust, fact_269_powr__zero__eq__one, fact_267_power__zero__numeral, fact_77_of__int__le__1__iff, fact_189_full__nat__induct, fact_29_of__int__numeral, fact_9_of__int__le__of__int__power__cancel__iff, fact_67_of__int__1, fact_62_of__int__eq__1__iff, fact_51_numeral__le__iff, fact_127_of__nat__1, fact_207_lift__Suc__mono__le, fact_24_nat__numeral, fact_293_int__ops_I1_J, fact_94_verit__la__disequality, fact_172_of__nat__mono, fact_35_of__int__power__eq__of__int__cancel__iff, fact_18_of__int__power, fact_212_one__power2, fact_72_one__eq__numeral__iff, fact_30_of__int__numeral, fact_248_of__int__eq__0__iff, fact_292_nat__int__comparison_I1_J, fact_90_numeral__One, fact_150_of__nat__power__le__of__nat__cancel__iff, fact_216_dbl__simps_I3_J, fact_185_log2__of__power__eq, fact_209_power__increasing, fact_335_bot__nat__0_Oextremum__unique, fact_264_power__0__Suc, fact_176_n__not__Suc__n, fact_183_real__nat__ceiling__ge, fact_165_numeral__power__le__of__nat__cancel__iff, fact_324_nat__induct, fact_140_of__nat__power__eq__of__nat__cancel__iff, fact_191_Suc__n__not__le__n, fact_61_numeral__eq__iff, fact_254_nat__0__iff, fact_211_power__increasing, fact_36_numeral__power__eq__nat__cancel__iff, fact_147_Suc__1, fact_344_all__nat, fact_204_lift__Suc__mono__le, fact_173_numerals_I1_J, fact_52_numeral__le__iff, fact_41_ex__le__of__int, fact_188_nat__induct__at__least, fact_247_of__int__0__eq__iff, fact_346_powr__mono2, fact_69_numeral__eq__one__iff, fact_118_power__one, fact_121_of__nat__eq__1__iff, fact_132_of__nat__le__iff, fact_174_of__nat__ceiling, fact_337_less__eq__nat_Osimps_I1_J, fact_10_of__int__le__of__int__power__cancel__iff, fact_15_of__int__le__numeral__iff, fact_138_of__nat__power__eq__of__nat__cancel__iff, fact_6_numeral__power__eq__of__int__cancel__iff, fact_182_le__refl, fact_227_power2__eq__iff__nonneg, fact_96_verit__la__disequality, fact_266_power__zero__numeral, fact_224_powr__numeral, fact_220_order__refl, fact_291_int__if, fact_45_ceiling__le, fact_59_numeral__eq__iff, fact_283_powr__one__gt__zero__iff, fact_3_of__int__le__numeral__power__cancel__iff, fact_268_power__zero__numeral, fact_79_ceiling__le__one, fact_261_of__nat__le__0__iff, fact_98_two__realpow__ge__one, fact_321_old_Onat_Odistinct_I2_J, fact_119_power__one, fact_8_of__int__eq__numeral__power__cancel__iff, fact_128_of__nat__1, fact_286_zero__eq__power2, fact_43_ceiling__mono, fact_265_power__0__Suc, fact_88_one__le__numeral, fact_168_nat__one__as__int, fact_239_of__nat__eq__0__iff, fact_23_of__int__eq__iff, fact_322_old_Onat_Odistinct_I1_J, fact_233_of__nat__0, fact_70_numeral__eq__one__iff, fact_217_power__numeral, fact_93_verit__la__disequality, fact_31_of__int__eq__numeral__iff, fact_89_one__le__numeral, fact_21_of__int__eq__of__int__power__cancel__iff, fact_169_real__arch__simple, fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062, fact_34_of__int__power__eq__of__int__cancel__iff, fact_91_numeral__One, fact_178_nat__le__linear, fact_308_int__eq__iff, fact_198_one__le__power, fact_327_zero__induct, fact_58_verit__eq__simplify_I8_J, fact_240_of__nat__eq__0__iff, fact_153_of__nat__le__of__nat__power__cancel__iff, fact_242_power__Suc0__right, fact_241_power__Suc0__right, fact_12_of__int__power__le__of__int__cancel__iff, fact_95_verit__la__disequality, fact_312_le__numeral__extra_I3_J, fact_101_nat__numeral__as__int, fact_159_numeral__power__eq__of__nat__cancel__iff, fact_348_pow_Osimps_I1_J, fact_157_numeral__power__eq__of__nat__cancel__iff, fact_105_powr__one__eq__one, fact_338_less__eq__int__code_I1_J, fact_315_zero__neq__numeral, fact_341_zle__int, fact_44_ceiling__le__iff, fact_323_nat_OdiscI, fact_4_ceiling__numeral__power, fact_318_power__not__zero, fact_16_of__int__numeral__le__iff, fact_235_of__nat__0__eq__iff, fact_26_of__int__ceiling__cancel, fact_328_Suc__neq__Zero, fact_284_of__nat__nat, fact_60_numeral__eq__iff, fact_68_ceiling__one, fact_142_of__nat__eq__of__nat__power__cancel__iff, fact_243_power__Suc0__right, fact_112_power__one__right, fact_223_order__refl, fact_251_powr__0, fact_253_nat__le__0, fact_80_numeral__le__one__iff, fact_278_of__int__0__le__iff, fact_74_one__eq__numeral__iff, fact_177_Nat_Oex__has__greatest__nat, fact_175_Suc__inject, fact_133_of__nat__le__iff, fact_193_Suc__le__D
% 10.42/3.32 % No. of inferences in proof: 700
% 10.42/3.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2764 ms resp. 2105 ms w/o parsing
% 10.86/3.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.86/3.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------