TSTP Solution File: ITP130^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP130^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 07:48:05 EDT 2024
% Result : Theorem 11.05s 3.55s
% Output : Refutation 11.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 328
% Syntax : Number of formulae : 622 ( 242 unt; 36 typ; 0 def)
% Number of atoms : 1538 ( 418 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 5865 ( 152 ~; 44 |; 76 &;4861 @)
% ( 0 <=>; 732 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 8 con; 0-3 aty)
% Number of variables : 1272 ( 14 ^1180 !; 54 ?;1272 :)
% ( 24 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(field_type,type,
field:
!>[TA: $tType] : $o ).
thf(ring_1_type,type,
ring_1:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(division_ring_type,type,
division_ring:
!>[TA: $tType] : $o ).
thf(semiring_bits_type,type,
semiring_bits:
!>[TA: $tType] : $o ).
thf(semidom_divide_type,type,
semidom_divide:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[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(unique1598680935umeral_type,type,
unique1598680935umeral:
!>[TA: $tType] : $o ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(ring_1_of_int_type,type,
ring_1_of_int:
!>[TA: $tType] : ( int > TA ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(nthRoo220209705d_root_type,type,
nthRoo220209705d_root: nat > nat > $o ).
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(divide_divide_type,type,
divide_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(ny_type,type,
ny: real ).
thf(na_type,type,
na: int ).
thf(p_type,type,
p: nat ).
thf(pm_type,type,
pm: nat ).
thf(x_type,type,
x: int ).
thf(y_type,type,
y: int ).
thf(ya_type,type,
ya: int ).
thf(249,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_gr__zeroI) ).
thf(1036,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_linordered__field__no__lb) ).
thf(809,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(131,axiom,
( pm
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61__092_060open_062pm_A_061_A0_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
thf(629,plain,
( pm
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(37,axiom,
order @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder) ).
thf(365,plain,
order @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(271,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_gr0__conv__Suc) ).
thf(1105,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(23,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ C ) @ ( divide_divide @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_div__le__mono) ).
thf(333,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ C ) @ ( divide_divide @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
=> ( ord_less @ nat @ B @ ( power_power @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_power__gt__expt) ).
thf(893,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
=> ( ord_less @ nat @ B @ ( power_power @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Suc__mono) ).
thf(518,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(267,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_old_Onat_Oinject) ).
thf(1083,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',fact_101_lift__Suc__antimono__le) ).
thf(941,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)],[212]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Suc__less__eq) ).
thf(481,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(30,axiom,
x = y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_x) ).
thf(352,plain,
x = y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_le__SucI) ).
thf(977,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)],[229]) ).
thf(164,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( suc @ ( zero_zero @ nat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_power__Suc0__right) ).
thf(762,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)],[164]) ).
thf(150,axiom,
! [A: nat > $o] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_exists__least__lemma) ).
thf(683,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)],[150]) ).
thf(9,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_divide__nonneg__nonneg) ).
thf(308,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(263,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__not__refl) ).
thf(1073,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(45,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_8) ).
thf(379,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(122,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_old_Onat_Oinducts) ).
thf(597,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)],[122]) ).
thf(251,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__Suc__eq__0__disj) ).
thf(1041,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(193,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_bot__nat__0_Oextremum__strict) ).
thf(878,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(141,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_less__zeroE) ).
thf(655,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(94,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: int] : ( ord_less_eq @ TA @ A @ ( ring_1_of_int @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ex__le__of__int) ).
thf(511,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)],[94]) ).
thf(49,axiom,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_bits__div__0) ).
thf(385,plain,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(48,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(384,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',fact_23_of__int__eq__0__iff) ).
thf(1137,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)],[283]) ).
thf(110,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_not0__implies__Suc) ).
thf(550,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(90,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_zero__less__power) ).
thf(500,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(292,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/sandbox2/benchmark/theBenchmark.p',fact_168_transitive__stepwise__le) ).
thf(1164,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)],[292]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_dec__induct) ).
thf(715,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__antisym) ).
thf(472,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(177,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ int @ A @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_of__int__less__0__iff) ).
thf(814,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ int @ A @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(214,axiom,
( ( ord_less @ int @ ( zero_zero @ int ) @ ya )
| ( ya
= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062) ).
thf(945,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ya )
| ( ya
= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(145,axiom,
archim1804426504_field @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field) ).
thf(670,plain,
archim1804426504_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Suc__le__mono) ).
thf(1063,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)],[260]) ).
thf(26,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_divide__cancel__left) ).
thf(340,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(181,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_lessI) ).
thf(829,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(253,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: int] : ( ord_less @ TA @ A @ ( ring_1_of_int @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_ex__less__of__int) ).
thf(1046,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: int] : ( ord_less @ TA @ A @ ( ring_1_of_int @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(6,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_divide__le__0__iff) ).
thf(301,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(320,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(119,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_not__less0) ).
thf(587,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(154,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__mult_15) ).
thf(702,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(258,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_less__Suc__eq__le) ).
thf(1059,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Suc__less__SucD) ).
thf(542,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(178,axiom,
( p
= ( suc @ pm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_p) ).
thf(817,plain,
( p
= ( suc @ pm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(113,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_ex__least__nat__le) ).
thf(559,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_div__less) ).
thf(421,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',fact_102_lift__Suc__mono__le) ).
thf(969,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)],[225]) ).
thf(20,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_le__refl) ).
thf(325,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
semiring_bits @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Parity_Osemiring__bits) ).
thf(316,plain,
semiring_bits @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(194,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_gr0I) ).
thf(881,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(63,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_div__0) ).
thf(416,plain,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(81,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_linorder__neqE__linordered__idom) ).
thf(475,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(287,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_power__mono__iff) ).
thf(1151,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(244,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_bot__nat__0_Onot__eq__extremum) ).
thf(1020,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(255,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Ex__less__Suc) ).
thf(1051,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(273,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_Zero__neq__Suc) ).
thf(1109,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(18,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_zero__le) ).
thf(321,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(85,axiom,
! [A: nat] :
( ( divide_divide @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_div__by__Suc__0) ).
thf(485,plain,
! [A: nat] :
( ( divide_divide @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(183,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_of__int__less__iff) ).
thf(834,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Nat_OlessE) ).
thf(692,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fact_80_of__int__0__le__iff) ).
thf(428,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)],[68]) ).
thf(12,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(312,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_7) ).
thf(411,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(234,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_divide__nonpos__pos) ).
thf(988,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(46,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_zero__reorient) ).
thf(380,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(38,axiom,
semidom_divide @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemidom__divide) ).
thf(366,plain,
semidom_divide @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(103,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ C @ B ) @ ( divide_divide @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_div__le__mono2) ).
thf(534,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ C @ B ) @ ( divide_divide @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(220,axiom,
linordered_semidom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semidom_12) ).
thf(957,plain,
linordered_semidom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(53,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_division__ring__divide__zero) ).
thf(392,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(4,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_div__by__0) ).
thf(297,plain,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(66,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_divide__nonneg__pos) ).
thf(424,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(84,axiom,
order @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_17) ).
thf(484,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(248,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Suc__lessE) ).
thf(1032,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(35,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom_3) ).
thf(361,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(189,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_nat__neq__iff) ).
thf(852,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(293,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_infinite__descent0__measure) ).
thf(1178,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(76,axiom,
ord_less @ real @ ( zero_zero @ real ) @ ny,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_NY0) ).
thf(461,plain,
ord_less @ real @ ( zero_zero @ real ) @ ny,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(280,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Suc__lessI) ).
thf(1128,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',fact_9_of__int__eq__iff) ).
thf(842,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)],[186]) ).
thf(228,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_All__less__Suc) ).
thf(974,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_nat_Oinject) ).
thf(1012,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_less__not__refl2) ).
thf(583,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(99,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_zero__less__iff__neq__zero) ).
thf(522,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_measure__induct__rule) ).
thf(578,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(152,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_n__not__Suc__n) ).
thf(697,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(192,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ B )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_div__pos__pos__trivial) ).
thf(874,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ B )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(16,axiom,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_bits__div__by__0) ).
thf(317,plain,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(215,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: int] : ( ord_less @ TA @ ( ring_1_of_int @ TA @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_ex__of__int__less) ).
thf(948,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: int] : ( ord_less @ TA @ ( ring_1_of_int @ TA @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',fact_77_of__int__le__iff) ).
thf(615,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)],[126]) ).
thf(277,axiom,
zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_20) ).
thf(1121,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_le__antisym) ).
thf(403,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)],[57]) ).
thf(50,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_divide__right__mono) ).
thf(388,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_divide__nonpos__nonpos) ).
thf(356,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(171,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_inc__induct) ).
thf(783,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(195,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_divide__neg__pos) ).
thf(884,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(290,axiom,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_less__int__code_I1_J) ).
thf(1160,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_div__neg__pos__less0) ).
thf(488,plain,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(25,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult_6) ).
thf(339,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(209,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_not__gr__zero) ).
thf(933,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(104,axiom,
! [TA: $tType] :
( ( unique1598680935umeral @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_div__positive) ).
thf(537,plain,
! [TA: $tType] :
( ( unique1598680935umeral @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(201,axiom,
! [TA: $tType] :
( ( unique1598680935umeral @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_unique__euclidean__semiring__numeral__class_Odiv__less) ).
thf(901,plain,
! [TA: $tType] :
( ( unique1598680935umeral @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_less__or__eq__imp__le) ).
thf(590,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(250,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/sandbox2/benchmark/theBenchmark.p',fact_131_of__int__nonneg) ).
thf(1039,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)],[250]) ).
thf(109,axiom,
! [A: nat] :
( ( power_power @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_power__Suc__0) ).
thf(547,plain,
! [A: nat] :
( ( power_power @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(157,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_infinite__descent) ).
thf(706,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(184,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_frac__less2) ).
thf(837,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(137,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_divide__neg__neg) ).
thf(647,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(153,axiom,
field @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Ofield) ).
thf(701,plain,
field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(96,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_lift__Suc__mono__less__iff) ).
thf(515,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ B @ A )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_div__neg__neg__trivial) ).
thf(457,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ B @ A )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(169,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_linordered__field__no__ub) ).
thf(779,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(41,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_le__0__eq) ).
thf(371,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(269,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_nat__zero__less__power__iff) ).
thf(1099,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(232,axiom,
( nthRoo220209705d_root
= ( ^ [A: nat,B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_fixed__root__def) ).
thf(985,plain,
( nthRoo220209705d_root
= ( ^ [A: nat,B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(281,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ( power_power @ TA @ A @ ( suc @ B ) )
= ( power_power @ TA @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_power__inject__base) ).
thf(1131,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ( power_power @ TA @ A @ ( suc @ B ) )
= ( power_power @ TA @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(140,axiom,
ord_less @ real @ ( zero_zero @ real ) @ ( ring_1_of_int @ real @ na ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_n0) ).
thf(654,plain,
ord_less @ real @ ( zero_zero @ real ) @ ( ring_1_of_int @ real @ na ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(27,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_div__le__dividend) ).
thf(343,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(268,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ex__least__nat__less) ).
thf(1086,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(34,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_9) ).
thf(360,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(173,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__irrefl__nat) ).
thf(805,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(11,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_10) ).
thf(311,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(207,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_strict__inc__induct) ).
thf(921,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(246,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq @ nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_le__SucE) ).
thf(1026,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)],[246]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ A @ B ) )
= ( ( ord_less_eq @ nat @ B @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_div__greater__zero__iff) ).
thf(765,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ A @ B ) )
= ( ( ord_less_eq @ nat @ B @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(256,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_divide__strict__right__mono__neg) ).
thf(1054,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(61,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(412,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(223,axiom,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_zero__less__Suc) ).
thf(965,plain,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(127,axiom,
! [A: nat,B: nat] :
( ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( ord_less @ nat @ A @ B )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Euclidean__Division_Odiv__eq__0__iff) ).
thf(618,plain,
! [A: nat,B: nat] :
( ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( ord_less @ nat @ A @ B )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Suc__leI) ).
thf(513,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',fact_169_nat__induct__at__least) ).
thf(745,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)],[162]) ).
thf(73,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_nat__induct) ).
thf(444,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)],[73]) ).
thf(160,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_zero__induct) ).
thf(733,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)],[160]) ).
thf(288,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ( power_power @ TA @ B @ A )
= ( power_power @ TA @ C @ A ) )
= ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_power__eq__iff__eq__base) ).
thf(1154,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ( power_power @ TA @ B @ A )
= ( power_power @ TA @ C @ A ) )
= ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(179,axiom,
! [A: nat,B: real] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ A )
= B )
& ! [D: real] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( power_power @ real @ D @ A )
= B ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_realpow__pos__nth__unique) ).
thf(819,plain,
! [A: nat,B: real] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ A )
= B )
& ! [D: real] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( power_power @ real @ D @ A )
= B ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(202,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ C @ A ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_compare__pow__le__iff) ).
thf(904,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ C @ A ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(240,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_nat__less__induct) ).
thf(1007,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(56,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_less__eq__int__code_I1_J) ).
thf(402,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(167,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_old_Onat_Oexhaust) ).
thf(772,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(161,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_not__less__zero) ).
thf(743,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(158,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_pos__imp__zdiv__pos__iff) ).
thf(711,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq @ nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_le__Suc__eq) ).
thf(958,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)],[221]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_divide__pos__pos) ).
thf(545,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(62,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_zero__le__divide__iff) ).
thf(413,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(135,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ( power_power @ TA @ A @ B )
= ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_power__eq__imp__eq__base) ).
thf(641,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ( power_power @ TA @ A @ B )
= ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(52,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semidom) ).
thf(391,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(210,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ TA )
=> ! [A: TA,B: nat] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_power__not__zero) ).
thf(936,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)],[210]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_81_of__int__le__of__int__power__cancel__iff) ).
thf(572,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)],[114]) ).
thf(13,axiom,
semiri134348788visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors) ).
thf(313,plain,
semiri134348788visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(147,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__Suc0) ).
thf(672,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_22_of__int__0__eq__iff) ).
thf(979,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)],[230]) ).
thf(58,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_eq__imp__le) ).
thf(406,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_3_of__int__power) ).
thf(831,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)],[182]) ).
thf(275,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_divide__less__0__iff) ).
thf(1117,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(64,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_bot__nat__0_Oextremum) ).
thf(419,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(254,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_le__less__Suc__eq) ).
thf(1048,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(36,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_bot__nat__0_Oextremum__uniqueI) ).
thf(362,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(285,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_less__not__refl3) ).
thf(1144,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(278,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_old_Onat_Odistinct_I1_J) ).
thf(1122,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(43,axiom,
unique1598680935umeral @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Divides_Ounique__euclidean__semiring__numeral) ).
thf(377,plain,
unique1598680935umeral @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(235,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_neq0__conv) ).
thf(990,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_measure__induct) ).
thf(996,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_frac__less) ).
thf(509,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(138,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_le__neq__implies__less) ).
thf(649,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(70,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_less__mono__imp__le__mono) ).
thf(434,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(197,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_div__nonpos__pos__le0) ).
thf(890,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__trans__Suc) ).
thf(811,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(19,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_divide__nonpos__nonneg) ).
thf(323,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(291,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_power__strict__mono) ).
thf(1162,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(128,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_zdiv__mono1) ).
thf(621,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(247,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__nat__zero__code) ).
thf(1029,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Suc__le__eq) ).
thf(626,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(213,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_divide__pos__neg) ).
thf(943,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(22,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__zero__eq) ).
thf(330,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)],[22]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_4_of__int__eq__of__int__power__cancel__iff) ).
thf(494,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)],[88]) ).
thf(265,axiom,
ord_less @ int @ na @ ( power_power @ int @ ya @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_yyn) ).
thf(1080,plain,
ord_less @ int @ na @ ( power_power @ int @ ya @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_163_Nat_Oex__has__greatest__nat) ).
thf(345,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)],[28]) ).
thf(191,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_infinite__descent0) ).
thf(858,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_159_le__trans) ).
thf(367,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)],[39]) ).
thf(188,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ B @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_pos__imp__zdiv__neg__iff) ).
thf(848,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ B @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Suc__lessD) ).
thf(520,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',fact_129_zero__le__power) ).
thf(462,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)],[77]) ).
thf(208,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20__C1_Oprems_C_I3_J) ).
thf(932,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(204,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_divide__nonpos__neg) ).
thf(912,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(261,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_gr0__implies__Suc) ).
thf(1066,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(242,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_not__less__eq) ).
thf(1015,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(124,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_pos__imp__zdiv__nonneg__iff) ).
thf(608,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',fact_114_diff__induct) ).
thf(1113,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)],[274]) ).
thf(270,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ C @ A ) )
= ( ord_less @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_compare__pow__less__iff) ).
thf(1102,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ C @ A ) )
= ( ord_less @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(69,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( power_power @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_power__divide) ).
thf(431,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( power_power @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(142,axiom,
ord_less @ int @ ( power_power @ int @ y @ p ) @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_yyn_H) ).
thf(658,plain,
ord_less @ int @ ( power_power @ int @ y @ p ) @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(166,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Suc__neq__Zero) ).
thf(768,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_less__imp__le__nat) ).
thf(827,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(133,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_gr__implies__not0) ).
thf(636,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',fact_130_power__mono) ).
thf(1044,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)],[252]) ).
thf(92,axiom,
~ ( ( ord_less @ int @ ya @ ( zero_zero @ int ) )
| ( ord_less @ int @ na @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_not_I2_J) ).
thf(505,plain,
~ ( ( ord_less @ int @ ya @ ( zero_zero @ int ) )
| ( ord_less @ int @ na @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(71,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ B @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_neg__imp__zdiv__nonneg__iff) ).
thf(438,plain,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ B @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(264,axiom,
~ ( ( ord_less @ int @ ya @ ( zero_zero @ int ) )
| ( ord_less @ int @ na @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_not_I1_J) ).
thf(1076,plain,
~ ( ( ord_less @ int @ ya @ ( zero_zero @ int ) )
| ( ord_less @ int @ na @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',fact_170_full__nat__induct) ).
thf(675,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)],[148]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_Suc__le__lessD) ).
thf(426,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(102,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ C @ A ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_divide__less__cancel) ).
thf(531,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ C @ A ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_68_nat__power__eq__Suc__0__iff) ).
thf(680,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)],[149]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_less__Suc__induct) ).
thf(663,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(42,axiom,
( p
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_p0) ).
thf(374,plain,
( p
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(282,axiom,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Suc__n__not__le__n) ).
thf(1134,plain,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(266,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ D ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_frac__le) ).
thf(1081,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ D ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(211,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_power__less__imp__less__base) ).
thf(939,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(243,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ ( divide_divide @ nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Suc__div__le__mono) ).
thf(1018,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ ( divide_divide @ nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_5_of__int__power__eq__of__int__cancel__iff) ).
thf(553,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)],[111]) ).
thf(168,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
=> ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( power_power @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_nat__one__le__power) ).
thf(776,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
=> ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( power_power @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',fact_79_of__int__le__0__iff) ).
thf(525,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)],[100]) ).
thf(190,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Ex__less__Suc2) ).
thf(855,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(134,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ pm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_pm0) ).
thf(640,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ pm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(3,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_divide__nonneg__nonpos) ).
thf(295,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(156,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ya,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__C1_Oprems_C_I2_J) ).
thf(705,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ya,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(226,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_18) ).
thf(971,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(21,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_bot__nat__0_Oextremum__unique) ).
thf(327,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(218,axiom,
nthRoo220209705d_root @ p @ pm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_fixed__root__axioms) ).
thf(954,plain,
nthRoo220209705d_root @ p @ pm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(10,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__mult) ).
thf(310,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(236,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_not__less__less__Suc__eq) ).
thf(993,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(40,axiom,
semiring_bits @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Parity_Osemiring__bits_5) ).
thf(370,plain,
semiring_bits @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(91,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_zdiv__mono2) ).
thf(502,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(217,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_of__int__less__of__int__power__cancel__iff) ).
thf(951,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(174,axiom,
ord_less @ real @ ( zero_zero @ real ) @ ( ring_1_of_int @ real @ ya ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_y0) ).
thf(808,plain,
ord_less @ real @ ( zero_zero @ real ) @ ( ring_1_of_int @ real @ ya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(107,axiom,
ring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__1_19) ).
thf(544,plain,
ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_nat_OdiscI) ).
thf(907,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(24,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_divide__cancel__right) ).
thf(336,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(155,axiom,
( ny
= ( divide_divide @ real @ ( ring_1_of_int @ real @ na ) @ ( power_power @ real @ ( ring_1_of_int @ real @ ya ) @ pm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_NY__def) ).
thf(703,plain,
( ny
= ( divide_divide @ real @ ( ring_1_of_int @ real @ na ) @ ( power_power @ real @ ( ring_1_of_int @ real @ ya ) @ pm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(245,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_not__gr0) ).
thf(1023,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(284,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ A @ B ) )
= ( ( ord_less_eq @ int @ B @ A )
& ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_nonneg1__imp__zdiv__pos__iff) ).
thf(1140,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ A @ B ) )
= ( ( ord_less_eq @ int @ B @ A )
& ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(14,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_le0) ).
thf(314,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(121,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_of__int__pos) ).
thf(595,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(125,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Suc__less__eq2) ).
thf(612,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(89,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_less__SucE) ).
thf(497,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(187,axiom,
( ya
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_y00) ).
thf(845,plain,
( ya
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(112,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( zero_zero @ TA ) @ ( suc @ A ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_power__0__Suc) ).
thf(556,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)],[112]) ).
thf(105,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ TA )
=> ! [A: TA,B: nat] :
( ( ( power_power @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_power__eq__0__iff) ).
thf(539,plain,
! [TA: $tType] :
( ( semiri134348788visors @ TA )
=> ! [A: TA,B: nat] :
( ( ( power_power @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(146,axiom,
division_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Odivision__ring) ).
thf(671,plain,
division_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(289,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_less__Suc__eq) ).
thf(1157,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_divide__strict__right__mono) ).
thf(581,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( nthRoo220209705d_root @ A @ B )
=> ( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_fixed__root_Op) ).
thf(759,plain,
! [A: nat,B: nat] :
( ( nthRoo220209705d_root @ A @ B )
=> ( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(279,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat] : ( ord_less_eq @ nat @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_less__eq__Suc__le) ).
thf(1126,plain,
( ( ord_less @ nat )
= ( ^ [A: nat] : ( ord_less_eq @ nat @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(272,axiom,
semiri134348788visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_11) ).
thf(1108,plain,
semiri134348788visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( nthRoo220209705d_root @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_fixed__root_Ointro) ).
thf(961,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( nthRoo220209705d_root @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(199,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_infinite__descent__measure) ).
thf(896,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(7,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0) ).
thf(304,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(259,axiom,
ord_less_eq @ int @ na @ ( power_power @ int @ ya @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64__C1_Oprems_C_I1_J) ).
thf(1062,plain,
ord_less_eq @ int @ na @ ( power_power @ int @ ya @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(51,axiom,
ring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__1) ).
thf(390,plain,
ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(132,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_old_Onat_Odistinct_I2_J) ).
thf(632,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Suc__leD) ).
thf(781,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)],[170]) ).
thf(139,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_nat__less__le) ).
thf(652,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(29,axiom,
semiri134348788visors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_2) ).
thf(351,plain,
semiri134348788visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',fact_82_of__int__power__le__of__int__cancel__iff) ).
thf(478,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)],[82]) ).
thf(47,axiom,
semidom_divide @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide_4) ).
thf(383,plain,
semidom_divide @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(200,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_le__eq__less__or__eq) ).
thf(899,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(205,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Zero__not__Suc) ).
thf(914,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(44,axiom,
wellorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(378,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(5,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_y_H0) ).
thf(300,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(238,axiom,
! [A: real,B: nat] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ ( suc @ B ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_realpow__pos__nth2) ).
thf(999,plain,
! [A: real,B: nat] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ ( suc @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(216,axiom,
semidom_divide @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemidom__divide_14) ).
thf(950,plain,
semidom_divide @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(286,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Suc__le__D) ).
thf(1148,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)],[286]) ).
thf(59,axiom,
unique1598680935umeral @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral_1) ).
thf(410,plain,
unique1598680935umeral @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(224,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ ( suc @ B ) ) @ ( power_power @ TA @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_power__le__imp__le__base) ).
thf(967,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ ( suc @ B ) ) @ ( power_power @ TA @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(8,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_divide__eq__0__iff) ).
thf(305,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_nat__le__linear) ).
thf(358,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)],[33]) ).
thf(257,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_of__int__0__less__iff) ).
thf(1056,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(55,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_less__eq__nat_Osimps_I1_J) ).
thf(400,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(219,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_lift__Suc__mono__less) ).
thf(955,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(196,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Suc__inject) ).
thf(886,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1,conjecture,
ord_less @ real @ ( ring_1_of_int @ real @ na ) @ ( power_power @ real @ ( ring_1_of_int @ real @ ya ) @ ( suc @ pm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ real @ ( ring_1_of_int @ real @ na ) @ ( power_power @ real @ ( ring_1_of_int @ real @ ya ) @ ( suc @ pm ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(294,plain,
~ ( ord_less @ real @ ( ring_1_of_int @ real @ na ) @ ( power_power @ real @ ( ring_1_of_int @ real @ ya ) @ ( suc @ pm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(206,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( zero_zero @ int ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_of__int__0) ).
thf(918,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)],[206]) ).
thf(172,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_gr__implies__not__zero) ).
thf(801,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(233,axiom,
linordered_field @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(987,plain,
linordered_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(78,axiom,
! [A: nat,B: real] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_realpow__pos__nth) ).
thf(464,plain,
! [A: nat,B: real] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(115,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_divide__le__cancel) ).
thf(575,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(101,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_linorder__neqE__nat) ).
thf(528,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(136,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ A @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_nat__power__less__imp__less) ).
thf(644,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ A @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__SucI) ).
thf(442,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(276,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom_13) ).
thf(1120,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(123,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1_16) ).
thf(607,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( nthRoo220209705d_root @ A @ B )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_fixed__root_Op0) ).
thf(395,plain,
! [A: nat,B: nat] :
( ( nthRoo220209705d_root @ A @ B )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(129,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_divide__nonneg__neg) ).
thf(624,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(185,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq @ nat @ A @ B ) )
= ( ord_less_eq @ nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_not__less__eq__eq) ).
thf(839,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)],[185]) ).
thf(231,axiom,
( na
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n00) ).
thf(982,plain,
( na
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(239,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_of__int__power__less__of__int__cancel__iff) ).
thf(1004,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(79,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_zero__less__divide__iff) ).
thf(469,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(31,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_divide__right__mono__neg) ).
thf(354,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(143,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_nat_Odistinct_I1_J) ).
thf(659,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(87,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_All__less__Suc2) ).
thf(491,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(227,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_le__imp__less__Suc) ).
thf(972,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(74,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_zero__power) ).
thf(454,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(262,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_neg__imp__zdiv__neg__iff) ).
thf(1069,plain,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1185,plain,
$false,
inference(e,[status(thm)],[1036,809,629,365,1105,333,893,518,1083,941,481,352,977,762,683,308,1073,379,597,1041,878,655,511,385,384,1137,550,500,1164,715,472,814,945,670,1063,340,829,1046,301,320,587,702,1059,542,817,559,421,969,325,316,881,416,475,1151,1020,1051,1109,321,485,834,692,428,312,411,988,380,366,534,957,392,297,424,484,1032,361,852,1178,461,1128,842,974,1012,583,522,578,697,874,317,948,615,1121,403,388,356,783,884,1160,488,339,933,537,901,590,1039,547,706,837,647,701,515,457,779,371,1099,985,1131,654,343,1086,360,805,311,921,1026,765,1054,412,965,618,513,745,444,733,1154,819,904,1007,402,772,743,711,958,545,413,641,391,936,572,313,672,979,406,831,1117,419,1048,362,1144,1122,377,990,996,509,649,434,890,811,323,1162,621,1029,626,943,330,494,1080,345,858,367,848,520,462,932,912,1066,1015,608,1113,1102,431,658,768,827,636,1044,505,438,1076,675,426,531,680,663,374,1134,1081,939,1018,553,776,525,855,640,295,705,971,327,954,310,993,370,502,951,808,544,907,336,703,1023,1140,314,595,612,497,845,556,539,671,1157,581,759,1126,1108,961,896,304,1062,390,632,781,652,351,478,383,899,914,378,300,999,950,1148,410,967,305,358,1056,400,955,886,294,918,801,987,464,575,528,644,442,1120,607,395,624,839,982,1004,469,354,659,491,972,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP130^2 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:48:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.02/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.18 % [INFO] Parsing done (272ms).
% 1.99/1.19 % [INFO] Running in sequential loop mode.
% 2.53/1.39 % [INFO] eprover registered as external prover.
% 2.53/1.40 % [INFO] cvc4 registered as external prover.
% 2.53/1.40 % [INFO] Scanning for conjecture ...
% 2.77/1.49 % [INFO] Found a conjecture and 291 axioms. Running axiom selection ...
% 2.94/1.58 % [INFO] Axiom selection finished. Selected 291 axioms (removed 0 axioms).
% 3.62/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 3.62/1.76 % [INFO] Type checking passed.
% 3.62/1.76 % [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 ...
% 11.05/3.54 % External prover 'e' found a proof!
% 11.05/3.54 % [INFO] Killing All external provers ...
% 11.05/3.54 % Time passed: 3012ms (effective reasoning time: 2346ms)
% 11.05/3.54 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 11.05/3.55 % Axioms used in derivation (291): fact_119_old_Onat_Oexhaust, fact_114_diff__induct, tcon_HOL_Obool___Orderings_Oorder_10, fact_65_p, fact_45_measure__induct__rule, fact_36_less__Suc__eq, fact_170_full__nat__induct, fact_28_strict__inc__induct, fact_133_power__strict__mono, fact_229_x, tcon_Real_Oreal___Nat_Oring__char__0_18, fact_3_of__int__power, tcon_Int_Oint___Rings_Olinordered__semidom, fact_68_nat__power__eq__Suc__0__iff, tcon_Nat_Onat___Rings_Olinordered__semidom_3, fact_220_frac__less, tcon_Nat_Onat___Groups_Ozero_9, fact_122_less__Suc__eq__0__disj, fact_100_nat__power__less__imp__less, fact_99_infinite__descent0__measure, fact_31_Suc__less__SucD, fact_180_less__or__eq__imp__le, fact_79_of__int__le__0__iff, fact_179_le__neq__implies__less, fact_18_not_I2_J, tcon_Int_Oint___Groups_Ozero, fact_75_zero__less__Suc, fact_138_zero__reorient, fact_139_gr__zeroI, fact_211_divide__neg__pos, fact_166_le__0__eq, fact_190_Suc__leI, tcon_Int_Oint___Nat_Oring__char__0, fact_20__C1_Oprems_C_I3_J, fact_146_y_H0, fact_155_bot__nat__0_Oextremum, fact_195_le__less__Suc__eq, fact_88_less__not__refl, fact_223_divide__nonneg__neg, fact_92_less__irrefl__nat, fact_238_div__by__0, tcon_Int_Oint___Rings_Oring__1, fact_106_exists__least__lemma, fact_224_divide__nonneg__pos, fact_168_transitive__stepwise__le, fact_230_div__by__Suc__0, tcon_Int_Oint___Groups_Omonoid__mult, fact_32_less__antisym, fact_149_division__ring__divide__zero, fact_245_div__neg__pos__less0, fact_94_infinite__descent, fact_191_Suc__le__eq, fact_188_nat__one__le__power, fact_71_less__nat__zero__code, fact_14_Suc__less__eq, fact_19__C1_Oprems_C_I2_J, fact_84_not__gr0, fact_87_nat__neq__iff, fact_54_not__gr__zero, tcon_Real_Oreal___Rings_Olinordered__semidom_12, fact_33_Suc__less__eq2, fact_142_zero__less__iff__neq__zero, fact_6_of__int__less__iff, fact_189_ex__least__nat__le, fact_169_nat__induct__at__least, tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_11, fact_215_divide__less__cancel, fact_161_le__antisym, fact_76_less__Suc0, fact_98_bot__nat__0_Oextremum__strict, fact_121_not0__implies__Suc, fact_201_ex__least__nat__less, tcon_Nat_Onat___Orderings_Oorder_8, fact_81_of__int__le__of__int__power__cancel__iff, fact_182_less__imp__le__nat, fact_235_Suc__div__le__mono, tcon_Nat_Onat___Rings_Osemiring__1_7, fact_126_Ex__less__Suc2, fact_96_linorder__neqE__nat, fact_241_zdiv__mono1, fact_213_divide__pos__pos, fact_204_divide__nonpos__nonneg, fact_234_Euclidean__Division_Odiv__eq__0__iff, fact_228_div__pos__pos__trivial, fact_72_bot__nat__0_Onot__eq__extremum, fact_206_divide__nonneg__nonneg, fact_124_All__less__Suc2, fact_93_nat__less__induct, fact_247_unique__euclidean__semiring__numeral__class_Odiv__less, fact_214_divide__less__0__iff, fact_233_div__le__dividend, fact_210_divide__neg__neg, fact_158_le__refl, fact_145_yyn_H, fact_90_less__not__refl3, fact_74_power__Suc0__right, fact_194_Suc__le__lessD, fact_184_fixed__root_Op0, fact_69_power__Suc__0, fact_8_y0, fact_108_less__eq__int__code_I1_J, fact_9_of__int__eq__iff, fact_137_realpow__pos__nth__unique, fact_209_divide__le__0__iff, fact_196_less__Suc__eq__le, fact_47_n__not__Suc__n, fact_212_divide__pos__neg, tcon_Real_Oreal___Orderings_Oorder_17, fact_250_neg__imp__zdiv__nonneg__iff, fact_141_gr__implies__not__zero, fact_40_Suc__lessI, fact_95_infinite__descent0, fact_187_fixed__root_Op, fact_7_n0, fact_178_less__mono__imp__le__mono, fact_203_divide__nonpos__nonpos, fact_154_bits__div__0, fact_197_less__eq__Suc__le, tcon_Int_Oint___Rings_Osemidom__divide, fact_127_power__eq__imp__eq__base, fact_86_less__zeroE, tcon_Real_Oreal___Rings_Olinordered__idom_13, fact_198_le__imp__less__Suc, tcon_Int_Oint___Rings_Olinordered__idom, fact_22_of__int__0__eq__iff, fact_156_le0, fact_226_divide__nonpos__pos, tcon_Int_Oint___Divides_Ounique__euclidean__semiring__numeral, fact_177_Suc__leD, fact_239_div__0, tcon_Nat_Onat___Parity_Osemiring__bits_5, tcon_Nat_Onat___Orderings_Owellorder, fact_227_div__neg__neg__trivial, fact_172_Suc__n__not__le__n, fact_131_of__int__nonneg, fact_186_fixed__root__def, fact_252_div__nonpos__pos__le0, tcon_Int_Oint___Orderings_Oorder, fact_13__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062, fact_39_less__SucE, fact_193_inc__induct, fact_140_not__less__zero, tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral_1, fact_134_power__inject__base, tcon_Real_Oreal___Rings_Osemiring__1_16, fact_232_div__le__mono, fact_144_zero__power, tcon_Nat_Onat___Groups_Omonoid__mult_6, fact_200_linordered__field__no__lb, fact_102_lift__Suc__mono__le, fact_143_power__not__zero, fact_5_of__int__power__eq__of__int__cancel__iff, fact_243_pos__imp__zdiv__neg__iff, tcon_Int_Oint___Rings_Osemiring__1, fact_181_le__eq__less__or__eq, fact_246_div__positive, fact_110_old_Onat_Odistinct_I2_J, fact_148_compare__pow__le__iff, fact_130_power__mono, fact_208_divide__right__mono, fact_104_power__divide, fact_248_nonneg1__imp__zdiv__pos__iff, fact_109_nat_Odistinct_I1_J, fact_2_of__int__power__less__of__int__cancel__iff, fact_123_gr0__implies__Suc, fact_112_nat_OdiscI, fact_151_divide__cancel__right, fact_113_nat__induct, fact_173_le__Suc__eq, fact_25_of__int__0__less__iff, fact_118_Zero__not__Suc, fact_171_not__less__eq__eq, fact_152_divide__eq__0__iff, fact_162_nat__le__linear, fact_78_power__mono__iff, fact_82_of__int__power__le__of__int__cancel__iff, fact_231_div__less, fact_157_Suc__le__mono, fact_236_div__greater__zero__iff, fact_26_less__int__code_I1_J, fact_58_ex__of__int__less, fact_117_Zero__neq__Suc, fact_12_y00, fact_125_gr0__conv__Suc, tcon_Real_Oreal___Rings_Oring__1_19, fact_1_of__int__less__of__int__power__cancel__iff, fact_21_of__int__0, fact_43_Nat_OlessE, fact_132_power__less__imp__less__base, fact_153_divide__cancel__left, fact_205_divide__nonneg__nonpos, fact_207_zero__le__divide__iff, fact_38_less__SucI, fact_202_divide__right__mono__neg, fact_216_zero__less__divide__iff, fact_128_power__eq__iff__eq__base, fact_199_linordered__field__no__ub, fact_136_realpow__pos__nth, fact_240_linorder__neqE__linordered__idom, tcon_Int_Oint___Parity_Osemiring__bits, fact_116_Suc__neq__Zero, fact_62_p0, fact_23_of__int__eq__0__iff, fact_56_zero__less__power, fact_10_nat_Oinject, fact_64__C1_Oprems_C_I1_J, fact_63_pm0, fact_183_nat__less__le, tcon_Real_Oreal___Fields_Olinordered__field, fact_77_of__int__le__iff, fact_101_lift__Suc__antimono__le, fact_30_less__trans__Suc, fact_41_Suc__lessE, fact_107_power__gt__expt, fact_17_not_I1_J, fact_55_realpow__pos__nth2, tcon_Real_Oreal___Groups_Omonoid__mult_15, fact_53_power__eq__0__iff, fact_73_nat__zero__less__power__iff, fact_37_Ex__less__Suc, fact_237_div__le__mono2, fact_185_fixed__root_Ointro, fact_174_Suc__le__D, fact_219_frac__le, fact_217_divide__strict__right__mono, fact_103_zero__le, fact_42_Suc__lessD, fact_4_of__int__eq__of__int__power__cancel__iff, tcon_Nat_Onat___Rings_Osemidom__divide_4, tcon_Real_Oreal___Groups_Ozero_20, fact_163_Nat_Oex__has__greatest__nat, fact_83_gr0I, fact_91_gr__implies__not0, fact_27_not__less__less__Suc__eq, fact_70_neq0__conv, fact_15_Suc__mono, fact_105_ex__le__of__int, fact_60_yyn, fact_67_le__zero__eq, fact_251_pos__imp__zdiv__pos__iff, fact_160_eq__imp__le, fact_147_compare__pow__less__iff, fact_221_frac__less2, fact_16_lessI, fact_129_zero__le__power, fact_165_bot__nat__0_Oextremum__unique, fact_89_less__not__refl2, fact_46_measure__induct, fact_97_infinite__descent__measure, fact_48_Suc__inject, fact_59_ex__less__of__int, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_50_lift__Suc__mono__less, fact_29_less__Suc__induct, fact_175_le__SucI, fact_85_not__less0, fact_135_power__le__imp__le__base, fact_44_of__int__pos, fact_11_old_Onat_Oinject, fact_66_fixed__root__axioms, tcon_Real_Oreal___Rings_Osemidom__divide_14, fact_164_bot__nat__0_Oextremum__uniqueI, tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field, fact_24_of__int__less__0__iff, fact_176_le__SucE, fact_218_divide__strict__right__mono__neg, fact_249_pos__imp__zdiv__nonneg__iff, fact_159_le__trans, fact_0_n00, fact_35_not__less__eq, fact_34_All__less__Suc, fact_225_divide__nonpos__neg, fact_52_NY0, fact_192_dec__induct, fact_115_zero__induct, fact_49_lift__Suc__mono__less__iff, fact_120_old_Onat_Oinducts, fact_57_NY__def, fact_111_old_Onat_Odistinct_I1_J, tcon_Real_Oreal___Fields_Ofield, fact_61__092_060open_062pm_A_061_A0_A_092_060Longrightarrow_062_AFalse_092_060close_062, fact_51_power__0__Suc, fact_244_neg__imp__zdiv__neg__iff, tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_2, fact_222_divide__le__cancel, tcon_Real_Oreal___Fields_Odivision__ring, tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors, fact_242_zdiv__mono2, fact_167_less__eq__nat_Osimps_I1_J, fact_150_bits__div__by__0, fact_80_of__int__0__le__iff
% 11.05/3.55 % No. of inferences in proof: 586
% 11.05/3.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3012 ms resp. 2346 ms w/o parsing
% 11.75/3.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.75/3.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------