TSTP Solution File: ITP097^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP097^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 07:47:48 EDT 2024
% Result : Theorem 21.13s 7.12s
% Output : Refutation 21.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 374
% Syntax : Number of formulae : 701 ( 301 unt; 49 typ; 0 def)
% Number of atoms : 1555 ( 598 equ; 6 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 5276 ( 90 ~; 17 |; 34 &;4575 @)
% ( 0 <=>; 560 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 101 ( 101 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 9 con; 0-4 aty)
% Number of variables : 1240 ( 28 ^1149 !; 26 ?;1240 :)
% ( 37 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
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(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(numeral_type,type,
numeral:
!>[TA: $tType] : $o ).
thf(power_type,type,
power:
!>[TA: $tType] : $o ).
thf(ring_1_type,type,
ring_1:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(ln_type,type,
ln:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(semiring_numeral_type,type,
semiring_numeral:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(archim1727834104eiling_type,type,
archim1727834104eiling:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(semiri134348788visors_type,type,
semiri134348788visors:
!>[TA: $tType] : $o ).
thf(archim1804426504_field_type,type,
archim1804426504_field:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(archimedean_ceiling_type,type,
archimedean_ceiling:
!>[TA: $tType] : ( TA > int ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(nat2_type,type,
nat2: int > nat ).
thf(ring_1_of_int_type,type,
ring_1_of_int:
!>[TA: $tType] : ( int > TA ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(neg_numeral_dbl_type,type,
neg_numeral_dbl:
!>[TA: $tType] : ( TA > TA ) ).
thf(bit0_type,type,
bit0: num > num ).
thf(one2_type,type,
one2: num ).
thf(numeral_numeral_type,type,
numeral_numeral:
!>[TA: $tType] : ( num > TA ) ).
thf(pow_type,type,
pow: num > num > num ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_type,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(log_type,type,
log: real > real > real ).
thf(powr_type,type,
powr:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(d_type,type,
d: int ).
thf(n_type,type,
n: nat ).
thf(259,axiom,
semiring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Osemiring__char__0_35) ).
thf(1036,plain,
semiring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(161,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_105_Nat_Oex__has__greatest__nat) ).
thf(760,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)],[161]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA,B: TA] :
( ( ( powr @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_powr__eq__0__iff) ).
thf(347,plain,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA,B: TA] :
( ( ( powr @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(221,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less_eq @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_of__int__power__le__of__int__cancel__iff) ).
thf(941,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less_eq @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(313,axiom,
( ( zero_zero @ nat )
= ( nat2 @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_nat__zero__as__int) ).
thf(1179,plain,
( ( zero_zero @ nat )
= ( nat2 @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(166,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: nat] : ( ord_less_eq @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_real__arch__simple) ).
thf(777,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: nat] : ( ord_less_eq @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_le__funE) ).
thf(645,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(205,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA )
=> ! [A: num,B: num] :
( ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ nat @ B ) )
= ( numeral_numeral @ TA @ ( pow @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_power__numeral) ).
thf(892,plain,
! [TA: $tType] :
( ( semiring_numeral @ TA )
=> ! [A: num,B: num] :
( ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ nat @ B ) )
= ( numeral_numeral @ TA @ ( pow @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(56,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_25) ).
thf(479,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(286,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ TA @ ( nat2 @ A ) )
= ( ring_1_of_int @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_of__nat__nat) ).
thf(1105,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ TA @ ( nat2 @ A ) )
= ( ring_1_of_int @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(213,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_115_transitive__stepwise__le) ).
thf(909,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)],[213]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_ord__le__eq__subst) ).
thf(628,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(256,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: num] :
( ( semiring_1_of_nat @ TA @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_of__nat__numeral) ).
thf(1031,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: num] :
( ( semiring_1_of_nat @ TA @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(278,axiom,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit0 @ A ) @ one2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_semiring__norm_I69_J) ).
thf(1083,plain,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit0 @ A ) @ one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(228,axiom,
! [A: int,B: nat] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ nat @ B @ ( nat2 @ A ) )
= ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_le__nat__iff) ).
thf(962,plain,
! [A: int,B: nat] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ nat @ B @ ( nat2 @ A ) )
= ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(481,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_dbl__simps_I2_J) ).
thf(352,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
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_150_nat__le__0) ).
thf(1200,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(245,axiom,
linordered_semidom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semidom_32) ).
thf(1005,plain,
linordered_semidom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(135,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_le0) ).
thf(683,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(271,axiom,
( ( ring_1_of_int @ real @ d )
= ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062) ).
thf(1068,plain,
( ( ring_1_of_int @ real @ d )
= ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(240,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( power_power @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A ) @ B )
=> ( ord_less_eq @ real @ ( semiring_1_of_nat @ real @ A ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_le__log2__of__power) ).
thf(994,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( power_power @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A ) @ B )
=> ( ord_less_eq @ real @ ( semiring_1_of_nat @ real @ A ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(274,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_int__ops_I1_J) ).
thf(1073,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(449,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(133,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_of__int__0__le__iff) ).
thf(677,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(104,axiom,
semiri134348788visors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors) ).
thf(597,plain,
semiri134348788visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(310,axiom,
linord1659791738miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(1173,plain,
linord1659791738miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(73,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_112_powr__powr__swap) ).
thf(523,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)],[73]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_linear) ).
thf(582,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(276,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( power_power @ nat @ A @ B ) )
= ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_of__nat__power) ).
thf(1078,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( power_power @ nat @ A @ B ) )
= ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(298,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_order__refl) ).
thf(1137,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(77,axiom,
power @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Power_Opower) ).
thf(533,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(85,axiom,
! [A: int,B: nat] :
( ( ord_less_eq @ nat @ ( nat2 @ A ) @ B )
= ( ord_less_eq @ int @ A @ ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_nat__le__iff) ).
thf(550,plain,
! [A: int,B: nat] :
( ( ord_less_eq @ nat @ ( nat2 @ A ) @ B )
= ( ord_less_eq @ int @ A @ ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(150,axiom,
! [A: real] : ( ord_less_eq @ real @ A @ ( semiring_1_of_nat @ real @ ( nat2 @ ( archimedean_ceiling @ real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_real__nat__ceiling__ge) ).
thf(715,plain,
! [A: real] : ( ord_less_eq @ real @ A @ ( semiring_1_of_nat @ real @ ( nat2 @ ( archimedean_ceiling @ real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(53,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( semiring_1_of_nat @ TA @ ( suc @ A ) )
!= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_of__nat__neq__0) ).
thf(472,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( semiring_1_of_nat @ TA @ ( suc @ A ) )
!= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(8,axiom,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA] :
( ( powr @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_powr__0) ).
thf(340,plain,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA] :
( ( powr @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(182,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int @ TA @ A )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( A
= ( power_power @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_of__int__power__eq__of__int__cancel__iff) ).
thf(829,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int @ TA @ A )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( A
= ( power_power @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(207,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_less__eq__int__code_I1_J) ).
thf(898,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(243,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: num,B: nat,C: nat] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B ) @ ( semiring_1_of_nat @ TA @ C ) )
= ( ord_less_eq @ nat @ ( power_power @ nat @ ( numeral_numeral @ nat @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_numeral__power__le__of__nat__cancel__iff) ).
thf(1001,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: num,B: nat,C: nat] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B ) @ ( semiring_1_of_nat @ TA @ C ) )
= ( ord_less_eq @ nat @ ( power_power @ nat @ ( numeral_numeral @ nat @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(168,axiom,
archim1727834104eiling @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Archimedean__Field_Ofloor__ceiling) ).
thf(782,plain,
archim1727834104eiling @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(187,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: num,C: nat] :
( ( ( ring_1_of_int @ TA @ A )
= ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( A
= ( power_power @ int @ ( numeral_numeral @ int @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_of__int__eq__numeral__power__cancel__iff) ).
thf(841,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: num,C: nat] :
( ( ( ring_1_of_int @ TA @ A )
= ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( A
= ( power_power @ int @ ( numeral_numeral @ int @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(92,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__mult_38) ).
thf(570,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(158,axiom,
! [A: num] :
( ( nat2 @ ( numeral_numeral @ int @ A ) )
= ( numeral_numeral @ nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_nat__numeral) ).
thf(751,plain,
! [A: num] :
( ( nat2 @ ( numeral_numeral @ int @ A ) )
= ( numeral_numeral @ nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(269,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_dbl__simps_I3_J) ).
thf(1059,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(99,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__mult) ).
thf(587,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(186,axiom,
! [A: int,B: nat] :
( ( ( nat2 @ A )
= B )
= ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( A
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( B
= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_nat__eq__iff) ).
thf(838,plain,
! [A: int,B: nat] :
( ( ( nat2 @ A )
= B )
= ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( A
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( B
= ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(218,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_order_Otrans) ).
thf(934,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(319,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ TA )
=> ! [A: TA,B: nat] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_power__not__zero) ).
thf(1191,plain,
! [TA: $tType] :
( ( semiri134348788visors @ TA )
=> ! [A: TA,B: nat] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(80,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder) ).
thf(542,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(46,axiom,
semiring_numeral @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Osemiring__numeral_7) ).
thf(460,plain,
semiring_numeral @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(88,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_numeral__eq__one__iff) ).
thf(559,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(248,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_24_nat__le__numeral__power__cancel__iff) ).
thf(1013,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)],[248]) ).
thf(200,axiom,
! [A: nat] : ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_two__realpow__ge__one) ).
thf(881,plain,
! [A: nat] : ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(284,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_124_Suc__leD) ).
thf(1100,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)],[284]) ).
thf(230,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: int] : ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_ex__le__of__int) ).
thf(969,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: int] : ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(108,axiom,
! [A: nat] :
( ( power_power @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_power__Suc__0) ).
thf(606,plain,
! [A: nat] :
( ( power_power @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(54,axiom,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA] :
( ( powr @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_powr__one__eq__one) ).
thf(475,plain,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA] :
( ( powr @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(171,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_le__cases3) ).
thf(789,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(102,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_order__class_Oorder_Oantisym) ).
thf(591,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(115,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_le__refl) ).
thf(623,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(60,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_of__nat__eq__0__iff) ).
thf(485,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(251,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_order__class_Oorder_Oeq__iff) ).
thf(1020,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(173,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ ( archimedean_ceiling @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_le__of__int__ceiling) ).
thf(806,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ ( archimedean_ceiling @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(229,axiom,
! [A: int] :
( ( ( nat2 @ A )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_nat__0__iff) ).
thf(966,plain,
! [A: int] :
( ( ( nat2 @ A )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(211,axiom,
! [A: real,B: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( powr @ real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_powr__ge__pzero) ).
thf(905,plain,
! [A: real,B: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( powr @ real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(266,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_one__eq__numeral__iff) ).
thf(1051,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_order__subst1) ).
thf(821,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(198,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_bot__nat__0_Oextremum__unique) ).
thf(877,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(226,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_semiring__norm_I87_J) ).
thf(956,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(42,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_26) ).
thf(453,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(165,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_power2__less__eq__zero__iff) ).
thf(774,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(237,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1_39) ).
thf(988,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(234,axiom,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Suc__n__not__le__n) ).
thf(981,plain,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(162,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_verit__eq__simplify_I8_J) ).
thf(766,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(75,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oone) ).
thf(529,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(82,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0) ).
thf(546,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_le__numeral__extra_I3_J) ).
thf(810,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_nat_OdiscI) ).
thf(381,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(78,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_117_full__nat__induct) ).
thf(534,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)],[78]) ).
thf(306,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_of__nat__0__le__iff) ).
thf(1163,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(324,axiom,
! [A: nat,B: int] :
( ( ( semiring_1_of_nat @ int @ A )
= B )
= ( ( A
= ( nat2 @ B ) )
& ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_int__eq__iff) ).
thf(1206,plain,
! [A: nat,B: int] :
( ( ( semiring_1_of_nat @ int @ A )
= B )
= ( ( A
= ( nat2 @ B ) )
& ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(41,axiom,
order @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oorder_21) ).
thf(452,plain,
order @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(262,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( zero_zero @ TA )
= ( ring_1_of_int @ TA @ A ) )
= ( A
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_of__int__0__eq__iff) ).
thf(1042,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( zero_zero @ TA )
= ( ring_1_of_int @ TA @ A ) )
= ( A
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(195,axiom,
! [A: num] :
( ( semiring_1_of_nat @ int @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_int__ops_I3_J) ).
thf(862,plain,
! [A: num] :
( ( semiring_1_of_nat @ int @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(311,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_23_numeral__power__le__nat__cancel__iff) ).
thf(1174,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)],[311]) ).
thf(105,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_numeral__eq__iff) ).
thf(598,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(34,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_205_old_Onat_Oinducts) ).
thf(424,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)],[34]) ).
thf(177,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: int] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ ( numeral_numeral @ int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__int__numeral__le__iff) ).
thf(815,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: int] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ ( numeral_numeral @ int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(50,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_of__nat__eq__iff) ).
thf(467,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(116,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: nat] :
( ( ring_1_of_int @ TA @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_of__int__of__nat__eq) ).
thf(625,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: nat] :
( ( ring_1_of_int @ TA @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(128,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less_eq @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_of__int__le__of__int__power__cancel__iff) ).
thf(665,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less_eq @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(47,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_23) ).
thf(461,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(63,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_of__nat__1) ).
thf(493,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(254,axiom,
preorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder_1) ).
thf(1027,plain,
preorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(160,axiom,
! [A: nat] :
( ( nat2 @ ( semiring_1_of_nat @ int @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_nat__int) ).
thf(757,plain,
! [A: nat] :
( ( nat2 @ ( semiring_1_of_nat @ int @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(147,axiom,
ord @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_3) ).
thf(710,plain,
ord @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(232,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_nonneg__int__cases) ).
thf(974,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(189,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: nat,C: int] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ 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(847,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: nat,C: int] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less_eq @ int @ ( power_power @ int @ ( numeral_numeral @ int @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(59,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_8) ).
thf(484,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(124,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_224_ex__nat) ).
thf(650,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)],[124]) ).
thf(250,axiom,
! [TA: $tType] :
( ( numeral @ TA )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_numeral__One) ).
thf(1017,plain,
! [TA: $tType] :
( ( numeral @ TA )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(292,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: int] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ceiling__le__iff) ).
thf(1121,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: int] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(288,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_169_powr__one) ).
thf(1111,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)],[288]) ).
thf(153,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_of__nat__le__0__iff) ).
thf(725,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(283,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_134_powr__numeral) ).
thf(1096,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)],[283]) ).
thf(246,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_226_eq__nat__nat__iff) ).
thf(1006,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)],[246]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(356,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(110,axiom,
! [A: real,B: nat] :
( ( ord_less_eq @ nat @ ( nat2 @ ( archimedean_ceiling @ real @ A ) ) @ B )
= ( ord_less_eq @ real @ A @ ( semiring_1_of_nat @ real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_nat__ceiling__le__eq) ).
thf(610,plain,
! [A: real,B: nat] :
( ( ord_less_eq @ nat @ ( nat2 @ ( archimedean_ceiling @ real @ A ) ) @ B )
= ( ord_less_eq @ real @ A @ ( semiring_1_of_nat @ real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(238,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: num] :
( ( ring_1_of_int @ TA @ ( numeral_numeral @ int @ A ) )
= ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_of__int__numeral) ).
thf(989,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: num] :
( ( ring_1_of_int @ TA @ ( numeral_numeral @ int @ A ) )
= ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(71,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_17) ).
thf(519,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(155,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_121_Suc__le__D) ).
thf(742,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)],[155]) ).
thf(197,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_73_Suc__le__mono) ).
thf(874,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)],[197]) ).
thf(301,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_of__nat__le__iff) ).
thf(1143,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(169,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B )
= ( semiring_1_of_nat @ TA @ C ) )
= ( ( power_power @ nat @ A @ B )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_of__nat__eq__of__nat__power__cancel__iff) ).
thf(783,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B )
= ( semiring_1_of_nat @ TA @ C ) )
= ( ( power_power @ nat @ A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(291,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_of__int__eq__0__iff) ).
thf(1118,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(202,axiom,
! [A: real] :
( ( log @ A @ ( one_one @ real ) )
= ( zero_zero @ real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_log__one) ).
thf(884,plain,
! [A: real] :
( ( log @ A @ ( one_one @ real ) )
= ( zero_zero @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(305,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_160_powr__nonneg__iff) ).
thf(1160,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)],[305]) ).
thf(255,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_of__int__le__iff) ).
thf(1028,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(61,axiom,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_One__nat__def) ).
thf(488,plain,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(7,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom_6) ).
thf(339,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(315,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_antisym__conv) ).
thf(1182,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(121,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( one_one @ nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_power__one__right) ).
thf(642,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( one_one @ nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(74,axiom,
! [A: num,B: nat] :
( ( ord_less_eq @ real @ ( numeral_numeral @ real @ A ) @ ( semiring_1_of_nat @ real @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_numeral__le__real__of__nat__iff) ).
thf(526,plain,
! [A: num,B: nat] :
( ( ord_less_eq @ real @ ( numeral_numeral @ real @ A ) @ ( semiring_1_of_nat @ real @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(119,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( power_power @ TA @ ( semiring_1_of_nat @ TA @ B ) @ C ) )
= ( ord_less_eq @ nat @ A @ ( power_power @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_of__nat__power__le__of__nat__cancel__iff) ).
thf(637,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( power_power @ TA @ ( semiring_1_of_nat @ TA @ B ) @ C ) )
= ( ord_less_eq @ nat @ A @ ( power_power @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(83,axiom,
one @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oone_48) ).
thf(547,plain,
one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(145,axiom,
order @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_40) ).
thf(706,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(328,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(52,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_18) ).
thf(471,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(209,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ num @ A @ one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_numeral__le__one__iff) ).
thf(901,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ num @ A @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(275,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
=> ( ord_less_eq @ nat @ B @ ( power_power @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_self__le__ge2__pow) ).
thf(1075,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
=> ( ord_less_eq @ nat @ B @ ( power_power @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(249,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0) ).
thf(1016,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(101,axiom,
preorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_36) ).
thf(590,plain,
preorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(289,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_118_not__less__eq__eq) ).
thf(1114,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)],[289]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_le__fun__def) ).
thf(647,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(141,axiom,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_int__ops_I2_J) ).
thf(701,plain,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(296,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_109_le__trans) ).
thf(1131,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)],[296]) ).
thf(44,axiom,
ord @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oord_22) ).
thf(457,plain,
ord @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(235,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_225_all__nat) ).
thf(984,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)],[235]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( A
= ( power_power @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ B ) )
=> ( ( semiring_1_of_nat @ real @ B )
= ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_log2__of__power__eq) ).
thf(721,plain,
! [A: nat,B: nat] :
( ( A
= ( power_power @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ B ) )
=> ( ( semiring_1_of_nat @ real @ B )
= ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(167,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( one_one @ TA ) )
= ( A
= ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_of__int__eq__1__iff) ).
thf(779,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( one_one @ TA ) )
= ( A
= ( one_one @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(107,axiom,
ln @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Transcendental_Oln) ).
thf(605,plain,
ln @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(9,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Zero__not__Suc) ).
thf(343,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(267,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_eq__refl) ).
thf(1054,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(309,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: nat] :
( ( archimedean_ceiling @ TA @ ( semiring_1_of_nat @ TA @ A ) )
= ( semiring_1_of_nat @ int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ceiling__of__nat) ).
thf(1170,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: nat] :
( ( archimedean_ceiling @ TA @ ( semiring_1_of_nat @ TA @ A ) )
= ( semiring_1_of_nat @ int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(258,axiom,
linord1659791738miring @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_31) ).
thf(1035,plain,
linord1659791738miring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(273,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_le__funD) ).
thf(1071,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(308,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: int] :
( ( archimedean_ceiling @ TA @ ( ring_1_of_int @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_ceiling__of__int) ).
thf(1167,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: int] :
( ( archimedean_ceiling @ TA @ ( ring_1_of_int @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(76,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_39_semiring__norm_I71_J) ).
thf(530,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)],[76]) ).
thf(127,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: num] :
( ( archimedean_ceiling @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_ceiling__numeral) ).
thf(662,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: num] :
( ( archimedean_ceiling @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(215,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_one__le__numeral) ).
thf(926,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(279,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_power__mono) ).
thf(1086,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(220,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_120_le__Suc__eq) ).
thf(938,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)],[220]) ).
thf(317,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semidom) ).
thf(1187,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(132,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ( ( archimedean_ceiling @ TA @ ( one_one @ TA ) )
= ( one_one @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_ceiling__one) ).
thf(674,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ( ( archimedean_ceiling @ TA @ ( one_one @ TA ) )
= ( one_one @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(225,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( one_one @ int ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_of__int__1__le__iff) ).
thf(953,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(316,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_zero__le) ).
thf(1185,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(302,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_bot__nat__0_Oextremum) ).
thf(1146,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(180,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_of__nat__mono) ).
thf(824,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(156,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_68_numeral__powr__numeral__real) ).
thf(745,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)],[156]) ).
thf(94,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ int @ A @ ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_of__int__le__1__iff) ).
thf(573,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ int @ A @ ( one_one @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(21,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( one_one @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( A
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_of__nat__1__eq__iff) ).
thf(375,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( one_one @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( A
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_eq__imp__le) ).
thf(601,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(98,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_power__one) ).
thf(584,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(33,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder_10) ).
thf(423,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(164,axiom,
( ( suc @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Suc__1) ).
thf(772,plain,
( ( suc @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(96,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( power_power @ TA @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( power_power @ TA @ B @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) )
= ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_power2__eq__iff__nonneg) ).
thf(579,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( power_power @ TA @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( power_power @ TA @ B @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) )
= ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(293,axiom,
( ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) )
= ( ring_1_of_int @ real @ ( power_power @ int @ ( numeral_numeral @ int @ ( bit0 @ one2 ) ) @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66__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(1124,plain,
( ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) )
= ( ring_1_of_int @ real @ ( power_power @ int @ ( numeral_numeral @ int @ ( bit0 @ one2 ) ) @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(89,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_power__increasing) ).
thf(562,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(210,axiom,
neg_numeral @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Oneg__numeral_41) ).
thf(904,plain,
neg_numeral @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(181,axiom,
! [A: nat,B: num] :
( ( ( semiring_1_of_nat @ int @ A )
= ( numeral_numeral @ int @ B ) )
= ( A
= ( numeral_numeral @ nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_int__eq__iff__numeral) ).
thf(826,plain,
! [A: nat,B: num] :
( ( ( semiring_1_of_nat @ int @ A )
= ( numeral_numeral @ int @ B ) )
= ( A
= ( numeral_numeral @ nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(148,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_not__numeral__le__zero) ).
thf(711,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(268,axiom,
numeral @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Onumeral_46) ).
thf(1058,plain,
numeral @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(281,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_of__int__le__0__iff) ).
thf(1090,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(143,axiom,
neg_numeral @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Oneg__numeral) ).
thf(704,plain,
neg_numeral @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(223,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_170_powr__one__gt__zero__iff) ).
thf(947,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)],[223]) ).
thf(11,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(350,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,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_192_exists__least__lemma) ).
thf(391,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)],[26]) ).
thf(299,axiom,
ring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__1) ).
thf(1139,plain,
ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(39,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Suc__neq__Zero) ).
thf(445,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(219,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_one__le__power) ).
thf(936,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(149,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_lift__Suc__antimono__le) ).
thf(713,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(498,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(320,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num,B: nat,C: int] :
( ( ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B )
= ( ring_1_of_int @ TA @ C ) )
= ( ( power_power @ int @ ( numeral_numeral @ int @ A ) @ B )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_numeral__power__eq__of__int__cancel__iff) ).
thf(1194,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num,B: nat,C: int] :
( ( ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B )
= ( ring_1_of_int @ TA @ C ) )
= ( ( power_power @ int @ ( numeral_numeral @ int @ A ) @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(325,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ TA )
=> ! [A: TA] :
( ( ( power_power @ TA @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_zero__eq__power2) ).
thf(1209,plain,
! [TA: $tType] :
( ( semiri134348788visors @ TA )
=> ! [A: TA] :
( ( ( power_power @ TA @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(290,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom_33) ).
thf(1117,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Suc__inject) ).
thf(419,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(264,axiom,
numeral @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Onumeral) ).
thf(1048,plain,
numeral @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(241,axiom,
! [A: num] :
( ( pow @ A @ one2 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_pow_Osimps_I1_J) ).
thf(996,plain,
! [A: num] :
( ( pow @ A @ one2 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(91,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_nat__0__le) ).
thf(567,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(112,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(616,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(70,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_197_nat__induct) ).
thf(509,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)],[70]) ).
thf(199,axiom,
power @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Power_Opower_45) ).
thf(880,plain,
power @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(35,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_of__nat__0) ).
thf(434,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(204,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_122_le__SucI) ).
thf(890,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)],[204]) ).
thf(25,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_nat_Odistinct_I1_J) ).
thf(387,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(193,axiom,
ord @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_43) ).
thf(858,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(109,axiom,
ring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__1_44) ).
thf(609,plain,
ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(103,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ( ( archimedean_ceiling @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_ceiling__zero) ).
thf(594,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ( ( archimedean_ceiling @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(114,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_nat__int__comparison_I1_J) ).
thf(621,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(58,axiom,
power @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Power_Opower_15) ).
thf(483,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(206,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int,B: nat] :
( ( ring_1_of_int @ TA @ ( power_power @ int @ A @ B ) )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_of__int__power) ).
thf(895,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int,B: nat] :
( ( ring_1_of_int @ TA @ ( power_power @ int @ A @ B ) )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) @ ( semiring_1_of_nat @ TA @ C ) )
= ( ord_less_eq @ nat @ ( power_power @ nat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_of__nat__le__of__nat__power__cancel__iff) ).
thf(769,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) @ ( semiring_1_of_nat @ TA @ C ) )
= ( ord_less_eq @ nat @ ( power_power @ nat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(129,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: num,C: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( A
= ( power_power @ nat @ ( numeral_numeral @ nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_real__of__nat__eq__numeral__power__cancel__iff) ).
thf(668,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: num,C: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( A
= ( power_power @ nat @ ( numeral_numeral @ nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(312,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_less__eq__nat_Osimps_I1_J) ).
thf(1177,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(140,axiom,
semiring_numeral @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Osemiring__numeral_34) ).
thf(700,plain,
semiring_numeral @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(72,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: num] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( numeral_numeral @ int @ B ) )
= ( ord_less_eq @ TA @ A @ ( numeral_numeral @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ceiling__le__numeral) ).
thf(520,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: num] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( numeral_numeral @ int @ B ) )
= ( ord_less_eq @ TA @ A @ ( numeral_numeral @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(136,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( zero_zero @ int ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_ceiling__le__zero) ).
thf(685,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( zero_zero @ int ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(227,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: num,C: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( ord_less_eq @ nat @ A @ ( power_power @ nat @ ( numeral_numeral @ nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_of__nat__le__numeral__power__cancel__iff) ).
thf(959,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: num,C: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( ord_less_eq @ nat @ A @ ( power_power @ nat @ ( numeral_numeral @ nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(138,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_verit__eq__simplify_I10_J) ).
thf(695,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(201,axiom,
ord_less_eq @ real @ ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) @ ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67__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(883,plain,
ord_less_eq @ real @ ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) @ ( powr @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( semiring_1_of_nat @ real @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(236,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( archimedean_ceiling @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_ceiling__mono) ).
thf(986,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( archimedean_ceiling @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(191,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ord__le__eq__trans) ).
thf(851,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(285,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( zero_zero @ int ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_of__int__0) ).
thf(1102,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( zero_zero @ int ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(69,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_199_diff__induct) ).
thf(505,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)],[69]) ).
thf(37,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_old_Onat_Odistinct_I2_J) ).
thf(438,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(257,axiom,
linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_37) ).
thf(1034,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(62,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(490,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(323,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( one_one @ int ) )
= ( ord_less_eq @ TA @ A @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_ceiling__le__one) ).
thf(1203,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ ( one_one @ int ) )
= ( ord_less_eq @ TA @ A @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(222,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_107_le__antisym) ).
thf(944,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)],[222]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_int__int__eq) ).
thf(680,plain,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(84,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_25_nat__mono) ).
thf(548,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)],[84]) ).
thf(20,axiom,
preorder @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Opreorder_19) ).
thf(374,plain,
preorder @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(297,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_dbl__simps_I5_J) ).
thf(1134,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(176,axiom,
! [A: nat,B: int] :
( ( A
= ( nat2 @ B ) )
= ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( B
= ( semiring_1_of_nat @ int @ A ) ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( A
= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_nat__eq__iff2) ).
thf(812,plain,
! [A: nat,B: int] :
( ( A
= ( nat2 @ B ) )
= ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( B
= ( semiring_1_of_nat @ int @ A ) ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( A
= ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(277,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: int] :
( ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ B ) )
=> ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ceiling__le) ).
thf(1081,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA,B: int] :
( ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ B ) )
=> ( ord_less_eq @ int @ ( archimedean_ceiling @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(113,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_semiring__norm_I83_J) ).
thf(617,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(14,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_29) ).
thf(355,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(159,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: num,C: nat] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( ord_less_eq @ int @ A @ ( power_power @ int @ ( numeral_numeral @ int @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_of__int__le__numeral__power__cancel__iff) ).
thf(754,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: num,C: nat] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( ord_less_eq @ int @ A @ ( power_power @ int @ ( numeral_numeral @ int @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(86,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_123_le__SucE) ).
thf(553,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)],[86]) ).
thf(185,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_lift__Suc__mono__le) ).
thf(836,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(265,axiom,
! [A: num] : ( ord_less_eq @ num @ one2 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_semiring__norm_I68_J) ).
thf(1049,plain,
! [A: num] : ( ord_less_eq @ num @ one2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(458,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(314,axiom,
order @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_2) ).
thf(1181,plain,
order @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(192,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( suc @ ( zero_zero @ nat ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_power__Suc0__right) ).
thf(855,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( suc @ ( zero_zero @ nat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(120,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_106_nat__le__linear) ).
thf(640,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)],[120]) ).
thf(253,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( power_power @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_power2__nat__le__imp__le) ).
thf(1025,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( power_power @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(272,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(1070,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(144,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_47) ).
thf(705,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(146,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_le__zero__eq) ).
thf(707,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(203,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_22_nat__eq__numeral__power__cancel__iff) ).
thf(887,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)],[203]) ).
thf(1,conjecture,
ord_less_eq @ int @ d @ ( power_power @ int @ ( numeral_numeral @ int @ ( bit0 @ one2 ) ) @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( 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 @ one2 ) ) @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(327,plain,
~ ( ord_less_eq @ int @ d @ ( power_power @ int @ ( numeral_numeral @ int @ ( bit0 @ one2 ) ) @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_27) ).
thf(414,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(231,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( A
= ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_zero__le__imp__eq__int) ).
thf(971,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( A
= ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(131,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_42) ).
thf(673,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(261,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ord__eq__le__trans) ).
thf(1038,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(151,axiom,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_semiring__norm_I85_J) ).
thf(717,plain,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(68,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_old_Onat_Oinject) ).
thf(502,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(463,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(174,axiom,
( ( nat2 @ ( one_one @ int ) )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_nat__1) ).
thf(808,plain,
( ( nat2 @ ( one_one @ int ) )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(16,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Zero__neq__Suc) ).
thf(359,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(212,axiom,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_numerals_I1_J) ).
thf(907,plain,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(4,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(331,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(318,axiom,
! [TA: $tType] :
( ( power @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_power__0) ).
thf(1188,plain,
! [TA: $tType] :
( ( power @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(51,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_9) ).
thf(470,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: num] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ int @ A @ ( numeral_numeral @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_of__int__le__numeral__iff) ).
thf(576,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: num] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ int @ A @ ( numeral_numeral @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(6,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_not0__implies__Suc) ).
thf(336,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(142,axiom,
semiri134348788visors @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_30) ).
thf(703,plain,
semiri134348788visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(252,axiom,
( ( one_one @ nat )
= ( nat2 @ ( one_one @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_nat__one__as__int) ).
thf(1023,plain,
( ( one_one @ nat )
= ( nat2 @ ( one_one @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(111,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_eq__iff) ).
thf(613,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(93,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_nat__int__comparison_I3_J) ).
thf(571,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(65,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_28) ).
thf(497,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(194,axiom,
! [A: num] :
( ( ord_less_eq @ num @ A @ one2 )
= ( A = one2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_le__num__One__iff) ).
thf(859,plain,
! [A: num] :
( ( ord_less_eq @ num @ A @ one2 )
= ( A = one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(24,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_12) ).
thf(386,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(233,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_numeral__le__iff) ).
thf(978,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(300,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_153_nat__power__eq__Suc__0__iff) ).
thf(1140,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)],[300]) ).
thf(49,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_24) ).
thf(465,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(130,axiom,
( ( numeral_numeral @ nat )
= ( ^ [A: num] : ( nat2 @ ( numeral_numeral @ int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nat__numeral__as__int) ).
thf(671,plain,
( ( numeral_numeral @ nat )
= ( ^ [A: num] : ( nat2 @ ( numeral_numeral @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(304,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_227_powr__mono2) ).
thf(1157,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)],[304]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_ord__eq__le__subst) ).
thf(688,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(294,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: num,B: nat] :
( ( archimedean_ceiling @ TA @ ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B ) )
= ( power_power @ int @ ( numeral_numeral @ int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ceiling__numeral__power) ).
thf(1126,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: num,B: nat] :
( ( archimedean_ceiling @ TA @ ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B ) )
= ( power_power @ int @ ( numeral_numeral @ int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(247,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_128_powr__mono) ).
thf(1010,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)],[247]) ).
thf(188,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_one__power2) ).
thf(844,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(287,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_verit__la__disequality) ).
thf(1108,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(17,axiom,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_powr__zero__eq__one) ).
thf(363,plain,
! [TA: $tType] :
( ( ln @ TA )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(87,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_63_verit__la__generic) ).
thf(556,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)],[87]) ).
thf(217,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( one_one @ int ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_of__int__1) ).
thf(931,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( one_one @ int ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(79,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( power_power @ TA @ ( semiring_1_of_nat @ TA @ B ) @ C ) )
= ( A
= ( power_power @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_of__nat__power__eq__of__nat__cancel__iff) ).
thf(539,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat,C: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( power_power @ TA @ ( semiring_1_of_nat @ TA @ B ) @ C ) )
= ( A
= ( power_power @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(157,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( ring_1_of_int @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_of__int__eq__iff) ).
thf(748,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( ring_1_of_int @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(270,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_power__0__left) ).
thf(1062,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(100,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_le__cases) ).
thf(588,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(139,axiom,
ord_less @ int @ ( zero_zero @ int ) @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_d_I2_J) ).
thf(699,plain,
ord_less @ int @ ( zero_zero @ int ) @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(125,axiom,
! [A: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= A ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_int__nat__eq) ).
thf(652,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= A ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(12,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_5) ).
thf(351,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(31,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_13) ).
thf(418,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(170,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B )
= ( ring_1_of_int @ TA @ C ) )
= ( ( power_power @ int @ A @ B )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__int__eq__of__int__power__cancel__iff) ).
thf(786,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B )
= ( ring_1_of_int @ TA @ C ) )
= ( ( power_power @ int @ A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(22,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_zero__reorient) ).
thf(378,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(55,axiom,
numeral @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral_16) ).
thf(478,plain,
numeral @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(326,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_zle__int) ).
thf(1212,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(208,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_of__int__nonneg) ).
thf(899,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(183,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_bot__nat__0_Oextremum__uniqueI) ).
thf(832,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(263,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_21_numeral__power__eq__nat__cancel__iff) ).
thf(1045,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)],[263]) ).
thf(242,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_zero__le__power) ).
thf(999,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(28,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_old_Onat_Odistinct_I1_J) ).
thf(410,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(178,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_antisym) ).
thf(818,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(303,axiom,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_int__if) ).
thf(1148,plain,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(196,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_56_complete__real) ).
thf(865,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)],[196]) ).
thf(19,axiom,
semiri134348788visors @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_4) ).
thf(373,plain,
semiri134348788visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(224,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] :
( ( ( ring_1_of_int @ TA @ ( archimedean_ceiling @ TA @ A ) )
= A )
= ( ? [B: int] :
( A
= ( ring_1_of_int @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_of__int__ceiling__cancel) ).
thf(950,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] :
( ( ( ring_1_of_int @ TA @ ( archimedean_ceiling @ TA @ A ) )
= A )
= ( ? [B: int] :
( A
= ( ring_1_of_int @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(184,axiom,
ord_less_eq @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( one_one @ real ) ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31__092_060open_062log_A2_A1_A_092_060le_062_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062) ).
thf(835,plain,
ord_less_eq @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( one_one @ real ) ) @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(90,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num,B: nat,C: nat] :
( ( ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B )
= ( semiring_1_of_nat @ TA @ C ) )
= ( ( power_power @ nat @ ( numeral_numeral @ nat @ A ) @ B )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_numeral__power__eq__of__nat__cancel__iff) ).
thf(564,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num,B: nat,C: nat] :
( ( ( power_power @ TA @ ( numeral_numeral @ TA @ A ) @ B )
= ( semiring_1_of_nat @ TA @ C ) )
= ( ( power_power @ nat @ ( numeral_numeral @ nat @ A ) @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(36,axiom,
linorder @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Olinorder_20) ).
thf(437,plain,
linorder @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_le__funI) ).
thf(635,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(307,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( semiring_1_of_nat @ TA @ ( nat2 @ ( archimedean_ceiling @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_of__nat__ceiling) ).
thf(1165,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( semiring_1_of_nat @ TA @ ( nat2 @ ( archimedean_ceiling @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(27,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_200_zero__induct) ).
thf(400,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)],[27]) ).
thf(321,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_order__subst2) ).
thf(1197,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(216,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_zero__neq__numeral) ).
thf(928,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(30,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( one_one @ TA ) )
= ( A
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_of__nat__eq__1__iff) ).
thf(415,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( one_one @ TA ) )
= ( A
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(282,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_le__0__eq) ).
thf(1093,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(154,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_116_nat__induct__at__least) ).
thf(728,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)],[154]) ).
thf(239,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_le__numeral__extra_I4_J) ).
thf(992,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(190,axiom,
archim1804426504_field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field) ).
thf(850,plain,
archim1804426504_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(244,axiom,
semiring_numeral @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Osemiring__numeral) ).
thf(1004,plain,
semiring_numeral @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(38,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_of__nat__0__eq__iff) ).
thf(442,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(67,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_14) ).
thf(501,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(18,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_n__not__Suc__n) ).
thf(369,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_old_Onat_Oexhaust) ).
thf(332,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(295,axiom,
( n
= ( suc @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_n__def) ).
thf(1129,plain,
( n
= ( suc @ ( nat2 @ ( archimedean_ceiling @ real @ ( log @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ ( ring_1_of_int @ real @ d ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(172,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: num] :
( ( ( ring_1_of_int @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A
= ( numeral_numeral @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_of__int__eq__numeral__iff) ).
thf(803,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: num] :
( ( ( ring_1_of_int @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A
= ( numeral_numeral @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(214,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( zero_zero @ TA ) @ ( suc @ A ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_power__0__Suc) ).
thf(923,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( zero_zero @ TA ) @ ( suc @ A ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( power_power @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( power_power @ nat @ B @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_power2__nat__le__eq__le) ).
thf(659,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( power_power @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( power_power @ nat @ B @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(81,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: num] :
( ( power_power @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ nat @ A ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_power__zero__numeral) ).
thf(543,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: num] :
( ( power_power @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ nat @ A ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(260,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(1037,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(280,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_zero__le__numeral) ).
thf(1088,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(64,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult_11) ).
thf(496,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_nat_Oinject) ).
thf(454,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1221,plain,
$false,
inference(e,[status(thm)],[1036,760,347,941,1179,777,645,892,479,1105,909,628,1031,1083,962,481,352,1200,1005,683,1068,994,1073,449,677,597,1173,523,582,1078,1137,533,550,715,472,340,829,898,1001,782,841,570,751,1059,587,838,934,1191,542,460,559,1013,881,1100,969,606,475,789,591,623,485,1020,806,966,905,1051,821,877,956,453,774,988,981,766,529,546,810,381,534,1163,1206,452,1042,862,1174,598,424,815,467,625,665,461,493,1027,757,710,974,847,484,650,1017,1121,1111,725,1096,1006,356,610,989,519,742,874,1143,783,1118,884,1160,1028,488,339,1182,642,526,637,547,706,328,471,901,1075,1016,590,1114,647,701,1131,457,984,721,779,605,343,1054,1170,1035,1071,1167,530,662,926,1086,938,1187,674,953,1185,1146,824,745,573,375,601,584,423,772,579,1124,562,904,826,711,1058,1090,704,947,350,391,1139,445,936,713,498,1194,1209,1117,419,1048,996,567,616,509,880,434,890,387,858,609,594,621,483,895,769,668,1177,700,520,685,959,695,883,986,851,1102,505,438,1034,490,1203,944,680,548,374,1134,812,1081,617,355,754,553,836,1049,458,1181,855,640,1025,1070,705,707,887,327,414,971,673,1038,717,502,463,808,359,907,331,1188,470,576,336,703,1023,613,571,497,859,386,978,1140,465,671,1157,688,1126,1010,844,1108,363,556,931,539,748,1062,588,699,652,351,418,786,378,478,1212,899,832,1045,999,410,818,1148,865,373,950,835,564,437,635,1165,400,1197,928,415,1093,728,992,850,1004,442,501,369,332,1129,803,923,659,543,1037,1088,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : ITP097^2 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.18 % Command : run_Leo-III %s %d
% 0.18/0.40 % Computer : n002.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Mon May 6 14:38:24 EDT 2024
% 0.18/0.40 % CPUTime :
% 1.00/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.14 % [INFO] Parsing done (244ms).
% 1.61/1.15 % [INFO] Running in sequential loop mode.
% 2.65/1.37 % [INFO] eprover registered as external prover.
% 2.65/1.37 % [INFO] cvc4 registered as external prover.
% 2.65/1.38 % [INFO] Scanning for conjecture ...
% 2.94/1.48 % [INFO] Found a conjecture and 325 axioms. Running axiom selection ...
% 3.25/1.59 % [INFO] Axiom selection finished. Selected 324 axioms (removed 1 axioms).
% 3.98/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 3.98/1.76 % [INFO] Type checking passed.
% 3.98/1.76 % [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 ...
% 21.13/7.11 % External prover 'e' found a proof!
% 21.13/7.11 % [INFO] Killing All external provers ...
% 21.13/7.11 % Time passed: 6549ms (effective reasoning time: 5956ms)
% 21.13/7.11 % 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)>
% 21.13/7.12 % Axioms used in derivation (324): fact_208_bot__nat__0_Oextremum__unique, tcon_Real_Oreal___Rings_Osemiring__1_39, fact_124_Suc__leD, fact_178_nonneg__int__cases, fact_192_exists__least__lemma, fact_93_numeral__power__eq__of__nat__cancel__iff, fact_140_of__nat__0, tcon_Real_Oreal___Groups_Ozero_47, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_5, fact_96_of__nat__le__numeral__power__cancel__iff, tcon_Int_Oint___Rings_Olinordered__semidom, fact_128_powr__mono, fact_146_of__int__eq__0__iff, fact_33_semiring__norm_I83_J, fact_122_le__SucI, fact_79_of__nat__eq__1__iff, fact_95_nat__ceiling__le__eq, fact_215_zle__int, fact_227_powr__mono2, fact_5_of__int__le__of__int__power__cancel__iff, fact_22_nat__eq__numeral__power__cancel__iff, fact_51_one__eq__numeral__iff, fact_198_One__nat__def, fact_242_eq__refl, fact_165_dbl__simps_I5_J, fact_125_one__le__power, fact_117_full__nat__induct, fact_13_nat__numeral, fact_224_ex__nat, tcon_Nat_Onat___Orderings_Oord_14, fact_213_of__int__nonneg, fact_167_of__int__le__0__iff, tcon_Real_Oreal___Num_Osemiring__numeral_34, fact_109_le__trans, fact_14_ceiling__of__int, fact_78_power__one, tcon_Int_Oint___Groups_Ozero, fact_102_of__nat__ceiling, fact_232_le__funE, fact_239_eq__iff, tcon_Int_Oint___Orderings_Oorder_2, tcon_Real_Oreal___Num_Oneg__numeral_41, fact_234_le__fun__def, tcon_Num_Onum___Orderings_Olinorder_20, tcon_HOL_Obool___Orderings_Opreorder_26, fact_225_all__nat, fact_138_d_I2_J, tcon_Int_Oint___Nat_Oring__char__0, fact_4_of__int__eq__numeral__power__cancel__iff, fact_243_le__cases, fact_246_antisym__conv, fact_214_nat__int__comparison_I3_J, fact_241_linear, fact_212_le__nat__iff, fact_174_int__if, fact_39_semiring__norm_I71_J, fact_185_power__0__left, fact_179_int__int__eq, fact_164_int__nat__eq, fact_17_of__int__numeral, tcon_Int_Oint___Groups_Omonoid__mult, tcon_fun___Orderings_Oord, fact_154_nat__int, tcon_Int_Oint___Rings_Oring__1, fact_87_of__nat__eq__of__nat__power__cancel__iff, fact_16_of__int__le__iff, fact_247_order__class_Oorder_Oeq__iff, fact_60_verit__la__disequality, fact_49_ceiling__one, fact_0_numeral__power__le__of__int__cancel__iff, fact_67__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_10_of__int__power, fact_153_nat__power__eq__Suc__0__iff, tcon_Real_Oreal___Rings_Olinordered__semidom_32, fact_135_power2__eq__iff__nonneg, fact_80_of__nat__1__eq__iff, fact_196_nat_OdiscI, tcon_Real_Oreal___Orderings_Oorder_40, fact_216_int__ops_I3_J, fact_161_nat__1, fact_197_nat__induct, fact_150_nat__le__0, fact_155_dbl__simps_I2_J, fact_59_numeral__One, tcon_Nat_Onat___Orderings_Oorder_13, fact_19_ceiling__numeral, fact_30_ceiling__le, fact_32_semiring__norm_I69_J, fact_130_one__power2, fact_194_old_Onat_Odistinct_I2_J, fact_29_ceiling__le__iff, fact_177_zero__le__imp__eq__int, tcon_Nat_Onat___Nat_Osemiring__char__0_8, fact_220_zero__le__power, fact_156_of__nat__le__0__iff, fact_63_verit__la__generic, fact_160_powr__nonneg__iff, fact_65_nat__numeral__as__int, fact_186_nat__0__le, fact_57_le__numeral__extra_I4_J, fact_162_int__eq__iff__numeral, fact_151_nat__0__iff, tcon_Int_Oint___Orderings_Opreorder_1, fact_55_numeral__le__one__iff, fact_86_of__nat__power__eq__of__nat__cancel__iff, fact_98_nat__one__as__int, fact_64_verit__eq__simplify_I10_J, fact_62_two__realpow__ge__one, fact_183_zero__le, fact_105_Nat_Oex__has__greatest__nat, fact_69_powr__one__eq__one, fact_126_lift__Suc__antimono__le, fact_35_numeral__le__iff, fact_127_lift__Suc__mono__le, fact_101_numerals_I1_J, fact_48_of__int__1, fact_6_of__int__power__le__of__int__cancel__iff, fact_145_of__int__0__eq__iff, fact_132_power__numeral, fact_113_log2__of__power__eq, fact_228_powr__ge__pzero, fact_249_ord__le__eq__trans, fact_237_ord__eq__le__subst, tcon_Nat_Onat___Orderings_Olinorder_10, tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_30, fact_245_le__cases3, fact_139_le__zero__eq, tcon_Nat_Onat___Rings_Osemiring__1_12, fact_34_semiring__norm_I85_J, fact_103_Suc__inject, fact_157_power__0__Suc, fact_170_powr__one__gt__zero__iff, fact_141_of__nat__0__eq__iff, fact_171_of__nat__nat, tcon_Real_Oreal___Power_Opower_45, help_If_1_1_T, fact_248_ord__eq__le__trans, tcon_Int_Oint___Num_Onumeral, fact_233_le__funI, fact_25_nat__mono, fact_52_of__int__1__le__iff, fact_77_of__nat__eq__iff, fact_191_power__not__zero, tcon_HOL_Obool___Orderings_Oorder_28, fact_100_of__nat__mono, tcon_Nat_Onat___Groups_Ozero_17, fact_104_n__not__Suc__n, tcon_Set_Oset___Orderings_Opreorder_23, tcon_Int_Oint___Rings_Olinordered__idom, fact_70_self__le__ge2__pow, fact_112_powr__powr__swap, tcon_Nat_Onat___Groups_Oone_18, tcon_Real_Oreal___Nat_Oring__char__0_42, fact_24_nat__le__numeral__power__cancel__iff, fact_193_nat_Odistinct_I1_J, fact_147_powr__eq__0__iff, fact_189_le__numeral__extra_I3_J, tcon_Int_Oint___Orderings_Olinorder, fact_9_of__int__numeral__le__iff, fact_240_antisym, fact_223_of__nat__neq__0, fact_176_int__ops_I1_J, fact_133_order__refl, fact_28_ceiling__mono, fact_226_eq__nat__nat__iff, fact_184_nat__zero__as__int, fact_56_complete__real, fact_202_Zero__neq__Suc, fact_175_nat__int__comparison_I1_J, fact_187_int__eq__iff, fact_222_power__0, tcon_Real_Oreal___Nat_Osemiring__char__0_35, tcon_Int_Oint___Power_Opower, fact_144_of__int__0, fact_43_of__int__eq__1__iff, fact_158_power__zero__numeral, tcon_Int_Oint___Rings_Osemiring__1, fact_231_le__funD, tcon_Num_Onum___Orderings_Oorder_21, fact_110_le__refl, fact_85_of__nat__numeral, fact_115_transitive__stepwise__le, fact_235_order__subst1, fact_195_old_Onat_Odistinct_I1_J, fact_84_of__nat__le__iff, tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_4, fact_206_not0__implies__Suc, fact_120_le__Suc__eq, fact_221_of__nat__0__le__iff, fact_88_of__nat__power, fact_209_le__0__eq, fact_152_power__Suc__0, tcon_Real_Oreal___Groups_Omonoid__mult_38, fact_163_log__one, tcon_Real_Oreal___Archimedean__Field_Ofloor__ceiling, fact_38_semiring__norm_I68_J, fact_181_nat__eq__iff, fact_166_of__int__0__le__iff, fact_72_power2__nat__le__imp__le, fact_108_eq__imp__le, fact_99_real__arch__simple, fact_168_ceiling__le__zero, tcon_Nat_Onat___Rings_Olinordered__semidom_6, help_If_3_1_T, fact_68_numeral__powr__numeral__real, help_If_2_1_T, fact_238_ord__le__eq__subst, tcon_Int_Oint___Num_Oneg__numeral, fact_143_power__Suc0__right, fact_54_ceiling__le__one, fact_20_of__int__power__eq__of__int__cancel__iff, fact_244_order_Otrans, fact_31__092_060open_062log_A2_A1_A_092_060le_062_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062, fact_42_numeral__eq__iff, fact_190_zero__neq__numeral, fact_204_old_Onat_Oexhaust, tcon_Num_Onum___Orderings_Opreorder_19, tcon_Real_Oreal___Transcendental_Oln, fact_76_old_Onat_Oinject, fact_211_less__eq__int__code_I1_J, fact_123_le__SucE, fact_116_nat__induct__at__least, tcon_Nat_Onat___Groups_Omonoid__mult_11, fact_61_le__num__One__iff, fact_21_numeral__power__eq__nat__cancel__iff, fact_136_le0, fact_230_nat__le__iff, fact_200_zero__induct, fact_12_of__int__eq__iff, fact_172_zero__eq__power2, fact_97_numeral__power__le__of__nat__cancel__iff, fact_218_not__numeral__le__zero, fact_11_of__int__eq__of__int__power__cancel__iff, tcon_HOL_Obool___Orderings_Olinorder_27, fact_159_powr__zero__eq__one, fact_75_nat_Oinject, fact_15_of__int__ceiling__cancel, fact_106_nat__le__linear, fact_53_of__int__le__1__iff, tcon_Real_Oreal___Num_Onumeral_46, tcon_Real_Oreal___Groups_Oone_48, fact_37_n__def, tcon_fun___Orderings_Opreorder, fact_217_zero__le__numeral, fact_250_order__class_Oorder_Oantisym, fact_119_Suc__n__not__le__n, fact_45_Collect__mem__eq, tcon_Real_Oreal___Rings_Oring__1_44, fact_129_power__increasing, fact_73_Suc__le__mono, fact_111_real__nat__ceiling__ge, fact_92_real__of__nat__eq__numeral__power__cancel__iff, fact_36__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062, fact_66__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_91_of__nat__le__of__nat__power__cancel__iff, fact_2_ceiling__numeral__power, tcon_Set_Oset___Orderings_Oorder_24, fact_18_of__int__eq__numeral__iff, fact_8_of__int__le__numeral__iff, fact_89_Suc__1, fact_131_dbl__simps_I3_J, tcon_Int_Oint___Nat_Osemiring__char__0, fact_229_pow_Osimps_I1_J, fact_58_one__le__numeral, fact_82_of__int__of__nat__eq, fact_50_numeral__eq__one__iff, tcon_Nat_Onat___Num_Onumeral_16, tcon_fun___Orderings_Oorder, tcon_Real_Oreal___Rings_Olinordered__idom_33, tcon_Num_Onum___Orderings_Oord_22, fact_236_order__subst2, fact_107_le__antisym, fact_149_ceiling__zero, fact_180_nat__eq__iff2, fact_1_of__int__le__numeral__power__cancel__iff, fact_118_not__less__eq__eq, fact_90_of__nat__power__le__of__nat__cancel__iff, tcon_Real_Oreal___Orderings_Oord_43, fact_210_less__eq__nat_Osimps_I1_J, fact_7_ceiling__le__numeral, tcon_Real_Oreal___Orderings_Olinorder_37, tcon_Nat_Onat___Power_Opower_15, fact_3_numeral__power__eq__of__int__cancel__iff, fact_74_power__one__right, tcon_Set_Oset___Orderings_Oord_25, fact_173_power2__less__eq__zero__iff, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_23_numeral__power__le__nat__cancel__iff, fact_203_Zero__not__Suc, fact_121_Suc__le__D, fact_71_power2__nat__le__eq__le, fact_137_bot__nat__0_Oextremum, fact_182_zero__reorient, fact_81_of__nat__1, fact_134_powr__numeral, tcon_Nat_Onat___Orderings_Opreorder_9, tcon_Nat_Onat___Num_Osemiring__numeral_7, fact_201_Suc__neq__Zero, tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field, fact_26_ex__le__of__int, fact_83_ceiling__of__nat, fact_205_old_Onat_Oinducts, tcon_Int_Oint___Orderings_Oord_3, fact_142_of__nat__eq__0__iff, fact_41_verit__eq__simplify_I8_J, fact_188_int__ops_I2_J, fact_27_le__of__int__ceiling, fact_40_semiring__norm_I87_J, fact_219_power__mono, tcon_Int_Oint___Num_Osemiring__numeral, fact_148_powr__0, fact_199_diff__induct, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_31, tcon_Int_Oint___Groups_Oone, fact_94_numeral__le__real__of__nat__iff, fact_46_Collect__cong, fact_44_mem__Collect__eq, fact_169_powr__one, tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors, fact_114_le__log2__of__power, fact_207_bot__nat__0_Oextremum__uniqueI, tcon_HOL_Obool___Orderings_Oord_29, tcon_Real_Oreal___Orderings_Opreorder_36
% 21.13/7.12 % No. of inferences in proof: 652
% 21.13/7.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6549 ms resp. 5956 ms w/o parsing
% 21.63/7.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.63/7.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------