TSTP Solution File: NUM926^3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM926^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 08:02:03 EDT 2024
% Result : Theorem 24.40s 6.43s
% Output : Refutation 26.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1259
% Syntax : Number of formulae : 2460 (1321 unt; 60 typ; 0 def)
% Number of atoms : 5875 (2192 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 22323 ( 516 ~; 140 |; 329 &;19268 @)
% ( 0 <=>;2070 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 56 usr; 14 con; 0-3 aty)
% Number of variables : 5181 ( 2 ^5131 !; 48 ?;5181 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(div_mod_int_type,type,
div_mod_int: int > int > int ).
thf(div_mod_nat_type,type,
div_mod_nat: nat > nat > nat ).
thf(minus_minus_int_type,type,
minus_minus_int: int > int > int ).
thf(minus_minus_nat_type,type,
minus_minus_nat: nat > nat > nat ).
thf(minus_minus_real_type,type,
minus_minus_real: real > real > real ).
thf(one_one_int_type,type,
one_one_int: int ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(one_one_real_type,type,
one_one_real: real ).
thf(plus_plus_int_type,type,
plus_plus_int: int > int > int ).
thf(plus_plus_nat_type,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_real_type,type,
plus_plus_real: real > real > real ).
thf(times_times_int_type,type,
times_times_int: int > int > int ).
thf(times_times_nat_type,type,
times_times_nat: nat > nat > nat ).
thf(times_times_real_type,type,
times_times_real: real > real > real ).
thf(zero_zero_int_type,type,
zero_zero_int: int ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(zero_zero_real_type,type,
zero_zero_real: real ).
thf(multInv_type,type,
multInv: int > int > int ).
thf(d22set_type,type,
d22set: int > int > $o ).
thf(zfact_type,type,
zfact: int > int ).
thf(zcong_type,type,
zcong: int > int > int > $o ).
thf(zprime_type,type,
zprime: int > $o ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(min_type,type,
min: int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_int_type,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
thf(number267125858f_real_type,type,
number267125858f_real: int > real ).
thf(ord_less_int_type,type,
ord_less_int: int > int > $o ).
thf(ord_less_nat_type,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_real_type,type,
ord_less_real: real > real > $o ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: real > real > $o ).
thf(power_power_int_type,type,
power_power_int: int > nat > int ).
thf(power_power_nat_type,type,
power_power_nat: nat > nat > nat ).
thf(power_power_real_type,type,
power_power_real: real > nat > real ).
thf(product_Pair_int_int_type,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(legendre_type,type,
legendre: int > int > int ).
thf(quadRes_type,type,
quadRes: int > int > $o ).
thf(sr_type,type,
sr: int > int > $o ).
thf(standardRes_type,type,
standardRes: int > int > int ).
thf(dvd_dvd_int_type,type,
dvd_dvd_int: int > int > $o ).
thf(dvd_dvd_nat_type,type,
dvd_dvd_nat: nat > nat > $o ).
thf(dvd_dvd_real_type,type,
dvd_dvd_real: real > real > $o ).
thf(collect_int_type,type,
collect_int: ( int > $o ) > int > $o ).
thf(twoSqu919416604sum2sq_type,type,
twoSqu919416604sum2sq: int > $o ).
thf(twoSqu2057625106sum2sq_type,type,
twoSqu2057625106sum2sq: product_prod_int_int > int ).
thf(inv_type,type,
inv: int > int > int ).
thf(wset_type,type,
wset: int > int > int > $o ).
thf(member_int_type,type,
member_int: int > ( int > $o ) > $o ).
thf(m_type,type,
m: int ).
thf(s1_type,type,
s1: int ).
thf(s_type,type,
s: int ).
thf(t_type,type,
t: int ).
thf(331,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ ( minus_minus_nat @ B @ C ) )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( dvd_dvd_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_dvd__diffD1) ).
thf(2163,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ ( minus_minus_nat @ B @ C ) )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( dvd_dvd_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(52,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_not__add__less1) ).
thf(1337,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ B )
& ( ord_less_eq_nat @ A @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ B @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ A ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_split__mult__neg__le) ).
thf(1369,plain,
! [A: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ B )
& ( ord_less_eq_nat @ A @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ B @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ A ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(920,axiom,
! [A: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__special_I3_J) ).
thf(3798,plain,
! [A: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(790,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_semiring__one__add__one__is__two) ).
thf(3434,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(465,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_add__mult__distrib2) ).
thf(2544,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(260,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_bin__less__0__simps_I1_J) ).
thf(1956,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(374,axiom,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_realpow__minus__mult) ).
thf(2280,plain,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(362,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_dvd__refl) ).
thf(2250,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(642,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_nat__diff__add__eq1) ).
thf(3021,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(165,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_even__less__0__iff) ).
thf(1665,plain,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1024,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_pos__zmult__eq__1__iff__lemma) ).
thf(4101,plain,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(761,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_real__mult__right__cancel) ).
thf(3345,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(992,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ C @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_zprime__power__zdvd__cancel__left) ).
thf(4005,plain,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ C @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1081,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_plus__numeral__code_I9_J) ).
thf(4262,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(197,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( dvd_dvd_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_dvd__reduce) ).
thf(1767,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( dvd_dvd_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(873,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_zadd__0__right) ).
thf(3666,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(184,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( plus_plus_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_pos__add__strict) ).
thf(1729,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( plus_plus_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1091,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(4290,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(883,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(3698,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(777,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_rel__simps_I39_J) ).
thf(3397,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(242,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_le__imp__power__dvd) ).
thf(1899,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_776_mult__mono) ).
thf(1315,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(447,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_804_mult__nonneg__nonpos) ).
thf(2499,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(424,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_zdvd__imp__le) ).
thf(2427,plain,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(979,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ( ~ ( quadRes @ C @ B )
=> ~ ( zcong @ A @ ( times_times_int @ B @ ( multInv @ C @ A ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_MultInvPair__distinct) ).
thf(3969,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ( ~ ( quadRes @ C @ B )
=> ~ ( zcong @ A @ ( times_times_int @ B @ ( multInv @ C @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(269,axiom,
! [A: nat,B: nat,C: int,D: int] :
( ( dvd_dvd_int @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_dvd__power__le) ).
thf(1982,plain,
! [A: nat,B: nat,C: int,D: int] :
( ( dvd_dvd_int @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(471,axiom,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_less__0__number__of) ).
thf(2559,plain,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(796,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rel__simps_I33_J) ).
thf(3449,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_dvd_Oless__asym) ).
thf(1750,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(986,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_s) ).
thf(3990,plain,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1015,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of_int @ min ) @ B )
=> ~ ( zcong @ A @ one_one_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_zcong__neg__1__impl__ne__1) ).
thf(4075,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of_int @ min ) @ B )
=> ~ ( zcong @ A @ one_one_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(494,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ( inv @ B @ A )
!= zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_inv__not__0) ).
thf(2622,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ( inv @ B @ A )
!= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(411,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2381,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(86,axiom,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_power__eq__0__iff) ).
thf(1443,plain,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(690,axiom,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ C @ ( times_times_real @ ( times_times_real @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(3153,plain,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ C @ ( times_times_real @ ( times_times_real @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(70,axiom,
ord_less_eq_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_rel__simps_I23_J) ).
thf(1401,plain,
ord_less_eq_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(255,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1939,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(958,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(3910,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(638,axiom,
! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751_dvd__triv__left) ).
thf(3012,plain,
! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(139,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
= ( ord_less_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_rel__simps_I13_J) ).
thf(1591,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
= ( ord_less_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(815,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_power__strict__increasing__iff) ).
thf(3498,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(40,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ B @ A )
=> ( dvd_dvd_int @ B @ ( div_mod_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_zdvd__zmod) ).
thf(1305,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ B @ A )
=> ( dvd_dvd_int @ B @ ( div_mod_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1158,axiom,
ord_less_eq_int @ one_one_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(4479,plain,
ord_less_eq_int @ one_one_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(225,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_power__strict__decreasing) ).
thf(1855,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(877,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_zadd__left__commute) ).
thf(3680,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(830,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_zero__less__power2) ).
thf(3534,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(662,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_782_mult__left__mono__neg) ).
thf(3072,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(250,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ C @ A @ B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_zcong__zless__imp__eq) ).
thf(1924,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ C @ A @ B )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(348,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ A @ one_one_real )
=> ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_power__decreasing) ).
thf(2210,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ A @ one_one_real )
=> ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(750,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_one__less__power) ).
thf(3317,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1069,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).
thf(4226,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(1167,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_semiring__mult__2) ).
thf(4500,plain,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(114,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zle__trans) ).
thf(1522,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(906,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
=> ( dvd_dvd_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_dvd__mult__left) ).
thf(3762,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
=> ( dvd_dvd_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(416,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_power__strict__increasing__iff) ).
thf(2395,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(601,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_trans__less__add2) ).
thf(2908,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(820,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_number__of__diff) ).
thf(3509,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(738,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_gr__implies__not0) ).
thf(3285,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(580,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_diff__less) ).
thf(2854,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(118,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) @ ( times_times_int @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_zmult2__lemma__aux4) ).
thf(1533,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) @ ( times_times_int @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(171,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_mult__zero__right) ).
thf(1692,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1134,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(4408,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(84,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1437,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1162,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_odd__less__0) ).
thf(4487,plain,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(101,axiom,
! [A: int] :
( ( ord_less_int @ one_one_int @ A )
=> ? [B: int] :
( ( zprime @ B )
& ( dvd_dvd_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_zprime__factor__exists) ).
thf(1486,plain,
! [A: int] :
( ( ord_less_int @ one_one_int @ A )
=> ? [B: int] :
( ( zprime @ B )
& ( dvd_dvd_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1025,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_zspecial__product) ).
thf(4105,plain,
! [A: int,B: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(80,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_sum__squares__le__zero__iff) ).
thf(1426,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(167,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_add__less__mono) ).
thf(1671,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(918,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_numeral__1__eq__1) ).
thf(3794,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(788,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_number__of__Pls) ).
thf(3429,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(654,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_bin__less__0__simps_I3_J) ).
thf(3049,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_912_dvd_Oantisym) ).
thf(1310,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1067,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_power__inject__exp) ).
thf(4220,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(30,axiom,
! [A: nat,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_dvd__power__same) ).
thf(1275,plain,
! [A: nat,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(427,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_trans__le__add2) ).
thf(2434,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
= ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_922_dvd_Oless__le) ).
thf(1640,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
= ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(598,axiom,
! [A: int] :
( ( div_mod_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_zmod__zero) ).
thf(2901,plain,
! [A: int] :
( ( div_mod_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(259,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_mult__le__mono2) ).
thf(1954,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(91,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1458,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(735,axiom,
! [A: int,B: int] :
( ( member_int @ A @ ( sr @ B ) )
=> ( ( standardRes @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1193_StandardRes__SR__prop) ).
thf(3276,plain,
! [A: int,B: int] :
( ( member_int @ A @ ( sr @ B ) )
=> ( ( standardRes @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1180,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ~ ( zcong @ B @ zero_zero_int @ D )
=> ( ( zcong @ B @ ( times_times_int @ A @ ( multInv @ D @ C ) ) @ D )
=> ( zcong @ C @ ( times_times_int @ A @ ( multInv @ D @ B ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_MultInv__zcong__prop2) ).
thf(4543,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ~ ( zcong @ B @ zero_zero_int @ D )
=> ( ( zcong @ B @ ( times_times_int @ A @ ( multInv @ D @ C ) ) @ D )
=> ( zcong @ C @ ( times_times_int @ A @ ( multInv @ D @ B ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(343,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_less__nat__zero__code) ).
thf(2195,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(175,axiom,
! [A: int,B: int,C: int] :
( ( ( div_mod_int @ A @ B )
= ( div_mod_int @ C @ B ) )
=> ( zcong @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_Residues_Oaux) ).
thf(1705,plain,
! [A: int,B: int,C: int] :
( ( ( div_mod_int @ A @ B )
= ( div_mod_int @ C @ B ) )
=> ( zcong @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(685,axiom,
! [A: int,B: int > $o,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ! [D: int] :
( ( B @ D )
=> ( B @ ( minus_minus_int @ D @ C ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ! [D: int] :
( ( B @ D )
=> ( B @ ( minus_minus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_decr__mult__lemma) ).
thf(3135,plain,
! [A: int,B: int > $o,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ! [D: int] :
( ( B @ D )
=> ( B @ ( minus_minus_int @ D @ C ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ! [D: int] :
( ( B @ D )
=> ( B @ ( minus_minus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(971,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_power__mult) ).
thf(3942,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(768,axiom,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_mult__nat__number__of) ).
thf(3365,plain,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(539,axiom,
! [A: nat,B: nat] :
( ( B != zero_zero_nat )
=> ( ( A != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_no__zero__divisors) ).
thf(2740,plain,
! [A: nat,B: nat] :
( ( B != zero_zero_nat )
=> ( ( A != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(605,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_mult__right__mono__neg) ).
thf(2918,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1001,axiom,
! [A: int,B: int,C: int,D: int] :
( ( dvd_dvd_int @ C @ D )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_mult__dvd__mono) ).
thf(4026,plain,
! [A: int,B: int,C: int,D: int] :
( ( dvd_dvd_int @ C @ D )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(651,axiom,
! [A: int,B: int] :
( ( member_int @ A @ ( d22set @ B ) )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_d22set__le) ).
thf(3044,plain,
! [A: int,B: int] :
( ( member_int @ A @ ( d22set @ B ) )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(386,axiom,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_add__numeral__0) ).
thf(2316,plain,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(795,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
= ( B
= ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_number__of__reorient) ).
thf(3446,plain,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
= ( B
= ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(432,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_divides__add__revr) ).
thf(2448,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) )
=> ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(609,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2933,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(858,axiom,
! [A: int,B: int,C: int] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_zcong__zmult__self) ).
thf(3616,plain,
! [A: int,B: int,C: int] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1087,axiom,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_le__nat__number__of) ).
thf(4279,plain,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(913,axiom,
! [A: int] :
( ( ( bit1 @ A )
= min )
= ( A = min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_rel__simps_I47_J) ).
thf(3781,plain,
! [A: int] :
( ( ( bit1 @ A )
= min )
= ( A = min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(1146,axiom,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_zero__eq__power2) ).
thf(4440,plain,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(496,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_power__less__imp__less__exp) ).
thf(2627,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(333,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_dvd_Oless__imp__neq) ).
thf(2168,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1009,axiom,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
= ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_number__of__reorient) ).
thf(4058,plain,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
= ( B
= ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(272,axiom,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_divisors__zero) ).
thf(1988,plain,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(436,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2459,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(680,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ C @ zero_zero_int )
=> ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_mult__less__cancel__left__neg) ).
thf(3121,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ C @ zero_zero_int )
=> ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(1093,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J) ).
thf(4294,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1144,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_semiring__norm_I110_J) ).
thf(4435,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(845,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_less__special_I1_J) ).
thf(3577,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( div_mod_nat @ B @ A )
= ( div_mod_nat @ ( minus_minus_nat @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1183_le__mod__geq) ).
thf(1222,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( div_mod_nat @ B @ A )
= ( div_mod_nat @ ( minus_minus_nat @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(952,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) )
= ( dvd_dvd_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_zdvd__reduce) ).
thf(3895,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) )
= ( dvd_dvd_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(890,axiom,
( ( ord_less_eq_int @ zero_zero_int @ s )
& ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_s0p) ).
thf(3717,plain,
( ( ord_less_eq_int @ zero_zero_int @ s )
& ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1038,axiom,
( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(4142,plain,
( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(988,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_zdiff__power2) ).
thf(3994,plain,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(817,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_sum__squares__gt__zero__iff) ).
thf(3502,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(283,axiom,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_add__numeral__0__right) ).
thf(2020,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(668,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_mult__pos__neg2) ).
thf(3088,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(973,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J) ).
thf(3947,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(592,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ord_less_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_power__strict__decreasing) ).
thf(2886,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ord_less_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(953,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_divisors__zero) ).
thf(3898,plain,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(586,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_mult__zero__left) ).
thf(2869,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(617,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(2957,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(934,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_semiring__norm_I113_J) ).
thf(3836,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1113,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ B )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(4343,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ B )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(721,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_803_mult__nonneg__nonpos) ).
thf(3236,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(763,axiom,
! [A: nat,B: nat] :
( ( A
= ( times_times_nat @ A @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1038_mult__eq__self__implies__10) ).
thf(3350,plain,
! [A: nat,B: nat] :
( ( A
= ( times_times_nat @ A @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(834,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_zadd__left__mono) ).
thf(3545,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(532,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(2723,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(548,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_real__mult__order) ).
thf(2763,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(203,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_power__0__left) ).
thf(1782,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(628,axiom,
! [A: int > $o,B: int,C: int] :
( ( A @ ( div_mod_int @ B @ C ) )
= ( ( ( C = zero_zero_int )
=> ( A @ B ) )
& ( ( ord_less_int @ zero_zero_int @ C )
=> ! [D: int,E: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ E )
& ( ord_less_int @ E @ C )
& ( B
= ( plus_plus_int @ ( times_times_int @ C @ D ) @ E ) ) )
=> ( A @ E ) ) )
& ( ( ord_less_int @ C @ zero_zero_int )
=> ! [D: int,E: int] :
( ( ( ord_less_int @ C @ E )
& ( ord_less_eq_int @ E @ zero_zero_int )
& ( B
= ( plus_plus_int @ ( times_times_int @ C @ D ) @ E ) ) )
=> ( A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_split__zmod) ).
thf(2985,plain,
! [A: int > $o,B: int,C: int] :
( ( A @ ( div_mod_int @ B @ C ) )
= ( ( ( C = zero_zero_int )
=> ( A @ B ) )
& ( ( ord_less_int @ zero_zero_int @ C )
=> ! [D: int,E: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ E )
& ( ord_less_int @ E @ C )
& ( B
= ( plus_plus_int @ ( times_times_int @ C @ D ) @ E ) ) )
=> ( A @ E ) ) )
& ( ( ord_less_int @ C @ zero_zero_int )
=> ! [D: int,E: int] :
( ( ( ord_less_int @ C @ E )
& ( ord_less_eq_int @ E @ zero_zero_int )
& ( B
= ( plus_plus_int @ ( times_times_int @ C @ D ) @ E ) ) )
=> ( A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1576,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(894,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zprime__2) ).
thf(3730,plain,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) )
= ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129_pow__divides__eq__nat) ).
thf(1645,plain,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) )
= ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(249,axiom,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_divides__exp2) ).
thf(1921,plain,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(66,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_power__0__left__number__of) ).
thf(1386,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(802,axiom,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_zero__power2) ).
thf(3466,plain,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1036,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_power__add) ).
thf(4137,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(182,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_divides__rev) ).
thf(1724,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(924,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ B @ C ) @ E )
= ( zcong @ A @ ( times_times_int @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_zcong__zmult__prop2) ).
thf(3809,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ B @ C ) @ E )
= ( zcong @ A @ ( times_times_int @ B @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(59,axiom,
! [A: int,B: int,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) )
= ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_pow__divides__eq__int) ).
thf(1366,plain,
! [A: int,B: int,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) )
= ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(418,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_less__eq__real__def) ).
thf(2400,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(300,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) @ zero_zero_int )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ F )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_zdiv__mono2__neg__lemma) ).
thf(2067,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) @ zero_zero_int )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ F )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1044,axiom,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_real__sum__squared__expand) ).
thf(4156,plain,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(209,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_trans__less__add1) ).
thf(1803,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(321,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( A
!= ( inv @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_inv__distinct) ).
thf(2136,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( A
!= ( inv @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(244,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ A )
=> ~ ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1029_nat__dvd__not__less) ).
thf(1904,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ A )
=> ~ ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1154,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_Int2_Oaux1) ).
thf(4467,plain,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(420,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_power__mult) ).
thf(2405,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(928,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ( zcong @ ( times_times_int @ ( times_times_int @ ( multInv @ D @ C ) @ C ) @ A ) @ ( times_times_int @ ( multInv @ D @ C ) @ B ) @ D )
=> ( zcong @ A @ ( times_times_int @ B @ ( multInv @ D @ C ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_aux______4) ).
thf(3820,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ( zcong @ ( times_times_int @ ( times_times_int @ ( multInv @ D @ C ) @ C ) @ A ) @ ( times_times_int @ ( multInv @ D @ C ) @ B ) @ D )
=> ( zcong @ A @ ( times_times_int @ B @ ( multInv @ D @ C ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(391,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ D @ C )
=> ~ ( dvd_dvd_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_divides__div__not) ).
thf(2328,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ D @ C )
=> ~ ( dvd_dvd_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(645,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_mult__right__mono) ).
thf(3029,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_power__eq__0__iff) ).
thf(1792,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(37,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ E @ A )
=> ( ord_less_eq_int @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_unique__quotient__lemma) ).
thf(1298,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ E @ A )
=> ( ord_less_eq_int @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1042,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_mult__2__right) ).
thf(4151,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(545,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_number__of__Bit0) ).
thf(2755,plain,
! [A: int] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(844,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(3574,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(658,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_mult__less__cancel__left__pos) ).
thf(3061,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(527,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( ord_less_eq_nat @ B @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_nat__le__add__iff2) ).
thf(2708,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( ord_less_eq_nat @ B @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(448,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_zdvd__not__zless) ).
thf(2501,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(371,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_dvd__0__right) ).
thf(2274,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(911,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__special_I3_J) ).
thf(3776,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(764,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ( inv @ B @ A )
!= ( minus_minus_int @ B @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_inv__not__p__minus__1) ).
thf(3353,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ( inv @ B @ A )
!= ( minus_minus_int @ B @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(922,axiom,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_power__even__eq) ).
thf(3803,plain,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1074,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(4243,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(726,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841_mult__pos__neg2) ).
thf(3248,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_le__add__diff__inverse2) ).
thf(1409,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(730,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_linorder__neqE__linordered__idom) ).
thf(3263,plain,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(35,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_diff__le__mono) ).
thf(1287,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(537,axiom,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_not__sum__squares__lt__zero) ).
thf(2735,plain,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(565,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ A @ ( wset @ B @ C ) )
=> ( ord_less_int @ one_one_int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_wset__g__1) ).
thf(2814,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ A @ ( wset @ B @ C ) )
=> ( ord_less_int @ one_one_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1187,axiom,
( ( t = one_one_int )
=> ? [A: int,B: int] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(4563,plain,
( ( t = one_one_int )
=> ? [A: int,B: int] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1139,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Bit0__Pls) ).
thf(4422,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(652,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_806_mult__nonneg__nonneg) ).
thf(3046,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(880,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__eq__number__of__int__code) ).
thf(3689,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(227,axiom,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1860,plain,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(351,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_mult__left__cancel) ).
thf(2217,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(47,axiom,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__special_I1_J) ).
thf(1323,plain,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(688,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B )
= ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_diff__add__assoc2) ).
thf(3148,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B )
= ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(833,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_rel__simps_I27_J) ).
thf(3542,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(43,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_mult__mono_H) ).
thf(1313,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(32,axiom,
! [A: real] : ( dvd_dvd_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_dvd__refl) ).
thf(1279,plain,
! [A: real] : ( dvd_dvd_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1115,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(4349,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(781,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_semiring__mult__2) ).
thf(3410,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(339,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_divisors__zero) ).
thf(2185,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(90,axiom,
! [A: real,B: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ A )
= ( times_times_real @ A @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_power__commutes) ).
thf(1455,plain,
! [A: real,B: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ A )
= ( times_times_real @ A @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(901,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_right__diff__distrib__number__of) ).
thf(3749,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(472,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2562,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1000,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_one__neq__zero) ).
thf(4023,plain,
one_one_int != zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(541,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ B @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_power__Suc__less) ).
thf(2745,plain,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ B @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(476,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_diff__diff__left) ).
thf(2571,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(402,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_power__eq__imp__eq__base) ).
thf(2356,plain,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(123,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ ( times_times_int @ A @ B ) @ C @ D )
=> ( zcong @ ( times_times_int @ ( times_times_int @ ( multInv @ D @ A ) @ A ) @ B ) @ ( times_times_int @ ( multInv @ D @ A ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_aux______3) ).
thf(1545,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ ( times_times_int @ A @ B ) @ C @ D )
=> ( zcong @ ( times_times_int @ ( times_times_int @ ( multInv @ D @ A ) @ A ) @ B ) @ ( times_times_int @ ( multInv @ D @ A ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(801,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_diff__bin__simps_I6_J) ).
thf(3463,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(145,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_mult__pos__pos) ).
thf(1609,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(714,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(3216,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(804,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rel__simps_I31_J) ).
thf(3470,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(748,axiom,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_eq_int @ ( div_mod_int @ A @ B ) @ zero_zero_int )
& ( ord_less_int @ B @ ( div_mod_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_neg__mod__conj) ).
thf(3312,plain,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_eq_int @ ( div_mod_int @ A @ B ) @ zero_zero_int )
& ( ord_less_int @ B @ ( div_mod_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(887,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ one_one_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_self__quotient__aux1) ).
thf(3708,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ one_one_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1082,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_zdiff__zmult__distrib2) ).
thf(4265,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(262,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1963,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(719,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_nat__mult__eq__one) ).
thf(3231,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(571,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_mult__left__mono) ).
thf(2829,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(419,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_real__mult__less__mono2) ).
thf(2403,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(111,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_real__zero__not__eq__one) ).
thf(1514,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(187,axiom,
! [A: int,B: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_add__number__of__eq) ).
thf(1741,plain,
! [A: int,B: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ B )
= ( times_times_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1398,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ B )
= ( times_times_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(896,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_zadd__zmult__distrib) ).
thf(3734,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(639,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_mult__nonpos__nonneg) ).
thf(3014,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(456,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_order__le__neq__implies__less) ).
thf(2520,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(535,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ B )
= ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_dvd__mult__cancel2) ).
thf(2730,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ B )
= ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(382,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ( ( ord_less_nat @ B @ C )
=> ( A @ C @ B ) )
=> ( ( ( B = C )
=> ( A @ C @ B ) )
=> ( ( ( ord_less_nat @ C @ B )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_nat__less__cases) ).
thf(2301,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ( ( ord_less_nat @ B @ C )
=> ( A @ C @ B ) )
=> ( ( ( B = C )
=> ( A @ C @ B ) )
=> ( ( ( ord_less_nat @ C @ B )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1151,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ B @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_dvd__mult) ).
thf(4460,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ B @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1128,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(4390,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1155,axiom,
( ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ s @ one_one_int ) )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
thf(4471,plain,
( ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ s @ one_one_int ) )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1170,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_rel__simps_I21_J) ).
thf(4507,plain,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(201,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_826_mult__strict__right__mono) ).
thf(1778,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(13,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( div_mod_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_mod__less__eq__dividend) ).
thf(1232,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( div_mod_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1078,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_sum__squares__eq__zero__iff) ).
thf(4253,plain,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(728,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_mult__right__mono) ).
thf(3258,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1130,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zadd__commute) ).
thf(4396,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(892,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( minus_minus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_diff__square) ).
thf(3724,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( minus_minus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(247,axiom,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_realpow__pos__nth__unique) ).
thf(1911,plain,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(366,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_crossproduct__eq) ).
thf(2259,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(805,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zadd__strict__right__mono) ).
thf(3473,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(792,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( times_times_int @ ( number_number_of_int @ B ) @ C ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_mult__number__of__left) ).
thf(3438,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( times_times_int @ ( number_number_of_int @ B ) @ C ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(394,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_nat__0__less__mult__iff) ).
thf(2335,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1046,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_705_mult__eq__0__iff) ).
thf(4162,plain,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(435,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(2456,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(279,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_dvd_Oless__imp__not__eq2) ).
thf(2007,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(336,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_le__cube) ).
thf(2178,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1135,axiom,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_power2__eq__square) ).
thf(4411,plain,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(102,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_power__0) ).
thf(1489,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1062,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ ( number_number_of_int @ B ) @ C ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_add__number__of__diff1) ).
thf(4205,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ ( number_number_of_int @ B ) @ C ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_divides__ge) ).
thf(1415,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(826,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_semiring__numeral__1__eq__1) ).
thf(3524,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(789,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_arith__simps_I32_J) ).
thf(3431,plain,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(389,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ord_less_int @ ( inv @ B @ A ) @ ( minus_minus_int @ B @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_inv__less__p__minus__1) ).
thf(2324,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ord_less_int @ ( inv @ B @ A ) @ ( minus_minus_int @ B @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(178,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_mult__less__cancel__left__pos) ).
thf(1714,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(286,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ B @ C ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_mult__less__cancel__left__disj) ).
thf(2027,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ B @ C ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(949,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_divides__cases) ).
thf(3887,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(978,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_nat__mult__2) ).
thf(3966,plain,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(707,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_zmult__zless__mono2) ).
thf(3199,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(968,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_power__increasing) ).
thf(3934,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1147,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_le__special_I3_J) ).
thf(4443,plain,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(213,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ C @ zero_zero_real )
=> ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_mult__less__cancel__left__neg) ).
thf(1811,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ C @ zero_zero_real )
=> ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(998,axiom,
! [A: int] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_power2__ge__self) ).
thf(4018,plain,
! [A: int] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(306,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_dvd_Oless__imp__not__less) ).
thf(2090,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(776,axiom,
! [A: real,B: nat] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_real )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_even__power__le__0__imp__0) ).
thf(3393,plain,
! [A: real,B: nat] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_real )
=> ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(153,axiom,
! [A: nat,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_power__mono) ).
thf(1632,plain,
! [A: nat,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1094,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_zcong__shift) ).
thf(4297,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(694,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ A )
= ( times_times_nat @ A @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_power__commutes) ).
thf(3163,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ A )
= ( times_times_nat @ A @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(506,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_bin__less__0__simps_I4_J) ).
thf(2650,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_le__neq__implies__less) ).
thf(1418,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)],[77]) ).
thf(356,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( times_times_real @ B @ A ) )
= ( times_times_real @ ( plus_plus_real @ B @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2236,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( times_times_real @ B @ A ) )
= ( times_times_real @ ( plus_plus_real @ B @ one_one_real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(860,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_power__less__power__Suc) ).
thf(3621,plain,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(267,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_semiring__numeral__0__eq__0) ).
thf(1978,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(65,axiom,
! [A: int,B: int] :
( ( ( div_mod_int @ A @ B )
= zero_zero_int )
=> ? [C: int] :
( A
= ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_zmod__eq__0D) ).
thf(1383,plain,
! [A: int,B: int] :
( ( ( div_mod_int @ A @ B )
= zero_zero_int )
=> ? [C: int] :
( A
= ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(364,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_diff__commute) ).
thf(2254,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(1185,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_number__of__add) ).
thf(4556,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(302,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2073,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(583,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_le__add1) ).
thf(2861,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(785,axiom,
! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_749_dvd__triv__right) ).
thf(3421,plain,
! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(150,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_mult__neg__pos) ).
thf(1622,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1098,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_p0) ).
thf(4307,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1,conjecture,
? [A: int,B: int] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: int,B: int] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1201,plain,
~ ? [A: int,B: int] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(561,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_rel__simps_I9_J) ).
thf(2804,plain,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(142,axiom,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_field__power__not__zero) ).
thf(1600,plain,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(712,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ord_less_int @ one_one_int @ ( inv @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_inv__g__1) ).
thf(3211,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ord_less_int @ one_one_int @ ( inv @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1064,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_semiring__mult__2) ).
thf(4211,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(771,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_power2__eq__square) ).
thf(3378,plain,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(451,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1158_pos__mod__sign) ).
thf(2508,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(620,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_nat__mult__eq__cancel1) ).
thf(2964,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(984,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(3986,plain,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(296,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_mult__strict__right__mono__neg) ).
thf(2058,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(406,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ zero_zero_int )
=> ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_zmult2__lemma__aux2) ).
thf(2367,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ zero_zero_int )
=> ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(831,axiom,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3537,plain,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(1008,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_semiring__mult__number__of) ).
thf(4055,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(661,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( dvd_dvd_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_dvd_Oeq__refl) ).
thf(3068,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( dvd_dvd_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1071,axiom,
! [A: int,B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ B ) )
=> ( ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) @ one_one_int ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ B ) )
=> ( ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int ) @ ( number_number_of_int @ B ) ) ) @ one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1135_zmod__number__of__Bit1) ).
thf(4230,plain,
! [A: int,B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ B ) )
=> ( ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) @ one_one_int ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ B ) )
=> ( ( div_mod_int @ ( number_number_of_int @ ( bit1 @ A ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int ) @ ( number_number_of_int @ B ) ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(63,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_nat__mult__1__right) ).
thf(1377,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1004,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__number__of) ).
thf(4033,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(573,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_real__add__mult__distrib) ).
thf(2833,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(818,axiom,
! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_dvd__triv__left) ).
thf(3505,plain,
! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(237,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( dvd_dvd_int @ A @ B )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_zdvd__antisym__nonneg) ).
thf(1886,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( dvd_dvd_int @ A @ B )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1169,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
= ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_zmult__eq__1__iff) ).
thf(4504,plain,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
= ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(457,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__special_I4_J) ).
thf(2523,plain,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(648,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_real__le__antisym) ).
thf(3036,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(460,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_zero__less__power) ).
thf(2530,plain,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(904,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_times__numeral__code_I5_J) ).
thf(3756,plain,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1178,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_rel__simps_I49_J) ).
thf(4536,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(724,axiom,
! [A: nat,B: int] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ B ) ) )
= ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_zero__less__power__nat__eq__number__of) ).
thf(3243,plain,
! [A: nat,B: int] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ B ) ) )
= ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(358,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
= ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_dvd_Oless__le__not__le) ).
thf(2242,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(55,axiom,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_ex__least__nat__less) ).
thf(1345,plain,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(849,axiom,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(3588,plain,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( A
= ( times_times_nat @ B @ C ) )
=> ( dvd_dvd_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_dvdI) ).
thf(1697,plain,
! [A: nat,B: nat,C: nat] :
( ( A
= ( times_times_nat @ B @ C ) )
=> ( dvd_dvd_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1089,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_one__add__one__is__two) ).
thf(4285,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(701,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_le__imp__power__dvd) ).
thf(3184,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(482,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_comm__mult__strict__left__mono) ).
thf(2586,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(591,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1128_dvd__pos__nat) ).
thf(2884,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(266,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1975,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1018,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_power__less__imp__less__exp) ).
thf(4082,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1160,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_zcong__scalar2) ).
thf(4483,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(130,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_881_real__le__linear) ).
thf(1564,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(228,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_less__special_I3_J) ).
thf(1863,plain,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1060,axiom,
! [A: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__special_I2_J) ).
thf(4199,plain,
! [A: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(477,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_power__increasing) ).
thf(2574,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(940,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_one__add__one__is__two) ).
thf(3852,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(829,axiom,
! [A: int] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_quartic__square__square) ).
thf(3531,plain,
! [A: int] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(702,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_dvd__power__le) ).
thf(3186,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(316,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_nat__mult__assoc) ).
thf(2118,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(292,axiom,
! [A: real,B: int] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_power__eq__0__iff__number__of) ).
thf(2047,plain,
! [A: real,B: int] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(502,axiom,
! [A: int,B: int] : ( zcong @ A @ ( div_mod_int @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_mod__mod__is__mod) ).
thf(2641,plain,
! [A: int,B: int] : ( zcong @ A @ ( div_mod_int @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1050,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_rel__simps_I38_J) ).
thf(4172,plain,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(616,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_le__diff__conv) ).
thf(2954,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(160,axiom,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_le__number__of__eq__not__less) ).
thf(1651,plain,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(689,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_real__add__left__mono) ).
thf(3151,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(280,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
| ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_zdvd__bounds) ).
thf(2011,plain,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
| ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(671,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(3097,plain,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(850,axiom,
( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(3591,plain,
( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(602,axiom,
! [A: int] :
( ( sr @ A )
= ( collect_int
@ ^ [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_SR__def) ).
thf(2910,plain,
! [A: int] :
( ( sr @ A )
= ( collect_int
@ ^ [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(744,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ B @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_zcong__not__zero) ).
thf(3301,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ B @ zero_zero_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(346,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_eq_int @ B @ zero_zero_int ) )
| ( ( ord_less_eq_int @ A @ zero_zero_int )
& ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_mult__le__0__iff) ).
thf(2204,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_eq_int @ B @ zero_zero_int ) )
| ( ( ord_less_eq_int @ A @ zero_zero_int )
& ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(745,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ~ ( member_int @ A @ ( wset @ ( minus_minus_int @ C @ one_one_int ) @ B ) )
=> ( ( member_int @ A @ ( wset @ C @ B ) )
=> ( ( A = C )
| ( A
= ( inv @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_wset__mem__imp__or) ).
thf(3303,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ~ ( member_int @ A @ ( wset @ ( minus_minus_int @ C @ one_one_int ) @ B ) )
=> ( ( member_int @ A @ ( wset @ C @ B ) )
=> ( ( A = C )
| ( A
= ( inv @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(983,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_dvd__mult2) ).
thf(3984,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(696,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_dvd_Oord__eq__le__trans) ).
thf(3169,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(1159,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_zpower__zadd__distrib) ).
thf(4480,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(504,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_mult__strict__right__mono) ).
thf(2646,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(95,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( power_power_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_zpower__zdvd__prop1) ).
thf(1470,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( power_power_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1708,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(908,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_rel__simps_I10_J) ).
thf(3767,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(380,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ ( div_mod_int @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_pos__mod__bound) ).
thf(2296,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ ( div_mod_int @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1192,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_comm__semiring__class_Odistrib) ).
thf(4576,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(1003,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ one_one_int @ B )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_one__le__power) ).
thf(4031,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ one_one_int @ B )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1101,axiom,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(4312,plain,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(556,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2790,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(510,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(2660,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(230,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_comm__mult__strict__left__mono) ).
thf(1868,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(515,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_mult__pos__neg) ).
thf(2673,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(526,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( times_times_nat @ B @ A ) )
= ( times_times_nat @ ( plus_plus_nat @ B @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2705,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( times_times_nat @ B @ A ) )
= ( times_times_nat @ ( plus_plus_nat @ B @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(464,axiom,
! [A: nat,B: int] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_power__eq__0__iff__number__of) ).
thf(2541,plain,
! [A: nat,B: int] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1123,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_sum__power2__eq__zero__iff) ).
thf(4375,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(856,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__int__code_I16_J) ).
thf(3610,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(622,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(2969,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(902,axiom,
! [A: int,B: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ A )
= ( times_times_int @ A @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_power__commutes) ).
thf(3752,plain,
! [A: int,B: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ A )
= ( times_times_int @ A @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(948,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( div_mod_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ) @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_neg__zmod__mult__2) ).
thf(3884,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( div_mod_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ) @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(459,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ B @ D ) @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_zmult2__lemma__aux1) ).
thf(2528,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ B @ D ) @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(236,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_double__eq__0__iff) ).
thf(1883,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(888,axiom,
! [A: int] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(3711,plain,
! [A: int] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(536,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_q__neg__lemma) ).
thf(2733,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(54,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_dvd_Oorder__trans) ).
thf(1343,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(997,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_power2__le__imp__le) ).
thf(4016,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(113,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_zcong__zero__equiv__div) ).
thf(1519,plain,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(486,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_nat__less__add__iff1) ).
thf(2596,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_dvd_Oantisym__conv) ).
thf(1570,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(169,axiom,
! [A: int > $o,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( A @ C )
=> ( ! [D: int] :
( ( ord_less_eq_int @ D @ C )
=> ( ( A @ D )
=> ( A @ ( minus_minus_int @ D @ one_one_int ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_int__le__induct) ).
thf(1676,plain,
! [A: int > $o,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( A @ C )
=> ( ! [D: int] :
( ( ord_less_eq_int @ D @ C )
=> ( ( A @ D )
=> ( A @ ( minus_minus_int @ D @ one_one_int ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(320,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ zero_zero_int )
=> ( ( div_mod_int @ B @ A )
= ( plus_plus_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_mod__pos__neg__trivial) ).
thf(2133,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ zero_zero_int )
=> ( ( div_mod_int @ B @ A )
= ( plus_plus_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(8,axiom,
! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_dvd__triv__right) ).
thf(1217,plain,
! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(325,axiom,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( dvd_dvd_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_zpower__zdvd__prop2) ).
thf(2147,plain,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( dvd_dvd_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1149,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_power__0__left) ).
thf(4449,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1164,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_Pls__def) ).
thf(4493,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(218,axiom,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_even__less__0__iff) ).
thf(1824,plain,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(149,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_rel__simps_I25_J) ).
thf(1619,plain,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(423,axiom,
! [A: int > $o,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( A @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ! [D: int] :
( ( ord_less_int @ D @ C )
=> ( ( A @ D )
=> ( A @ ( minus_minus_int @ D @ one_one_int ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_int__less__induct) ).
thf(2414,plain,
! [A: int > $o,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( A @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ! [D: int] :
( ( ord_less_int @ D @ C )
=> ( ( A @ D )
=> ( A @ ( minus_minus_int @ D @ one_one_int ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(727,axiom,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= ( plus_plus_nat @ A @ ( times_times_nat @ ( minus_minus_nat @ B @ one_one_nat ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_mult__eq__if) ).
thf(3250,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= ( plus_plus_nat @ A @ ( times_times_nat @ ( minus_minus_nat @ B @ one_one_nat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(710,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_diff__mult__distrib2) ).
thf(3207,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(822,axiom,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).
thf(3514,plain,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(1037,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ( ( zcong @ ( multInv @ C @ B ) @ ( multInv @ C @ A ) @ C )
=> ( zcong @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_MultInv__prop5) ).
thf(4140,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ( ( zcong @ ( multInv @ C @ B ) @ ( multInv @ C @ A ) @ C )
=> ( zcong @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(514,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_nat__add__left__cancel__less) ).
thf(2670,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(442,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_power__decreasing) ).
thf(2477,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(669,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_dvd_Ole__imp__less__or__eq) ).
thf(3090,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(742,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_real__le__refl) ).
thf(3297,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(587,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_Nat_Oadd__0__right) ).
thf(2872,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1184,axiom,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_mult__zero__left) ).
thf(4553,plain,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(490,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ? [C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
& ( ord_less_int @ C @ B )
& ( zcong @ A @ C @ B )
& ! [D: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ D )
& ( ord_less_int @ D @ B )
& ( zcong @ A @ D @ B ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_zcong__zless__unique) ).
thf(2609,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ? [C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
& ( ord_less_int @ C @ B )
& ( zcong @ A @ C @ B )
& ! [D: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ D )
& ( ord_less_int @ D @ B )
& ( zcong @ A @ D @ B ) )
=> ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1056,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(4187,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(686,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_zero__less__power) ).
thf(3144,plain,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( div_mod_nat @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_mod__less__divisor) ).
thf(1210,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( div_mod_nat @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(965,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(3926,plain,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(73,axiom,
! [A: int] :
( ( zprime @ A )
=> ( zcong @ ( zfact @ ( minus_minus_int @ A @ one_one_int ) ) @ ( number_number_of_int @ min ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_Wilson__Russ) ).
thf(1407,plain,
! [A: int] :
( ( zprime @ A )
=> ( zcong @ ( zfact @ ( minus_minus_int @ A @ one_one_int ) ) @ ( number_number_of_int @ min ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(154,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_power__inject__exp) ).
thf(1634,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(967,axiom,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_number__of__is__id) ).
thf(3931,plain,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(133,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_zero__less__diff) ).
thf(1573,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(507,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_power__strict__increasing) ).
thf(2653,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(737,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_power__mult__distrib) ).
thf(3282,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(79,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1423,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(695,axiom,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( C @ A ) @ B ) @ ( C @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_mono__nat__linear__lb) ).
thf(3166,plain,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( C @ A ) @ B ) @ ( C @ ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(431,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ( dvd_dvd_nat @ A @ zero_zero_nat )
& ~ ( dvd_dvd_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_gcd__lcm__complete__lattice__nat_Oless__top) ).
thf(2445,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ( dvd_dvd_nat @ A @ zero_zero_nat )
& ~ ( dvd_dvd_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(704,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_nat__power__eq__0__iff) ).
thf(3191,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(546,axiom,
! [A: real] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2758,plain,
! [A: real] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(732,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(3269,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(859,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Bit1__def) ).
thf(3618,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(511,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_pos__zmult__pos) ).
thf(2663,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(127,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_nat__le__add__iff1) ).
thf(1555,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(392,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zadd__zless__mono) ).
thf(2332,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(216,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_805_mult__nonneg__nonneg) ).
thf(1819,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1106,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__special_I4_J) ).
thf(4327,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( A != B )
=> ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_dvd_Ole__neq__trans) ).
thf(1624,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( A != B )
=> ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1132,axiom,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_mult__Pls) ).
thf(4402,plain,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(222,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ B )
& ( ord_less_real @ A @ C ) )
| ( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_mult__less__cancel__right__disj) ).
thf(1836,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ B )
& ( ord_less_real @ A @ C ) )
| ( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(466,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ E @ zero_zero_int )
=> ( ( ord_less_int @ A @ E )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_unique__quotient__lemma__neg) ).
thf(2547,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ E @ zero_zero_int )
=> ( ( ord_less_int @ A @ E )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(397,axiom,
! [A: nat,B: nat,C: int] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ C ) ) @ ( times_times_nat @ B @ ( number_number_of_nat @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_left__distrib__number__of) ).
thf(2344,plain,
! [A: nat,B: nat,C: int] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ C ) ) @ ( times_times_nat @ B @ ( number_number_of_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(893,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__special_I1_J) ).
thf(3727,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(33,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot) ).
thf(1281,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
=> ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(869,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_semiring__add__number__of) ).
thf(3647,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(314,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_power__add) ).
thf(2112,plain,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1017,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( zcong @ ( power_power_int @ B @ C ) @ one_one_int @ D )
=> ( zcong @ ( power_power_int @ B @ ( times_times_nat @ C @ A ) ) @ one_one_int @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_zcong__zpower__zmult) ).
thf(4080,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( zcong @ ( power_power_int @ B @ C ) @ one_one_int @ D )
=> ( zcong @ ( power_power_int @ B @ ( times_times_nat @ C @ A ) ) @ one_one_int @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(914,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( times_times_int @ A @ ( multInv @ B @ A ) ) @ one_one_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_MultInv__prop2) ).
thf(3784,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( times_times_int @ A @ ( multInv @ B @ A ) ) @ one_one_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(560,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
= ( ( ( ord_less_int @ zero_zero_int @ A )
& ( ord_less_int @ B @ C ) )
| ( ( ord_less_int @ A @ zero_zero_int )
& ( ord_less_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_mult__less__cancel__left__disj) ).
thf(2801,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
= ( ( ( ord_less_int @ zero_zero_int @ A )
& ( ord_less_int @ B @ C ) )
| ( ( ord_less_int @ A @ zero_zero_int )
& ( ord_less_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(944,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_Bit1__Min) ).
thf(3862,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1076,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) )
=> ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_wset__inv__mem__mem) ).
thf(4248,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) )
=> ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(772,axiom,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_not__sum__squares__lt__zero) ).
thf(3381,plain,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(12,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( times_times_real @ B @ C ) )
=> ( dvd_dvd_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_dvdI) ).
thf(1227,plain,
! [A: real,B: real,C: real] :
( ( A
= ( times_times_real @ B @ C ) )
=> ( dvd_dvd_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1142,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_semiring__numeral__0__eq__0) ).
thf(4429,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(105,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_power__mono) ).
thf(1498,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(673,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_zero__less__power) ).
thf(3102,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(900,axiom,
! [A: int,B: int] :
( ( quadRes @ A @ B )
= ( ? [C: int] : ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_QuadRes__def) ).
thf(3746,plain,
! [A: int,B: int] :
( ( quadRes @ A @ B )
= ( ? [C: int] : ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(192,axiom,
! [A: int,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( member_int @ B @ ( wset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_wset__mem__mem) ).
thf(1755,plain,
! [A: int,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( member_int @ B @ ( wset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(501,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_nat__less__le) ).
thf(2638,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_add__less__mono1) ).
thf(1402,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(895,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_diff__bin__simps_I9_J) ).
thf(3731,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(254,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_zcong__zless__0) ).
thf(1936,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1031,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_rel__simps_I22_J) ).
thf(4123,plain,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(57,axiom,
! [A: int,B: int] :
( ( ( div_mod_int @ A @ B )
= zero_zero_int )
= ( ? [C: int] :
( A
= ( times_times_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_zmod__eq__0__iff) ).
thf(1360,plain,
! [A: int,B: int] :
( ( ( div_mod_int @ A @ B )
= zero_zero_int )
= ( ? [C: int] :
( A
= ( times_times_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(14,axiom,
! [A: nat,B: real,C: nat,D: real] :
( ( dvd_dvd_real @ ( power_power_real @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_power__le__dvd) ).
thf(1234,plain,
! [A: nat,B: real,C: nat,D: real] :
( ( dvd_dvd_real @ ( power_power_real @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(121,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_mult__mono_H) ).
thf(1541,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(932,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ ( multInv @ D @ B ) ) @ ( times_times_int @ A @ ( multInv @ D @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_MultInv__zcong__prop1) ).
thf(3831,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ ( multInv @ D @ B ) ) @ ( times_times_int @ A @ ( multInv @ D @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(329,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(2157,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(315,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_crossproduct__eq) ).
thf(2115,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(195,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zle__refl) ).
thf(1762,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(454,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ one_one_real @ A )
=> ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_power__strict__increasing) ).
thf(2515,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ one_one_real @ A )
=> ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(310,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_mult__le__mono) ).
thf(2100,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(782,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_less__eq__int__code_I14_J) ).
thf(3413,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(28,axiom,
! [A: int > $o] :
( ( collect_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Collect__def) ).
thf(1270,plain,
! [A: int > $o] :
( ( collect_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(199,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_zcong__eq__zdvd__prop) ).
thf(1772,plain,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(23,axiom,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ B @ ( times_times_real @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_dvd__mult2) ).
thf(1259,plain,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ B @ ( times_times_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1026,axiom,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_power2__eq__square) ).
thf(4108,plain,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(403,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_real__le__eq__diff) ).
thf(2359,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(824,axiom,
! [A: int] :
( ( zprime @ A )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_prime__g__5) ).
thf(3518,plain,
! [A: int] :
( ( zprime @ A )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(977,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_zmult__1) ).
thf(3963,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(234,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_add__mult__distrib) ).
thf(1878,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(533,axiom,
~ ( ord_less_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_rel__simps_I3_J) ).
thf(2726,plain,
~ ( ord_less_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(498,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_mult__mono) ).
thf(2631,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_nat__neq__iff) ).
thf(1719,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)],[180]) ).
thf(582,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1041_mult__le__cancel1) ).
thf(2858,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(870,axiom,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__nat__number__of) ).
thf(3650,plain,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(995,axiom,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_zero__le__power2) ).
thf(4012,plain,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(369,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_nat__add__commute) ).
thf(2268,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(709,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_mult__right__mono__neg) ).
thf(3205,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(698,axiom,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( minus_minus_int @ ( div_mod_int @ A @ B ) @ C ) @ B )
= ( div_mod_int @ ( minus_minus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_zdiff__zmod__left) ).
thf(3176,plain,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( minus_minus_int @ ( div_mod_int @ A @ B ) @ C ) @ B )
= ( div_mod_int @ ( minus_minus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(641,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_plus__nat_Oadd__0) ).
thf(3018,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1092,axiom,
! [A: int] :
( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_Legendre__1mod4) ).
thf(4291,plain,
! [A: int] :
( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(559,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_diff__cancel2) ).
thf(2798,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(889,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_less__eq__int__code_I15_J) ).
thf(3714,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1181,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_zprime__power__zdvd__cancel__right) ).
thf(4545,plain,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1172,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_add__number__of__eq) ).
thf(4513,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(334,axiom,
! [A: int] :
( ( twoSqu919416604sum2sq @ A )
= ( ? [B: int,C: int] :
( ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ B @ C ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_is__sum2sq__def) ).
thf(2172,plain,
! [A: int] :
( ( twoSqu919416604sum2sq @ A )
= ( ? [B: int,C: int] :
( ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ B @ C ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1053,axiom,
! [A: nat,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_dvd__power__same) ).
thf(4180,plain,
! [A: nat,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1176,axiom,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(4530,plain,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1109,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( div_mod_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ) @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_pos__zmod__mult__2) ).
thf(4333,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( div_mod_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ) @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(1006,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_sum__power2__gt__zero__iff) ).
thf(4049,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1329,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1096,axiom,
~ ! [A: int] :
~ ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(4301,plain,
~ ! [A: int] :
~ ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(284,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_mult__nonneg__nonpos2) ).
thf(2023,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(754,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_real__mult__le__cancel__iff2) ).
thf(3326,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(256,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus_nat @ B @ C ) )
= ( ( ( ord_less_nat @ B @ C )
=> ( A @ zero_zero_nat ) )
& ! [D: nat] :
( ( B
= ( plus_plus_nat @ C @ D ) )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_nat__diff__split) ).
thf(1942,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus_nat @ B @ C ) )
= ( ( ( ord_less_nat @ B @ C )
=> ( A @ zero_zero_nat ) )
& ! [D: nat] :
( ( B
= ( plus_plus_nat @ C @ D ) )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1086,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_rel__simps_I32_J) ).
thf(4276,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(163,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_le__number__of__eq__not__less) ).
thf(1659,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(963,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_t) ).
thf(3922,plain,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(633,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_add__le__mono) ).
thf(3000,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(699,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_real__mult__le__cancel__iff1) ).
thf(3179,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(780,axiom,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(3407,plain,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(711,axiom,
ord_less_int @ min @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_bin__less__0__simps_I2_J) ).
thf(3210,plain,
ord_less_int @ min @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1048,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__mult__2__right) ).
thf(4167,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(186,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_mult__strict__left__mono) ).
thf(1739,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_mult__le__cancel2) ).
thf(1461,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1102,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ C @ B ) @ E )
= ( zcong @ A @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_zcong__zmult__prop1) ).
thf(4315,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ C @ B ) @ E )
= ( zcong @ A @ ( times_times_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(793,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_sum__power2__le__zero__iff) ).
thf(3441,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(384,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2312,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( div_mod_nat @ B @ C ) )
= ( div_mod_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_mod__mult__distrib2) ).
thf(1214,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( div_mod_nat @ B @ C ) )
= ( div_mod_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(705,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( zcong @ A @ one_one_int @ B )
| ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_zcong__square) ).
thf(3194,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( zcong @ A @ one_one_int @ B )
| ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(399,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_mult__nonpos__nonneg) ).
thf(2349,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(312,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ one_one_real @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_one__less__power) ).
thf(2108,plain,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ one_one_real @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(289,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_le__diff__conv2) ).
thf(2038,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(87,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_comm__semiring__class_Odistrib) ).
thf(1446,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(468,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_mult__nonneg__nonpos2) ).
thf(2551,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ( div_mod_nat @ A @ B )
= zero_zero_nat )
= ( ? [C: nat] :
( A
= ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_mod__eq__0__iff) ).
thf(1207,plain,
! [A: nat,B: nat] :
( ( ( div_mod_nat @ A @ B )
= zero_zero_nat )
= ( ? [C: nat] :
( A
= ( times_times_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(238,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ C @ A )
=> ( dvd_dvd_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_dvd__trans) ).
thf(1889,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ C @ A )
=> ( dvd_dvd_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(837,axiom,
! [A: int,B: int] :
( ( ord_less_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ pls @ B ) )
& ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_less__nat__number__of) ).
thf(3555,plain,
! [A: int,B: int] :
( ( ord_less_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ pls @ B ) )
& ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1150,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_less__int__code_I15_J) ).
thf(4457,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(741,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_mult__0) ).
thf(3294,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_eq__imp__le) ).
thf(1744,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= ( div_mod_nat @ ( minus_minus_nat @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_mod__geq) ).
thf(1263,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= ( div_mod_nat @ ( minus_minus_nat @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(463,axiom,
! [A: real,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_real ) )
=> ( dvd_dvd_real @ A @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_dvd__power) ).
thf(2536,plain,
! [A: real,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_real ) )
=> ( dvd_dvd_real @ A @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(899,axiom,
! [A: int] :
( ( power_power_real @ ( number267125858f_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_power2__eq__square__number__of) ).
thf(3743,plain,
! [A: int] :
( ( power_power_real @ ( number267125858f_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(474,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_less__diff__conv) ).
thf(2566,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1030,axiom,
! [A: int] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power2__eq__square__number__of) ).
thf(4120,plain,
! [A: int] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(270,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_le__square) ).
thf(1984,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(224,axiom,
! [A: nat] :
( ( A != one_one_nat )
= ( ( dvd_dvd_nat @ one_one_nat @ A )
& ~ ( dvd_dvd_nat @ A @ one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_gcd__lcm__complete__lattice__nat_Obot__less) ).
thf(1852,plain,
! [A: nat] :
( ( A != one_one_nat )
= ( ( dvd_dvd_nat @ one_one_nat @ A )
& ~ ( dvd_dvd_nat @ A @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(678,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3115,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1020,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_sum__squares__le__zero__iff) ).
thf(4086,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(885,axiom,
! [A: int,B: int] :
( ( twoSqu919416604sum2sq @ B )
=> ( ( twoSqu919416604sum2sq @ A )
=> ( twoSqu919416604sum2sq @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq) ).
thf(3703,plain,
! [A: int,B: int] :
( ( twoSqu919416604sum2sq @ B )
=> ( ( twoSqu919416604sum2sq @ A )
=> ( twoSqu919416604sum2sq @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(376,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_not__less0) ).
thf(2285,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(433,axiom,
! [A: int] :
( ( dvd_dvd_int @ zero_zero_int @ A )
=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_dvd__0__left) ).
thf(2450,plain,
! [A: int] :
( ( dvd_dvd_int @ zero_zero_int @ A )
=> ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(810,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_mult__Bit1) ).
thf(3486,plain,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(138,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1588,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(98,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_semiring__norm_I112_J) ).
thf(1478,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1126,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_semiring__add__number__of) ).
thf(4384,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(117,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ A @ B )
=> ( ( div_mod_int @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_mod__neg__neg__trivial) ).
thf(1530,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ A @ B )
=> ( ( div_mod_int @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(574,axiom,
! [A: int,B: int,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( times_times_real @ ( number267125858f_real @ B ) @ C ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mult__number__of__left) ).
thf(2836,plain,
! [A: int,B: int,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( times_times_real @ ( number267125858f_real @ B ) @ C ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(26,axiom,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( ( dvd_dvd_real @ B @ A )
=> ( dvd_dvd_real @ B @ ( plus_plus_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_dvd__add) ).
thf(1266,plain,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( ( dvd_dvd_real @ B @ A )
=> ( dvd_dvd_real @ B @ ( plus_plus_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1012,axiom,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_diff__bin__simps_I1_J) ).
thf(4068,plain,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(413,axiom,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ A @ B )
= ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_power__eq__imp__eq__base) ).
thf(2387,plain,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ A @ B )
= ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(909,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_zadd__0) ).
thf(3770,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(166,axiom,
! [A: int,B: int,C: int] :
( ( ( div_mod_int @ A @ B )
= ( div_mod_int @ C @ B ) )
= ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_zmod__eq__dvd__iff) ).
thf(1668,plain,
! [A: int,B: int,C: int] :
( ( ( div_mod_int @ A @ B )
= ( div_mod_int @ C @ B ) )
= ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(126,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_power__inject__exp) ).
thf(1552,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(579,axiom,
! [A: int] :
( ( div_mod_int @ A @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_zmod__self) ).
thf(2851,plain,
! [A: int] :
( ( div_mod_int @ A @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(359,axiom,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__special_I2_J) ).
thf(2243,plain,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(480,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_dvd_Oorder__refl) ).
thf(2581,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(438,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_941_le__antisym) ).
thf(2465,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)],[438]) ).
thf(1072,axiom,
! [A: nat,B: nat] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__sum) ).
thf(4237,plain,
! [A: nat,B: nat] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(775,axiom,
! [A: int,B: int,C: nat] :
( ( div_mod_int @ ( power_power_int @ ( div_mod_int @ A @ B ) @ C ) @ B )
= ( div_mod_int @ ( power_power_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_zpower__zmod) ).
thf(3390,plain,
! [A: int,B: int,C: nat] :
( ( div_mod_int @ ( power_power_int @ ( div_mod_int @ A @ B ) @ C ) @ B )
= ( div_mod_int @ ( power_power_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(716,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3222,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(446,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_add__leD2) ).
thf(2497,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1179,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_diff__bin__simps_I4_J) ).
thf(4540,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(832,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_semiring__numeral__0__eq__0) ).
thf(3540,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(81,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ( standardRes @ C @ A )
= ( standardRes @ C @ B ) )
= ( zcong @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_StandardRes__prop2) ).
thf(1429,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ( standardRes @ C @ A )
= ( standardRes @ C @ B ) )
= ( zcong @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1035,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_numeral__1__eq__1) ).
thf(4135,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(881,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(3692,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(294,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique) ).
thf(2052,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(523,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_mult__nonneg__nonpos2) ).
thf(2697,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(19,axiom,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
=> ( dvd_dvd_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_dvd__mult__left) ).
thf(1246,plain,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
=> ( dvd_dvd_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(659,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_comm__mult__left__mono) ).
thf(3064,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1080,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(4259,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(676,axiom,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_left__distrib__number__of) ).
thf(3109,plain,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(663,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_mult__is__0) ).
thf(3074,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(635,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1034_mult__less__mono1) ).
thf(3005,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(962,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_semiring__numeral__1__eq__1) ).
thf(3920,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1137,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A = zero_zero_int )
| ( A = one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_int__pos__lt__two__imp__zero__or__one) ).
thf(4416,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A = zero_zero_int )
| ( A = one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(708,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_zcong__eq__trans) ).
thf(3201,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(1068,axiom,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_power__even__eq) ).
thf(4223,plain,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(194,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_combine__common__factor) ).
thf(1759,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(67,axiom,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_right__diff__distrib__number__of) ).
thf(1393,plain,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(807,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Bit0__def) ).
thf(3476,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(903,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(3755,plain,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(1116,axiom,
! [A: int] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_number__of__Bit1) ).
thf(4352,plain,
! [A: int] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(736,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ B )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(3279,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ B )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_zero__less__mult__pos2) ).
thf(1695,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(942,axiom,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ D ) )
= ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_combine__common__factor) ).
thf(3856,plain,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ D ) )
= ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(746,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3306,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(303,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_gcd__lcm__complete__lattice__nat_Otop__le) ).
thf(2076,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(1005,axiom,
! [A: int > $o,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( A @ B )
=> ( ! [D: int] :
( ( ord_less_eq_int @ B @ D )
=> ( ( A @ D )
=> ( A @ ( plus_plus_int @ D @ one_one_int ) ) ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_int__ge__induct) ).
thf(4036,plain,
! [A: int > $o,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( A @ B )
=> ( ! [D: int] :
( ( ord_less_eq_int @ B @ D )
=> ( ( A @ D )
=> ( A @ ( plus_plus_int @ D @ one_one_int ) ) ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1183,axiom,
! [A: real,B: real] :
( ( power_power_real @ ( minus_minus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_power2__diff) ).
thf(4550,plain,
! [A: real,B: real] :
( ( power_power_real @ ( minus_minus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(1041,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_semiring__mult__number__of) ).
thf(4148,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(543,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2749,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(83,axiom,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_add__diff__add) ).
thf(1434,plain,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(226,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_sum__squares__eq__zero__iff) ).
thf(1857,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(273,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_le0) ).
thf(1991,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(555,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( standardRes @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_StandardRes__lbound) ).
thf(2788,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( standardRes @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(214,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_rel__simps_I28_J) ).
thf(1814,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(717,axiom,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(3225,plain,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(17,axiom,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_dvd__0__left) ).
thf(1241,plain,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
=> ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(525,axiom,
! [A: int,B: nat,C: nat] :
( ( times_times_nat @ ( number_number_of_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_right__distrib__number__of) ).
thf(2702,plain,
! [A: int,B: nat,C: nat] :
( ( times_times_nat @ ( number_number_of_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(840,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ one_one_int @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_one__less__power) ).
thf(3563,plain,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ one_one_int @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(547,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_le__trans) ).
thf(2761,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(697,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_add__0__iff) ).
thf(3173,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(1157,axiom,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_power__one) ).
thf(4476,plain,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(990,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_add__Bit0__Bit0) ).
thf(3999,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(752,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique) ).
thf(3321,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(866,axiom,
! [A: int] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_cube__square) ).
thf(3639,plain,
! [A: int] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(604,axiom,
! [A: int] :
( ( div_mod_int @ A @ ( number_number_of_int @ min ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_zmod__minus1__right) ).
thf(2915,plain,
! [A: int] :
( ( div_mod_int @ A @ ( number_number_of_int @ min ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(421,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_diff__mult__distrib) ).
thf(2408,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(557,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_mult__right__mono) ).
thf(2793,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(305,axiom,
ord_less_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_rel__simps_I6_J) ).
thf(2089,plain,
ord_less_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(936,axiom,
! [A: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_double__number__of__Bit0) ).
thf(3841,plain,
! [A: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(492,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ B @ A )
=> ( dvd_dvd_int @ B @ ( minus_minus_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_dvd__diff) ).
thf(2617,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ B @ A )
=> ( dvd_dvd_int @ B @ ( minus_minus_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(395,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
& ( ( plus_plus_nat @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_less__imp__add__positive) ).
thf(2338,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
& ( ( plus_plus_nat @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(275,axiom,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ord_less_int @ B @ ( div_mod_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_neg__mod__bound) ).
thf(1996,plain,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ord_less_int @ B @ ( div_mod_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(876,axiom,
! [A: int,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_int ) )
=> ( dvd_dvd_int @ A @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_dvd__power) ).
thf(3675,plain,
! [A: int,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_int ) )
=> ( dvd_dvd_int @ A @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(1099,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I19_J) ).
thf(4308,plain,
ord_less_eq_int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_Nat_Odiff__cancel) ).
thf(1906,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(183,axiom,
! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_757_one__dvd) ).
thf(1727,plain,
! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(517,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_mult__pos__pos) ).
thf(2677,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(599,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_mult__nonpos__nonpos) ).
thf(2904,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(470,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2556,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(650,axiom,
~ ( ord_less_int @ min @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_rel__simps_I7_J) ).
thf(3042,plain,
~ ( ord_less_int @ min @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(950,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_diff__bin__simps_I5_J) ).
thf(3890,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(29,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_le__imp__power__dvd) ).
thf(1273,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(251,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_less__diff__iff) ).
thf(1927,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(488,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
& ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1035_mult__less__cancel2) ).
thf(2602,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
& ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(770,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(3375,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(734,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( zcong @ ( times_times_int @ A @ ( inv @ B @ A ) ) @ one_one_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_inv__is__inv) ).
thf(3274,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( zcong @ ( times_times_int @ A @ ( inv @ B @ A ) ) @ one_one_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(879,axiom,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_power2__less__0) ).
thf(3686,plain,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(692,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) )
!= ( plus_plus_real @ ( times_times_real @ C @ B ) @ ( times_times_real @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_crossproduct__noteq) ).
thf(3158,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) )
!= ( plus_plus_real @ ( times_times_real @ C @ B ) @ ( times_times_real @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(317,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( C = A )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_dvd_Oord__less__eq__trans) ).
thf(2121,plain,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( C = A )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(324,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2144,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(610,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_le__iff__add) ).
thf(2936,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(159,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_le__number__of) ).
thf(1648,plain,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(871,axiom,
! [A: int] :
( ( zprime @ A )
=> ( ( d22set @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( wset @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_d22set__eq__wset) ).
thf(3660,plain,
! [A: int] :
( ( zprime @ A )
=> ( ( d22set @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( wset @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(277,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_realpow__minus__mult) ).
thf(2001,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(196,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1764,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(683,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_power__strict__mono) ).
thf(3130,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(288,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_less__or__eq__imp__le) ).
thf(2033,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)],[288]) ).
thf(326,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_nat__add__assoc) ).
thf(2149,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(530,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_add__eq__self__zero) ).
thf(2717,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(9,axiom,
! [A: nat,B: nat,C: nat] :
( ( div_mod_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ C ) @ B )
= ( div_mod_nat @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_mod__mult__self3) ).
thf(1219,plain,
! [A: nat,B: nat,C: nat] :
( ( div_mod_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ C ) @ B )
= ( div_mod_nat @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(855,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_rel__simps_I14_J) ).
thf(3607,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(812,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(3491,plain,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(100,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( div_mod_nat @ B @ C ) )
= ( ( ( C = zero_zero_nat )
=> ( A @ B ) )
& ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( ord_less_nat @ E @ C )
=> ( ( B
= ( plus_plus_nat @ ( times_times_nat @ C @ D ) @ E ) )
=> ( A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_split__mod) ).
thf(1483,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( div_mod_nat @ B @ C ) )
= ( ( ( C = zero_zero_nat )
=> ( A @ B ) )
& ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( ord_less_nat @ E @ C )
=> ( ( B
= ( plus_plus_nat @ ( times_times_nat @ C @ D ) @ E ) )
=> ( A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(665,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zle__antisym) ).
thf(3079,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1079,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(4256,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1129,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_crossproduct__noteq) ).
thf(4393,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(739,axiom,
! [A: int,B: int] :
( ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_eq_int @ zero_zero_int @ A ) )
| ( ( ord_less_eq_int @ B @ zero_zero_int )
& ( ord_less_eq_int @ A @ zero_zero_int ) ) )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_split__mult__pos__le) ).
thf(3289,plain,
! [A: int,B: int] :
( ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_eq_int @ zero_zero_int @ A ) )
| ( ( ord_less_eq_int @ B @ zero_zero_int )
& ( ord_less_eq_int @ A @ zero_zero_int ) ) )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1168,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_number__of2) ).
thf(4503,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(917,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_zero__power2) ).
thf(3792,plain,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(595,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_zcong__zmult__prop3) ).
thf(2894,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(62,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_real__two__squares__add__zero__iff) ).
thf(1374,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1200,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_zcong__zpower) ).
thf(4599,plain,
! [A: nat,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(774,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zle__add1__eq__le) ).
thf(3387,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(751,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_mult__strict__left__mono__neg) ).
thf(3319,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1016,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_rel__simps_I40_J) ).
thf(4077,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(723,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ ( times_times_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3240,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ ( times_times_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(972,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ ( times_times_int @ B @ ( multInv @ D @ C ) ) @ C ) @ D )
=> ( zcong @ ( times_times_int @ A @ C ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_aux______2) ).
thf(3945,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ ( times_times_int @ B @ ( multInv @ D @ C ) ) @ C ) @ D )
=> ( zcong @ ( times_times_int @ A @ C ) @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(733,axiom,
! [A: nat,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_power__mono) ).
thf(3272,plain,
! [A: nat,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1153,axiom,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(4465,plain,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(119,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_less__bin__lemma) ).
thf(1535,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(799,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_zdiff__zmult__distrib) ).
thf(3458,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(522,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_power__dvd__imp__le) ).
thf(2695,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(570,axiom,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_zcong__refl) ).
thf(2827,plain,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(713,axiom,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_le__special_I2_J) ).
thf(3213,plain,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1039,axiom,
zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_s1) ).
thf(4144,plain,
zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(769,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_less__special_I3_J) ).
thf(3372,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(835,axiom,
! [A: int,B: int,C: int] :
( ( A
= ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_dvdI) ).
thf(3547,plain,
! [A: int,B: int,C: int] :
( ( A
= ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(221,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_number__of__diff) ).
thf(1833,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1112,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_zero__power2) ).
thf(4341,plain,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1083,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_rel__simps_I51_J) ).
thf(4268,plain,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(865,axiom,
! [A: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_eq__0__number__of) ).
thf(3636,plain,
! [A: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(720,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_mult__mono) ).
thf(3234,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(578,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C )
=> ( ( zcong @ B @ zero_zero_int @ C )
| ( zcong @ A @ zero_zero_int @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_zcong__zprime__prod__zero) ).
thf(2849,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C )
=> ( ( zcong @ B @ zero_zero_int @ C )
| ( zcong @ A @ zero_zero_int @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(509,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B )
= ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_diff__add__assoc) ).
thf(2657,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B )
= ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1045,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_mult__2) ).
thf(4159,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(340,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( minus_minus_nat @ B @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_nat__diff__add__eq2) ).
thf(2188,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( minus_minus_nat @ B @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1100,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_semiring__mult__2__right) ).
thf(4309,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(415,axiom,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_mult__neg__pos) ).
thf(2393,plain,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(191,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_power__0) ).
thf(1752,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(731,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ A @ B ) )
& ( ord_less_int @ ( div_mod_int @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_pos__mod__conj) ).
thf(3266,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ A @ B ) )
& ( ord_less_int @ ( div_mod_int @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(282,axiom,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_realpow__pos__nth) ).
thf(2016,plain,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(206,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1795,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(417,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_zero__less__mult__pos2) ).
thf(2398,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(854,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(3604,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1125,axiom,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_not__sum__power2__lt__zero) ).
thf(4381,plain,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1197,axiom,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_power2__eq__imp__eq) ).
thf(4590,plain,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(779,axiom,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_power__eq__0__iff__number__of) ).
thf(3404,plain,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(946,axiom,
! [A: int > $o,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( A @ ( plus_plus_int @ B @ one_one_int ) )
=> ( ! [D: int] :
( ( ord_less_int @ B @ D )
=> ( ( A @ D )
=> ( A @ ( plus_plus_int @ D @ one_one_int ) ) ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_int__gr__induct) ).
thf(3868,plain,
! [A: int > $o,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( A @ ( plus_plus_int @ B @ one_one_int ) )
=> ( ! [D: int] :
( ( ord_less_int @ B @ D )
=> ( ( A @ D )
=> ( A @ ( plus_plus_int @ D @ one_one_int ) ) ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1161,axiom,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_zcong__1) ).
thf(4485,plain,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(342,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_mult__strict__right__mono) ).
thf(2193,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(910,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(3773,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(390,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( div_mod_nat @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_mod__le__divisor) ).
thf(2326,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( div_mod_nat @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(379,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_real @ D @ E )
=> ( ( ord_less_real @ C @ E )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ( plus_plus_real @ B @ A )
= one_one_real )
=> ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ B @ D ) @ ( times_times_real @ A @ C ) ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_convex__bound__lt) ).
thf(2293,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_real @ D @ E )
=> ( ( ord_less_real @ C @ E )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ( plus_plus_real @ B @ A )
= one_one_real )
=> ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ B @ D ) @ ( times_times_real @ A @ C ) ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(872,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_zero__less__power2) ).
thf(3663,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(634,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( dvd_dvd_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_nat__mult__dvd__cancel__disj) ).
thf(3002,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( dvd_dvd_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(50,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_gr0I) ).
thf(1332,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(295,axiom,
! [A: int,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_realpow__minus__mult) ).
thf(2055,plain,
! [A: int,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(884,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zpower__zpower) ).
thf(3700,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(241,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_dvd__trans) ).
thf(1897,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(783,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(3416,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(842,axiom,
! [A: int] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(3568,plain,
! [A: int] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(387,axiom,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_right__distrib__number__of) ).
thf(2319,plain,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(919,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rel__simps_I2_J) ).
thf(3796,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_eq__diff__iff) ).
thf(1503,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(679,axiom,
! [A: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_not__real__square__gt__zero) ).
thf(3118,plain,
! [A: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(352,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2220,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(594,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_Int2_Ozcong__zero) ).
thf(2891,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(664,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ ( div_mod_nat @ A @ D ) ) @ B ) @ ( times_times_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1195_mod__lemma) ).
thf(3077,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ ( div_mod_nat @ A @ D ) ) @ B ) @ ( times_times_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(882,axiom,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_power__even__eq) ).
thf(3695,plain,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(538,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_zero__le__power) ).
thf(2738,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(760,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_nat ) )
=> ( dvd_dvd_nat @ A @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_dvd__power) ).
thf(3340,plain,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ B )
| ( A = one_one_nat ) )
=> ( dvd_dvd_nat @ A @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1191,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_self__quotient__aux2) ).
thf(4573,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(16,axiom,
! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_dvd__0__right) ).
thf(1239,plain,
! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(430,axiom,
! [A: real,B: real] :
( ( B != zero_zero_real )
=> ( ( A != zero_zero_real )
=> ( ( times_times_real @ B @ A )
!= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_no__zero__divisors) ).
thf(2442,plain,
! [A: real,B: real] :
( ( B != zero_zero_real )
=> ( ( A != zero_zero_real )
=> ( ( times_times_real @ B @ A )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(791,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_power__Suc__less) ).
thf(3436,plain,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(93,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ A @ one_one_nat )
& ~ ( dvd_dvd_nat @ one_one_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot) ).
thf(1464,plain,
! [A: nat] :
~ ( ( dvd_dvd_nat @ A @ one_one_nat )
& ~ ( dvd_dvd_nat @ one_one_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(441,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_real__mult__1) ).
thf(2474,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(452,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_dvd__0__left) ).
thf(2510,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(518,axiom,
! [A: $o,B: $o,C: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( B = A ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ C )
=> B )
= ( ( ord_less_eq_int @ zero_zero_int @ C )
=> A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_imp__le__cong) ).
thf(2679,plain,
! [A: $o,B: $o,C: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( B = A ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ C )
=> B )
= ( ( ord_less_eq_int @ zero_zero_int @ C )
=> A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1070,axiom,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_two__realpow__ge__one) ).
thf(4228,plain,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1097,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_zcong__zmult) ).
thf(4305,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(309,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
= ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_nat__mult__dvd__cancel1) ).
thf(2097,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
= ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_mult__dvd__mono) ).
thf(1722,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(575,axiom,
! [A: int,B: int] :
( ( ~ ( zcong @ A @ zero_zero_int @ B ) )
= ( ( standardRes @ B @ A )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_StandardRes__prop3) ).
thf(2839,plain,
! [A: int,B: int] :
( ( ~ ( zcong @ A @ zero_zero_int @ B ) )
= ( ( standardRes @ B @ A )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(613,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_comm__semiring__class_Odistrib) ).
thf(2945,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(581,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) )
=> ( ( dvd_dvd_int @ B @ C )
| ( dvd_dvd_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_zprime__zdvd__zmult) ).
thf(2856,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) )
=> ( ( dvd_dvd_int @ B @ C )
| ( dvd_dvd_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(773,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_le__special_I2_J) ).
thf(3384,plain,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(299,axiom,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_zero__le__square) ).
thf(2065,plain,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(304,axiom,
! [A: int,B: int] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_Legendre__def) ).
thf(2079,plain,
! [A: int,B: int] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(383,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(2311,plain,
ord_less_eq_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1166,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_sum__power2__ge__zero) ).
thf(4498,plain,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1121,axiom,
! [A: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__special_I2_J) ).
thf(4369,plain,
! [A: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(355,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_power__0__left__number__of) ).
thf(2229,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(926,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_power2__less__imp__less) ).
thf(3815,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(722,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_power__gt1__lemma) ).
thf(3238,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(350,axiom,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_power__mult__distrib) ).
thf(2214,plain,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(907,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_zless__add1__eq) ).
thf(3764,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_998_nat__add__left__cancel__le) ).
thf(1894,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(975,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_left__distrib__number__of) ).
thf(3957,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(552,axiom,
! [A: int,B: int > $o,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ! [D: int] :
( ( B @ D )
=> ( B @ ( plus_plus_int @ D @ C ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ! [D: int] :
( ( B @ D )
=> ( B @ ( plus_plus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_incr__mult__lemma) ).
thf(2774,plain,
! [A: int,B: int > $o,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ! [D: int] :
( ( B @ D )
=> ( B @ ( plus_plus_int @ D @ C ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ! [D: int] :
( ( B @ D )
=> ( B @ ( plus_plus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(878,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3683,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(115,axiom,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_power__one) ).
thf(1524,plain,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(823,axiom,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_power__mult__distrib) ).
thf(3515,plain,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(912,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(3779,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(600,axiom,
! [A: nat,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_power__strict__mono) ).
thf(2906,plain,
! [A: nat,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(784,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_nat__number__of__Pls) ).
thf(3419,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(365,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_mult__le__mono1) ).
thf(2257,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(253,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zless__linear) ).
thf(1933,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(360,axiom,
ord_less_eq_int @ min @ min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_rel__simps_I24_J) ).
thf(2246,plain,
ord_less_eq_int @ min @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_add__diff__inverse) ).
thf(1492,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_diff__add__inverse2) ).
thf(1603,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(675,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(3106,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(803,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_power__le__imp__le__exp) ).
thf(3468,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1014,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_power2__less__imp__less) ).
thf(4073,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(208,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_mult__nonneg__nonneg) ).
thf(1801,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1043,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_zcong__zadd) ).
thf(4154,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(410,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_sum__squares__gt__zero__iff) ).
thf(2378,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(700,axiom,
! [A: real,B: real] :
( ( ord_less_real @ B @ zero_zero_real )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_mult__neg__neg) ).
thf(3182,plain,
! [A: real,B: real] :
( ( ord_less_real @ B @ zero_zero_real )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(848,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_semiring__one__add__one__is__two) ).
thf(3586,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(660,axiom,
! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_dvd__0__right) ).
thf(3066,plain,
! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(596,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_le__add__diff) ).
thf(2896,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_diff__is__0__eq) ).
thf(1969,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(41,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_power__mult) ).
thf(1307,plain,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(337,axiom,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ ( number267125858f_real @ B ) @ C ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_add__number__of__diff1) ).
thf(2180,plain,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ ( number267125858f_real @ B ) @ C ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(715,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ( div_mod_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_zdvd__iff__zmod__eq__0__number__of) ).
thf(3219,plain,
! [A: int,B: int] :
( ( dvd_dvd_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ( div_mod_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(489,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_dvd_Oless__imp__not__eq) ).
thf(2605,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1189,axiom,
quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(4569,plain,
quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1152,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_rel__simps_I16_J) ).
thf(4462,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1002,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__number__of__int__code) ).
thf(4028,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(246,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_power__Suc__less) ).
thf(1909,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1063,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_sum__power2__eq__zero__iff) ).
thf(4208,plain,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(1108,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(4332,plain,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(647,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_zcong__not) ).
thf(3034,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(363,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_less__imp__le__nat) ).
thf(2252,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(607,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_eq_int @ zero_zero_int @ B ) )
| ( ( ord_less_eq_int @ A @ zero_zero_int )
& ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_zero__le__mult__iff) ).
thf(2928,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_eq_int @ zero_zero_int @ B ) )
| ( ( ord_less_eq_int @ A @ zero_zero_int )
& ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(624,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ B @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_Euler_Oaux1) ).
thf(2974,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ B @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(258,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_add__leD1) ).
thf(1952,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(951,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zless__imp__add1__zle) ).
thf(3893,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(479,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
& ~ ( dvd_dvd_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less) ).
thf(2578,plain,
! [A: nat] :
~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
& ~ ( dvd_dvd_nat @ A @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(285,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_dvd__power__same) ).
thf(2025,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(564,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ A @ ( times_times_int @ B @ ( multInv @ C @ D ) ) @ C )
=> ( zcong @ ( times_times_int @ A @ D ) @ ( times_times_int @ ( times_times_int @ B @ ( multInv @ C @ D ) ) @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_aux______1) ).
thf(2812,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ A @ ( times_times_int @ B @ ( multInv @ C @ D ) ) @ C )
=> ( zcong @ ( times_times_int @ A @ D ) @ ( times_times_int @ ( times_times_int @ B @ ( multInv @ C @ D ) ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(656,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(3055,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(994,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__number__of__left) ).
thf(4009,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(385,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_divides__mul__l) ).
thf(2314,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(495,axiom,
! [A: nat,B: real] :
( ( ord_less_eq_real @ one_one_real @ B )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_one__le__power) ).
thf(2625,plain,
! [A: nat,B: real] :
( ( ord_less_eq_real @ one_one_real @ B )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1011,axiom,
! [A: int] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_rel__simps_I45_J) ).
thf(4064,plain,
! [A: int] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(274,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1993,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(217,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_less__special_I4_J) ).
thf(1821,plain,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(185,axiom,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_power__eq__if) ).
thf(1731,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(554,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2785,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(485,axiom,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ ( number267125858f_real @ B ) @ C ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__number__of__left) ).
thf(2593,plain,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ ( number267125858f_real @ B ) @ C ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(809,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(3483,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(980,axiom,
! [A: int] :
( ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( zfact @ A )
= one_one_int ) )
& ( ~ ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( zfact @ A )
= ( times_times_int @ A @ ( zfact @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1071_zfact_Osimps) ).
thf(3971,plain,
! [A: int] :
( ( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( zfact @ A )
= one_one_int ) )
& ( ~ ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( zfact @ A )
= ( times_times_int @ A @ ( zfact @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(847,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_zmult__assoc) ).
thf(3583,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(373,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_trans__le__add1) ).
thf(2278,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(469,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_real__mult__less__iff1) ).
thf(2553,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(97,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( C = A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_dvd_Oord__le__eq__trans) ).
thf(1474,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( C = A )
=> ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(140,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1594,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(157,axiom,
~ ( ord_less_eq_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_rel__simps_I20_J) ).
thf(1643,plain,
~ ( ord_less_eq_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(961,axiom,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_add__Pls) ).
thf(3917,plain,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(407,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( div_mod_int @ ( number_number_of_int @ min ) @ A )
= ( minus_minus_int @ A @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_zmod__minus1) ).
thf(2369,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( div_mod_int @ ( number_number_of_int @ min ) @ A )
= ( minus_minus_int @ A @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(640,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( dvd_dvd_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_dvd__mult__cancel) ).
thf(3016,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( dvd_dvd_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(499,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2633,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(1059,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_diff__bin__simps_I10_J) ).
thf(4196,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(762,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
=> ( dvd_dvd_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_dvd__mult__left) ).
thf(3348,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
=> ( dvd_dvd_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(347,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2207,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(210,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_power__less__imp__less__base) ).
thf(1805,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(585,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ B @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_diff__less__mono2) ).
thf(2867,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ B @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_add__lessD1) ).
thf(1396,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(429,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_nat__mult__commute) ).
thf(2439,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(619,axiom,
! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_gcd__lcm__complete__lattice__nat_Obot__least) ).
thf(2962,plain,
! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(405,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( dvd_dvd_int @ ( power_power_int @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_power__le__dvd) ).
thf(2365,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( dvd_dvd_int @ ( power_power_int @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(349,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_divides__mul__r) ).
thf(2212,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(862,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3627,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(905,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_diff__bin__simps_I7_J) ).
thf(3759,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(935,axiom,
! [A: int] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_number__of__Bit0) ).
thf(3838,plain,
! [A: int] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(549,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_nat__mult__less__cancel1) ).
thf(2765,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(786,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_crossproduct__eq) ).
thf(3423,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(444,axiom,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_ex__least__nat__le) ).
thf(2481,plain,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(322,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_nat__zero__less__power__iff) ).
thf(2139,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)],[322]) ).
thf(923,axiom,
! [A: int,B: int] :
( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int @ B )
= ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_inv__not__p__minus__1__aux) ).
thf(3806,plain,
! [A: int,B: int] :
( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int @ B )
= ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(608,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
=> ( dvd_dvd_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_dvd__mult__right) ).
thf(2931,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
=> ( dvd_dvd_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(377,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_nat__power__less__imp__less) ).
thf(2288,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(200,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( dvd_dvd_int @ C @ B )
=> ( ( div_mod_int @ ( div_mod_int @ A @ B ) @ C )
= ( div_mod_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_zmod__zdvd__zmod) ).
thf(1775,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( dvd_dvd_int @ C @ B )
=> ( ( div_mod_int @ ( div_mod_int @ A @ B ) @ C )
= ( div_mod_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(544,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_minus__nat_Odiff__0) ).
thf(2752,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(621,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_power__less__power__Suc) ).
thf(2967,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(414,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2390,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(21,axiom,
! [A: real,B: real,C: real,D: real] :
( ( dvd_dvd_real @ C @ D )
=> ( ( dvd_dvd_real @ A @ B )
=> ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_mult__dvd__mono) ).
thf(1250,plain,
! [A: real,B: real,C: real,D: real] :
( ( dvd_dvd_real @ C @ D )
=> ( ( dvd_dvd_real @ A @ B )
=> ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(821,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
=> ( dvd_dvd_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_dvd__mult__right) ).
thf(3512,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
=> ( dvd_dvd_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1088,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_mult__numeral__1) ).
thf(4282,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(957,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_one__is__num__one) ).
thf(3908,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(521,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_zero__less__mult__pos) ).
thf(2693,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(450,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_power__less__power__Suc) ).
thf(2506,plain,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1156,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_rel__simps_I44_J) ).
thf(4473,plain,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(1019,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(4084,plain,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(947,axiom,
! [A: nat] :
( ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= one_one_int )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( number_number_of_int @ min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_neg__one__power) ).
thf(3881,plain,
! [A: nat] :
( ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= one_one_int )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( number_number_of_int @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(637,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(3009,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1141,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( dvd_dvd_int @ D @ E )
=> ( ( dvd_dvd_int @ D @ ( plus_plus_int @ B @ C ) )
= ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_zdvd__period) ).
thf(4426,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( dvd_dvd_int @ D @ E )
=> ( ( dvd_dvd_int @ D @ ( plus_plus_int @ B @ C ) )
= ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(212,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_le__add2) ).
thf(1809,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(164,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_crossproduct__noteq) ).
thf(1662,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_diff__add__inverse) ).
thf(1873,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(969,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ A @ B ) ) @ ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_mult__sum2sq) ).
thf(3936,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ A @ B ) ) @ ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ C @ D ) ) )
= ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(512,axiom,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_left__diff__distrib__number__of) ).
thf(2665,plain,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(370,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_add__gr__0) ).
thf(2271,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(440,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_diff__diff__cancel) ).
thf(2471,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(687,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_power__gt1__lemma) ).
thf(3146,plain,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(109,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ( minus_minus_nat @ C @ B )
= A )
= ( C
= ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_le__imp__diff__is__add) ).
thf(1509,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ( minus_minus_nat @ C @ B )
= A )
= ( C
= ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(497,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ C )
=> ( ( ord_less_eq_int @ B @ A )
| ( ord_less_eq_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_Euler_Oaux2) ).
thf(2629,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ C )
=> ( ( ord_less_eq_int @ B @ A )
| ( ord_less_eq_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(53,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_zcong__def) ).
thf(1340,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1117,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_nat__1__add__1) ).
thf(4355,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(740,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_mult__pos__neg) ).
thf(3292,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1110,axiom,
! [A: int,B: int,C: int] :
( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_Euler_Oaux____1) ).
thf(4336,plain,
! [A: int,B: int,C: int] :
( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(843,axiom,
! [A: nat] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_power__m1__even) ).
thf(3571,plain,
! [A: nat] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(794,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( zcong @ ( times_times_int @ ( standardRes @ C @ A ) @ ( standardRes @ C @ B ) ) @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_StandardRes__prop4) ).
thf(3444,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( zcong @ ( times_times_int @ ( standardRes @ C @ A ) @ ( standardRes @ C @ B ) ) @ ( times_times_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(357,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_mult__cancel1) ).
thf(2239,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1133,axiom,
( ~ ( quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
!= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(4405,plain,
( ~ ( quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
!= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(646,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_power__strict__increasing__iff) ).
thf(3031,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(566,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
thf(2816,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(94,axiom,
! [A: real,B: nat,C: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1467,plain,
! [A: real,B: nat,C: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(631,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_number__of__add) ).
thf(2994,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(693,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_number__of__Pls) ).
thf(3161,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(875,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_zmult__commute) ).
thf(3672,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(982,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3981,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(589,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_878_less__zeroE) ).
thf(2878,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(449,axiom,
! [A: int] :
( ( zprime @ A )
= ( ( ord_less_int @ one_one_int @ A )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_zprime__def) ).
thf(2503,plain,
! [A: int] :
( ( zprime @ A )
= ( ( ord_less_int @ one_one_int @ A )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(31,axiom,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( ( dvd_dvd_real @ C @ A )
=> ( dvd_dvd_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_dvd__trans) ).
thf(1277,plain,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( ( dvd_dvd_real @ C @ A )
=> ( dvd_dvd_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1007,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(4052,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(653,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_int__0__less__1) ).
thf(3048,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1188,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_int__0__neq__1) ).
thf(4566,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(798,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__int__code_I14_J) ).
thf(3455,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(96,axiom,
! [A: int] : ( dvd_dvd_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_dvd__refl) ).
thf(1472,plain,
! [A: int] : ( dvd_dvd_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(577,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_number__of__Bit1) ).
thf(2846,plain,
! [A: int] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(473,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_power__le__dvd) ).
thf(2564,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(1194,axiom,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_less__special_I2_J) ).
thf(4581,plain,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(261,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_dvd_Oneq__le__trans) ).
thf(1958,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(612,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B )
= ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_nat__eq__add__iff1) ).
thf(2942,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B )
= ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(453,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1069_norR__mem__unique__aux) ).
thf(2513,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(666,axiom,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_power__one) ).
thf(3082,plain,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(933,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3833,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= A ) )
& ( ~ ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= ( div_mod_nat @ ( minus_minus_nat @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1181_mod__if) ).
thf(1252,plain,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= A ) )
& ( ~ ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= ( div_mod_nat @ ( minus_minus_nat @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(531,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_power__one__right) ).
thf(2720,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1105,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_rel__simps_I12_J) ).
thf(4324,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(330,axiom,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_less__special_I1_J) ).
thf(2160,plain,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(572,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_zcong__zdiff) ).
thf(2831,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_986_le__eq__less__or__eq) ).
thf(1547,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(189,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( member_int @ A @ ( wset @ ( minus_minus_int @ C @ one_one_int ) @ B ) )
=> ( member_int @ A @ ( wset @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_wset__subset) ).
thf(1748,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( member_int @ A @ ( wset @ ( minus_minus_int @ C @ one_one_int ) @ B ) )
=> ( member_int @ A @ ( wset @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(207,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ C @ B @ A )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ B @ A )
=> ( C = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_zcong__less__eq) ).
thf(1798,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ C @ B @ A )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ B @ A )
=> ( C = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(381,axiom,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( ord_less_real @ A @ B )
=> ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_linorder__neqE__linordered__idom) ).
thf(2298,plain,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( ord_less_real @ A @ B )
=> ( ord_less_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(897,axiom,
! [A: int,B: int] :
( ( div_mod_int @ ( number_number_of_int @ ( bit0 @ A ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_zmod__number__of__Bit0) ).
thf(3737,plain,
! [A: int,B: int] :
( ( div_mod_int @ ( number_number_of_int @ ( bit0 @ A ) ) @ ( number_number_of_int @ ( bit0 @ B ) ) )
= ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(198,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_less__imp__diff__less) ).
thf(1770,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(584,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_real @ C @ ( times_times_real @ E @ A ) )
!= ( plus_plus_real @ D @ ( times_times_real @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_add__scale__eq__noteq) ).
thf(2863,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_real @ C @ ( times_times_real @ E @ A ) )
!= ( plus_plus_real @ D @ ( times_times_real @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(749,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1033_mult__less__mono2) ).
thf(3315,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1119,axiom,
! [A: int] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_eq__number__of__0) ).
thf(4360,plain,
! [A: int] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(819,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_semiring__one__add__one__is__two) ).
thf(3507,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1163,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_right__distrib__number__of) ).
thf(4490,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(677,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_mult__less__cancel1) ).
thf(3112,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(625,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2977,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(146,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_power__one__right) ).
thf(1611,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(409,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
= ( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_dvd_Ole__less) ).
thf(2375,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
= ( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(11,axiom,
! [A: nat,B: nat,C: real,D: real] :
( ( dvd_dvd_real @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_dvd__power__le) ).
thf(1225,plain,
! [A: nat,B: nat,C: real,D: real] :
( ( dvd_dvd_real @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(297,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_int__one__le__iff__zero__less) ).
thf(2060,plain,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_less__not__refl3) ).
thf(1566,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(955,axiom,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_add__Pls__right) ).
thf(3904,plain,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(729,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_real__mult__assoc) ).
thf(3260,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(483,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
= ( ord_less_eq_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_rel__simps_I26_J) ).
thf(2588,plain,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
= ( ord_less_eq_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(718,axiom,
! [A: int,B: int] :
( ( member_int @ A @ ( d22set @ B ) )
=> ( ord_less_int @ one_one_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_d22set__g__1) ).
thf(3228,plain,
! [A: int,B: int] :
( ( member_int @ A @ ( d22set @ B ) )
=> ( ord_less_int @ one_one_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(335,axiom,
! [A: int,B: int] :
( ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_eq_int @ A @ zero_zero_int ) )
| ( ( ord_less_eq_int @ B @ zero_zero_int )
& ( ord_less_eq_int @ zero_zero_int @ A ) ) )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_split__mult__neg__le) ).
thf(2175,plain,
! [A: int,B: int] :
( ( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_eq_int @ A @ zero_zero_int ) )
| ( ( ord_less_eq_int @ B @ zero_zero_int )
& ( ord_less_eq_int @ zero_zero_int @ A ) ) )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1090,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_power__increasing__iff) ).
thf(4287,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(202,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_mult__mono_H) ).
thf(1780,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(568,axiom,
! [A: nat,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_zero__le__power) ).
thf(2821,plain,
! [A: nat,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(915,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_less__eq__int__code_I13_J) ).
thf(3786,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(657,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_zcong__sym) ).
thf(3058,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1198,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__special_I4_J) ).
thf(4593,plain,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(593,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2888,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(204,axiom,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ord_less_eq_int @ ( div_mod_int @ A @ B ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_neg__mod__sign) ).
thf(1790,plain,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ord_less_eq_int @ ( div_mod_int @ A @ B ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(606,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_power__0__left) ).
thf(2920,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(999,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__int__code_I13_J) ).
thf(4020,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1040,axiom,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(4145,plain,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(243,axiom,
! [A: int] :
~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_not__square__less__zero) ).
thf(1901,plain,
! [A: int] :
~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(861,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_int @ C @ ( times_times_int @ E @ A ) )
!= ( plus_plus_int @ D @ ( times_times_int @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq) ).
thf(3623,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_int @ C @ ( times_times_int @ E @ A ) )
!= ( plus_plus_int @ D @ ( times_times_int @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(670,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_power__less__imp__less__exp) ).
thf(3095,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(439,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_nat__mult__eq__cancel__disj) ).
thf(2468,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(401,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_power__le__imp__le__exp) ).
thf(2354,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(177,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_nat__dvd__1__iff__1) ).
thf(1711,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(542,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2747,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(475,axiom,
! [A: int,B: int] : ( zcong @ A @ ( standardRes @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_StandardRes__prop1) ).
thf(2569,plain,
! [A: int,B: int] : ( zcong @ A @ ( standardRes @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(725,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_divides__exp) ).
thf(3246,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1145,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(4437,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(867,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_semiring__mult__2__right) ).
thf(3642,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1114,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_power__one__right) ).
thf(4346,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(1022,axiom,
~ ! [A: int] :
~ ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) ).
thf(4092,plain,
~ ! [A: int] :
~ ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1073,axiom,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_field__power__not__zero) ).
thf(4240,plain,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(307,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(2092,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(82,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_mult__pos__pos) ).
thf(1432,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1057,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( ? [D: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_zcong__iff__lin) ).
thf(4190,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( ? [D: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(332,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_one__neq__zero) ).
thf(2165,plain,
one_one_real != zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(38,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1300,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( standardRes @ A @ B )
= ( div_mod_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_StandardRes__def) ).
thf(1452,plain,
! [A: int,B: int] :
( ( standardRes @ A @ B )
= ( div_mod_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(155,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_mult__0__right) ).
thf(1637,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(519,axiom,
! [A: int,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( member_int @ B @ ( d22set @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_d22set__mem) ).
thf(2688,plain,
! [A: int,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( member_int @ B @ ( d22set @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(757,axiom,
! [A: real,B: nat,C: real] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_power__less__imp__less__base) ).
thf(3334,plain,
! [A: real,B: nat,C: real] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(806,axiom,
twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(3475,plain,
twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(644,axiom,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
= ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_number__of__reorient) ).
thf(3026,plain,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
= ( B
= ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(425,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_mult__strict__left__mono__neg) ).
thf(2429,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(372,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( member_int @ B @ ( d22set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_d22set__le__swap) ).
thf(2276,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( member_int @ B @ ( d22set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(921,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_zero__is__num__zero) ).
thf(3801,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(268,axiom,
! [A: real,B: real] :
( ( ord_less_real @ B @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_mult__neg__pos) ).
thf(1980,plain,
! [A: real,B: real] :
( ( ord_less_real @ B @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(318,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( times_times_int @ A @ B ) )
=> ( ( dvd_dvd_int @ C @ A )
| ( dvd_dvd_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_zprime__zdvd__zmult__better) ).
thf(2128,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( times_times_int @ A @ B ) )
=> ( ( dvd_dvd_int @ C @ A )
| ( dvd_dvd_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_order__le__neq__implies__less) ).
thf(1317,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)],[45]) ).
thf(220,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_rel__simps_I8_J) ).
thf(1830,plain,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(682,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_divides__antisym) ).
thf(3127,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(931,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_mult__Bit0) ).
thf(3828,plain,
! [A: int,B: int] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1034,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_add__0__iff) ).
thf(4132,plain,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(388,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_mult__left__mono) ).
thf(2322,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(120,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1538,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(487,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_real__mult__left__cancel) ).
thf(2599,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(938,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_rel__simps_I37_J) ).
thf(3847,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(766,axiom,
! [A: real] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_power2__less__0) ).
thf(3359,plain,
! [A: real] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(755,axiom,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_zero__le__square) ).
thf(3329,plain,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(291,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_linorder__neqE__nat) ).
thf(2044,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)],[291]) ).
thf(1029,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_eq__number__of) ).
thf(4117,plain,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(135,axiom,
! [A: int,B: int,C: int] :
( ( C != zero_zero_int )
=> ( ( dvd_dvd_int @ A @ B )
= ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_zdvd__mono) ).
thf(1579,plain,
! [A: int,B: int,C: int] :
( ( C != zero_zero_int )
=> ( ( dvd_dvd_int @ A @ B )
= ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(614,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_combine__common__factor) ).
thf(2948,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(422,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_divides__le) ).
thf(2411,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(122,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_zcong__trans) ).
thf(1543,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(174,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_number__of__mult) ).
thf(1702,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(34,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_le__0__eq) ).
thf(1284,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1143,axiom,
! [A: int] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_rel__simps_I42_J) ).
thf(4431,plain,
! [A: int] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(643,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_less__eq__nat_Osimps_I1_J) ).
thf(3024,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(611,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_less__add__eq__less) ).
thf(2939,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_diff__le__mono2) ).
thf(1372,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(516,axiom,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_mult__neg__neg) ).
thf(2675,plain,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_nat__mult__eq__1__iff) ).
thf(1404,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(56,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_power__less__imp__less__base) ).
thf(1358,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(361,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_le__add__diff__inverse) ).
thf(2247,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(681,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_left__add__mult__distrib) ).
thf(3124,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(630,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_mult__strict__left__mono) ).
thf(2992,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1075,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ A @ ( wset @ B @ C ) )
=> ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_wset__mem__inv__mem) ).
thf(4246,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ A @ ( wset @ B @ C ) )
=> ( member_int @ ( inv @ C @ A ) @ ( wset @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(765,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_nat__add__right__cancel) ).
thf(3356,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1171,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_rel__simps_I48_J) ).
thf(4510,plain,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(576,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( ( dvd_dvd_nat @ C @ A )
& ~ ( dvd_dvd_nat @ A @ C ) )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_dvd_Ole__less__trans) ).
thf(2843,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( ( dvd_dvd_nat @ C @ A )
& ~ ( dvd_dvd_nat @ A @ C ) )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(265,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_power__increasing__iff) ).
thf(1972,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(528,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( A != zero_zero_int )
=> ( dvd_dvd_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_zdvd__mult__cancel) ).
thf(2711,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( A != zero_zero_int )
=> ( dvd_dvd_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(108,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( ( dvd_dvd_nat @ C @ A )
& ~ ( dvd_dvd_nat @ A @ C ) )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_dvd_Oless__trans) ).
thf(1506,plain,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( ( dvd_dvd_nat @ C @ A )
& ~ ( dvd_dvd_nat @ A @ C ) )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1061,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_mult__2) ).
thf(4202,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(137,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_mult__zero__left) ).
thf(1585,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(534,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ A @ ( wset @ B @ C ) )
=> ( ord_less_int @ A @ ( minus_minus_int @ C @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_wset__less) ).
thf(2728,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( member_int @ A @ ( wset @ B @ C ) )
=> ( ord_less_int @ A @ ( minus_minus_int @ C @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(179,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_q__pos__lemma) ).
thf(1717,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(287,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( ( ( ord_less_int @ zero_zero_int @ B )
& ( ord_less_int @ A @ C ) )
| ( ( ord_less_int @ B @ zero_zero_int )
& ( ord_less_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_mult__less__cancel__right__disj) ).
thf(2030,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( ( ( ord_less_int @ zero_zero_int @ B )
& ( ord_less_int @ A @ C ) )
| ( ( ord_less_int @ B @ zero_zero_int )
& ( ord_less_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(235,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_le__refl) ).
thf(1881,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(562,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_diff__0__eq__0) ).
thf(2807,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(691,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( div_mod_int @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_zmod__le__nonneg__dividend) ).
thf(3156,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( div_mod_int @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(960,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_rel__simps_I15_J) ).
thf(3914,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(636,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_power__increasing) ).
thf(3007,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1173,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_int )
=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_even__power__le__0__imp__0) ).
thf(4516,plain,
! [A: int,B: nat] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_int )
=> ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1027,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rel__simps_I29_J) ).
thf(4111,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(1136,axiom,
! [A: int] : ( dvd_dvd_int @ one_one_int @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_one__dvd) ).
thf(4414,plain,
! [A: int] : ( dvd_dvd_int @ one_one_int @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(1066,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_left__diff__distrib__number__of) ).
thf(4217,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(148,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_781_mult__left__mono__neg) ).
thf(1617,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(588,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_less__irrefl__nat) ).
thf(2875,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(223,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ ( times_times_int @ B @ C ) @ D ) )
=> ( ( ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ D )
& ( ord_less_int @ D @ B ) ) )
& ( ~ ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ D )
& ( ord_less_eq_int @ D @ zero_zero_int ) ) ) )
=> ( ( B != zero_zero_int )
=> ( ( div_mod_int @ A @ B )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_divmod__int__rel__mod__eq) ).
thf(1839,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ ( times_times_int @ B @ C ) @ D ) )
=> ( ( ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ D )
& ( ord_less_int @ D @ B ) ) )
& ( ~ ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ D )
& ( ord_less_eq_int @ D @ zero_zero_int ) ) ) )
=> ( ( B != zero_zero_int )
=> ( ( div_mod_int @ A @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(797,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(3452,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(443,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ~ ( zcong @ B @ zero_zero_int @ C )
& ~ ( zcong @ A @ zero_zero_int @ C ) )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_zcong__zprime__prod__zero__contra) ).
thf(2479,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ~ ( zcong @ B @ zero_zero_int @ C )
& ~ ( zcong @ A @ zero_zero_int @ C ) )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1196,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_power3__eq__cube) ).
thf(4587,plain,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(567,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_le__diff__iff) ).
thf(2818,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(263,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_mult__le__0__iff) ).
thf(1966,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1047,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_power2__less__imp__less) ).
thf(4165,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1138,axiom,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(4419,plain,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(703,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_not__add__less2) ).
thf(3188,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1055,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_zcong__scalar) ).
thf(4185,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(649,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_neq0__conv) ).
thf(3039,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(78,axiom,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_zcong__id) ).
thf(1421,plain,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(281,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_add__leE) ).
thf(2013,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(248,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ F @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_zdiv__mono2__lemma) ).
thf(1918,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ F @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1140,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_semiring__norm_I112_J) ).
thf(4424,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(841,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_semiring__mult__number__of) ).
thf(3565,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(778,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_semiring__add__number__of) ).
thf(3401,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(215,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( div_mod_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_zdvd__zmod__imp__zdvd) ).
thf(1817,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( div_mod_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(618,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ ( minus_minus_nat @ B @ C ) )
=> ( ( dvd_dvd_nat @ A @ C )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_dvd__diffD) ).
thf(2960,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ ( minus_minus_nat @ B @ C ) )
=> ( ( dvd_dvd_nat @ A @ C )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(398,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ B )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_one__le__power) ).
thf(2347,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ B )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(161,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_le__special_I3_J) ).
thf(1654,plain,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_dvd_Oless__le__trans) ).
thf(1412,plain,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( dvd_dvd_nat @ C @ A )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1186,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_rel__simps_I50_J) ).
thf(4559,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(112,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_mult__strict__right__mono__neg) ).
thf(1517,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(540,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ ( standardRes @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1192_StandardRes__ubound) ).
thf(2743,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ ( standardRes @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(632,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_zle__diff1__eq) ).
thf(2997,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(313,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_Nat_Odiff__le__self) ).
thf(2110,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1049,axiom,
! [A: real,B: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_zero__le__even__power_H) ).
thf(4170,plain,
! [A: real,B: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(396,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(2342,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(36,axiom,
! [A: $o,B: $o,C: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( B = A ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ C )
& B )
= ( ( ord_less_eq_int @ zero_zero_int @ C )
& A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1062_conj__le__cong) ).
thf(1289,plain,
! [A: $o,B: $o,C: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( B = A ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ C )
& B )
= ( ( ord_less_eq_int @ zero_zero_int @ C )
& A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(354,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( B = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_zero__less__power__nat__eq) ).
thf(2226,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( B = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(503,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_rel__simps_I30_J) ).
thf(2643,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(229,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_mult__pos__neg2) ).
thf(1866,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(966,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_semiring__norm_I110_J) ).
thf(3929,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(211,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_diff__less__mono) ).
thf(1807,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1010,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_sum__power2__le__zero__iff) ).
thf(4061,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(276,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ ( power_power_real @ A @ B ) @ C )
= ( power_power_real @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1998,plain,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ ( power_power_real @ A @ B ) @ C )
= ( power_power_real @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(851,axiom,
~ ! [A: int] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(3593,plain,
~ ! [A: int] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(484,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_dvd__mult) ).
thf(2591,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(857,axiom,
! [A: nat] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(3613,plain,
! [A: nat] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(375,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_comm__mult__left__mono) ).
thf(2283,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(916,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_add__Bit0__Bit1) ).
thf(3789,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1021,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_mult__2__right) ).
thf(4089,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(461,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_eq_int @ A @ B )
=> ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_wset__mem) ).
thf(2532,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ B @ ( minus_minus_int @ C @ one_one_int ) )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_eq_int @ A @ B )
=> ( member_int @ A @ ( wset @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1077,axiom,
! [A: int,B: nat,C: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(4250,plain,
! [A: int,B: nat,C: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(758,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ A @ A )
& ~ ( dvd_dvd_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_dvd_Oless__irrefl) ).
thf(3336,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(863,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_double__eq__0__iff) ).
thf(3630,plain,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(623,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( times_times_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(2971,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( times_times_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1111,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_le__number__of) ).
thf(4338,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(756,axiom,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ B )
& ( ord_less_eq_real @ zero_zero_real @ A ) )
| ( ( ord_less_eq_real @ B @ zero_zero_real )
& ( ord_less_eq_real @ A @ zero_zero_real ) ) )
=> ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_split__mult__pos__le) ).
thf(3331,plain,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ B )
& ( ord_less_eq_real @ zero_zero_real @ A ) )
| ( ( ord_less_eq_real @ B @ zero_zero_real )
& ( ord_less_eq_real @ A @ zero_zero_real ) ) )
=> ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(667,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_diff__diff__right) ).
thf(3085,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(48,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_order__le__neq__implies__less) ).
thf(1326,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(959,axiom,
! [A: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_zero__eq__power2) ).
thf(3911,plain,
! [A: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(629,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_nat @ C @ ( times_times_nat @ E @ A ) )
!= ( plus_plus_nat @ D @ ( times_times_nat @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_add__scale__eq__noteq) ).
thf(2988,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_nat @ C @ ( times_times_nat @ E @ A ) )
!= ( plus_plus_nat @ D @ ( times_times_nat @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(945,axiom,
! [A: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_odd__nonzero) ).
thf(3864,plain,
! [A: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(378,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(2290,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(930,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_add__Bit1__Bit0) ).
thf(3825,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1032,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_mult__numeral__1) ).
thf(4126,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(569,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_less__not__refl2) ).
thf(2823,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_diff__is__0__eq_H) ).
thf(1629,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(674,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_dvd__add) ).
thf(3104,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(278,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( ord_less_nat @ B @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_nat__less__add__iff2) ).
thf(2004,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( ord_less_nat @ B @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(987,axiom,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_not__sum__power2__lt__zero) ).
thf(3991,plain,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(839,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ~ ( zcong @ ( multInv @ B @ A ) @ zero_zero_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_MultInv__prop3) ).
thf(3561,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ~ ( zcong @ ( multInv @ B @ A ) @ zero_zero_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(426,axiom,
! [A: int,B: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__number__of) ).
thf(2431,plain,
! [A: int,B: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(816,axiom,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(3501,plain,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(18,axiom,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ B @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_dvd__mult) ).
thf(1244,plain,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ B @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1165,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_zdiff__power3) ).
thf(4495,plain,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(319,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2130,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(943,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_zmult__1__right) ).
thf(3859,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(458,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_dvd_Oless__asym_H) ).
thf(2526,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1175,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_rel__simps_I17_J) ).
thf(4527,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(128,axiom,
! [A: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0) ).
thf(1558,plain,
! [A: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(327,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( zcong @ A @ B @ C )
= ( ( div_mod_int @ A @ C )
= ( div_mod_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_zcong__zmod__eq) ).
thf(2152,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( zcong @ A @ B @ C )
= ( ( div_mod_int @ A @ C )
= ( div_mod_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(367,axiom,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_IntPrimes_Ozcong__zero) ).
thf(2262,plain,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1054,axiom,
! [A: real] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(4182,plain,
! [A: real] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(412,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_nat__1__eq__mult__iff) ).
thf(2384,plain,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(753,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_real__le__trans) ).
thf(3324,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(85,axiom,
! [A: real] :
~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_not__square__less__zero) ).
thf(1440,plain,
! [A: real] :
~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(344,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_real__mult__commute) ).
thf(2198,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(828,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_power2__le__imp__le) ).
thf(3529,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(404,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ( inv @ B @ A )
!= one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_inv__not__1) ).
thf(2362,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
=> ( ( inv @ B @ A )
!= one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(868,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_one__not__neg__one__mod__m) ).
thf(3645,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1122,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(4372,plain,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(836,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_mult__numeral__1__right) ).
thf(3552,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( A = B )
= ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_dvd_Oeq__iff) ).
thf(1614,plain,
! [A: nat,B: nat] :
( ( A = B )
= ( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(170,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1689,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(981,axiom,
! [A: int] :
( ( ( div_mod_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
= ( ( div_mod_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_neq__one__mod__two) ).
thf(3978,plain,
! [A: int] :
( ( ( div_mod_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
= ( ( div_mod_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1104,axiom,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_power2__sum) ).
thf(4321,plain,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(290,axiom,
! [A: int,B: nat,C: int] :
( ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_pow__divides__pow__int) ).
thf(2041,plain,
! [A: int,B: nat,C: int] :
( ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1051,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_rel__simps_I4_J) ).
thf(4175,plain,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1065,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rel__simps_I5_J) ).
thf(4214,plain,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(937,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( times_times_int @ A @ B ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_number__of__mult) ).
thf(3844,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( times_times_int @ A @ B ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(505,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_zero__le__power) ).
thf(2648,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1095,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_power2__le__imp__le) ).
thf(4299,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(852,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_zadd__assoc) ).
thf(3598,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(437,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_mult__zero__right) ).
thf(2462,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1127,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_power2__eq__imp__eq) ).
thf(4387,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(478,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_790_mult__left__mono) ).
thf(2576,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(338,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_comm__mult__strict__left__mono) ).
thf(2183,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(6,axiom,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
=> ( dvd_dvd_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_dvd__mult__right) ).
thf(1212,plain,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
=> ( dvd_dvd_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(308,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_le__imp__0__less) ).
thf(2095,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(1148,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_four__x__squared) ).
thf(4446,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1023,axiom,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: int,B: int] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(4098,plain,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: int,B: int] :
( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(445,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_one__neq__zero) ).
thf(2494,plain,
one_one_nat != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1190,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right) ).
thf(4570,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(323,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_sum__squares__ge__zero) ).
thf(2142,plain,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(311,axiom,
! [A: $o,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( ( dvd_dvd_nat @ C @ B )
& ~ ( dvd_dvd_nat @ B @ C ) )
=> A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_dvd_Oless__imp__triv) ).
thf(2102,plain,
! [A: $o,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ B @ C )
& ~ ( dvd_dvd_nat @ C @ B ) )
=> ( ( ( dvd_dvd_nat @ C @ B )
& ~ ( dvd_dvd_nat @ B @ C ) )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_comm__mult__left__mono) ).
thf(1512,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(455,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_power__add) ).
thf(2517,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(886,axiom,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( times_times_int @ A @ B ) @ C )
= ( div_mod_int @ ( times_times_int @ A @ ( div_mod_int @ B @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_zmod__zmult1__eq) ).
thf(3705,plain,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( times_times_int @ A @ B ) @ C )
= ( div_mod_int @ ( times_times_int @ A @ ( div_mod_int @ B @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(627,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1039_dvd__imp__le) ).
thf(2983,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(853,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3601,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1199,axiom,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_add__numeral__0__right) ).
thf(4596,plain,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(985,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ A ) @ ( power_power_int @ ( number_number_of_int @ min ) @ B ) @ C )
=> ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( power_power_int @ ( number_number_of_int @ min ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_neg__one__power__eq__mod__m) ).
thf(3987,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ A ) @ ( power_power_int @ ( number_number_of_int @ min ) @ B ) @ C )
=> ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( power_power_int @ ( number_number_of_int @ min ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(672,axiom,
! [A: nat,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_power__strict__mono) ).
thf(3100,plain,
! [A: nat,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_dvd__antisym) ).
thf(1380,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(615,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_rel__simps_I11_J) ).
thf(2951,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(996,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ B @ A )
=> ( dvd_dvd_int @ B @ ( plus_plus_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_dvd__add) ).
thf(4014,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( ( dvd_dvd_int @ B @ A )
=> ( dvd_dvd_int @ B @ ( plus_plus_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1028,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( times_times_int @ B @ A )
= one_one_int )
= ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_pos__zmult__eq__1__iff) ).
thf(4114,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( times_times_int @ B @ A )
= one_one_int )
= ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1131,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_realpow__two__sum__zero__iff) ).
thf(4399,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(328,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_zero__less__mult__pos2) ).
thf(2155,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1124,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ B @ C ) ) @ D ) @ ( times_times_int @ ( minus_minus_int @ E @ ( times_times_int @ B @ F ) ) @ G ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ E @ G ) ) @ ( times_times_int @ B @ ( plus_plus_int @ ( times_times_int @ C @ D ) @ ( times_times_int @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_xzgcda__linear__aux1) ).
thf(4378,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ B @ C ) ) @ D ) @ ( times_times_int @ ( minus_minus_int @ E @ ( times_times_int @ B @ F ) ) @ G ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ E @ G ) ) @ ( times_times_int @ B @ ( plus_plus_int @ ( times_times_int @ C @ D ) @ ( times_times_int @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(462,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_power__le__imp__le__exp) ).
thf(2534,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(989,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( times_times_int @ ( times_times_int @ A @ ( multInv @ B @ A ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_Int2_Oaux____2) ).
thf(3997,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( times_times_int @ ( times_times_int @ A @ ( multInv @ B @ A ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(956,axiom,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_pos2) ).
thf(3907,plain,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(825,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_power2__diff) ).
thf(3521,plain,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(233,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_zero__less__mult__pos) ).
thf(1876,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_dvd_Oless__not__sym) ).
thf(1303,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(271,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_zero__less__mult__pos) ).
thf(1986,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(116,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_diff__add__0) ).
thf(1527,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(759,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ B )
= ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_dvd__mult__cancel1) ).
thf(3337,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ B )
= ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(168,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_Nat_Odiff__diff__eq) ).
thf(1673,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(684,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3132,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(20,axiom,
! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_dvd__triv__left) ).
thf(1248,plain,
! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(293,axiom,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_zprime__zdvd__power) ).
thf(2050,plain,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(193,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_add__le__mono1) ).
thf(1757,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1118,axiom,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_add__diff__add) ).
thf(4357,plain,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(814,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ A @ one_one_int )
=> ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_power__decreasing) ).
thf(3496,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ A @ one_one_int )
=> ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1193,axiom,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_zero__le__power2) ).
thf(4579,plain,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(550,axiom,
! [A: int,B: int > $o] :
( ! [C: int] :
( ( ( ord_less_int @ one_one_int @ C )
=> ( B @ ( minus_minus_int @ C @ one_one_int ) ) )
=> ( B @ C ) )
=> ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_d22set__induct__old) ).
thf(2768,plain,
! [A: int,B: int > $o] :
( ! [C: int] :
( ( ( ord_less_int @ one_one_int @ C )
=> ( B @ ( minus_minus_int @ C @ one_one_int ) ) )
=> ( B @ C ) )
=> ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(99,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_zero__neq__one) ).
thf(1480,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1052,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_power__strict__increasing) ).
thf(4178,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(345,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
= ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_real__less__def) ).
thf(2201,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
= ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(58,axiom,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( minus_minus_int @ A @ ( div_mod_int @ B @ C ) ) @ C )
= ( div_mod_int @ ( minus_minus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_zdiff__zmod__right) ).
thf(1363,plain,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( minus_minus_int @ A @ ( div_mod_int @ B @ C ) ) @ C )
= ( div_mod_int @ ( minus_minus_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(104,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_mult__cancel2) ).
thf(1495,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(838,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_mult__numeral__1__right) ).
thf(3558,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(993,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ~ ( zcong @ B @ zero_zero_int @ D )
=> ( ~ ( zcong @ A @ zero_zero_int @ D )
=> ( ( zcong @ ( times_times_int @ C @ ( multInv @ D @ A ) ) @ ( times_times_int @ C @ ( multInv @ D @ B ) ) @ D )
=> ( zcong @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_MultInv__zcong__prop3) ).
thf(4007,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ D )
=> ( ( zprime @ D )
=> ( ~ ( zcong @ C @ zero_zero_int @ D )
=> ( ~ ( zcong @ B @ zero_zero_int @ D )
=> ( ~ ( zcong @ A @ zero_zero_int @ D )
=> ( ( zcong @ ( times_times_int @ C @ ( multInv @ D @ A ) ) @ ( times_times_int @ C @ ( multInv @ D @ B ) ) @ D )
=> ( zcong @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(808,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_rel__simps_I46_J) ).
thf(3479,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(603,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_zdvd__zdiffD) ).
thf(2913,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(513,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_nat__le__linear) ).
thf(2668,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)],[513]) ).
thf(298,axiom,
! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_dvd__triv__right) ).
thf(2063,plain,
! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(553,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( dvd_dvd_nat @ B @ ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_dvd__diff__nat) ).
thf(2783,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( dvd_dvd_nat @ B @ ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(747,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_power__increasing__iff) ).
thf(3309,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(929,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3822,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(500,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_pos__add__strict) ).
thf(2636,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(162,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_mult__nonpos__nonpos) ).
thf(1657,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(393,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(2334,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ B @ ( times_times_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_dvd__mult2) ).
thf(1335,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ B @ ( times_times_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(301,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_diff__self__eq__0) ).
thf(2070,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(939,axiom,
! [A: int,B: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_zero__le__even__power_H) ).
thf(3850,plain,
! [A: int,B: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(129,axiom,
! [A: int,B: int > $o] :
( ( member_int @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mem__def) ).
thf(1561,plain,
! [A: int,B: int > $o] :
( ( member_int @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(529,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_nat__mult__1) ).
thf(2714,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(706,axiom,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ B )
& ( ord_less_eq_real @ A @ zero_zero_real ) )
| ( ( ord_less_eq_real @ B @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ A ) ) )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_split__mult__neg__le) ).
thf(3196,plain,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ B )
& ( ord_less_eq_real @ A @ zero_zero_real ) )
| ( ( ord_less_eq_real @ B @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ A ) ) )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(787,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_diff__bin__simps_I3_J) ).
thf(3426,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(239,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( div_mod_int @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_mod__pos__pos__trivial) ).
thf(1891,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( div_mod_int @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(353,axiom,
! [A: real,B: nat,C: real] :
( ( ( power_power_real @ A @ B )
= ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_power__eq__imp__eq__base) ).
thf(2223,plain,
! [A: real,B: nat,C: real] :
( ( ( power_power_real @ A @ B )
= ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(558,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_diffs0__imp__equal) ).
thf(2795,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(864,axiom,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( A != zero_zero_int )
=> ( ( times_times_int @ B @ A )
!= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_no__zero__divisors) ).
thf(3633,plain,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( A != zero_zero_int )
=> ( ( times_times_int @ B @ A )
!= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1058,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_add__numeral__0) ).
thf(4193,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(493,axiom,
! [A: int,B: int] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_arith__simps_I32_J) ).
thf(2619,plain,
! [A: int,B: int] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1103,axiom,
! [A: int] :
( ( min
= ( bit1 @ A ) )
= ( min = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_rel__simps_I43_J) ).
thf(4318,plain,
! [A: int] :
( ( min
= ( bit1 @ A ) )
= ( min = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(467,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ord_less_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_power__strict__decreasing) ).
thf(2549,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ord_less_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(252,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_add__diff__assoc2) ).
thf(1930,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( div_mod_nat @ A @ B ) @ C )
= ( div_mod_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_mod__mult__distrib) ).
thf(1236,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( div_mod_nat @ A @ B ) @ C )
= ( div_mod_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1033,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_zero__neq__one) ).
thf(4129,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(27,axiom,
! [A: real] : ( dvd_dvd_real @ one_one_real @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_one__dvd) ).
thf(1268,plain,
! [A: real] : ( dvd_dvd_real @ one_one_real @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(597,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_894_less__not__refl) ).
thf(2898,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(125,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_mult__pos__neg) ).
thf(1550,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(481,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_zero__le__mult__iff) ).
thf(2583,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(811,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ ( times_times_int @ ( times_times_int @ A @ ( multInv @ B @ A ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_Int2_Oaux____1) ).
thf(3489,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ ( times_times_int @ ( times_times_int @ A @ ( multInv @ B @ A ) ) @ ( multInv @ B @ ( multInv @ B @ A ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1013,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_power__gt1__lemma) ).
thf(4071,plain,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1084,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add1__zle__eq) ).
thf(4271,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(767,axiom,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_power3__eq__cube) ).
thf(3362,plain,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(563,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_zmult2__lemma__aux3) ).
thf(2810,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ A @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(219,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_nat__mult__dvd__cancel__disj_H) ).
thf(1827,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( dvd_dvd_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(24,axiom,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( ( dvd_dvd_real @ B @ A )
=> ( dvd_dvd_real @ B @ ( minus_minus_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_dvd__diff) ).
thf(1261,plain,
! [A: real,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( ( dvd_dvd_real @ B @ A )
=> ( dvd_dvd_real @ B @ ( minus_minus_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(136,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_nat__mult__le__cancel1) ).
thf(1582,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(368,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus_nat @ B @ C ) )
= ( ~ ( ( ( ord_less_nat @ B @ C )
& ~ ( A @ zero_zero_nat ) )
| ? [D: nat] :
( ( B
= ( plus_plus_nat @ C @ D ) )
& ~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1032_nat__diff__split__asm) ).
thf(2265,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus_nat @ B @ C ) )
= ( ~ ( ( ( ord_less_nat @ B @ C )
& ~ ( A @ zero_zero_nat ) )
| ? [D: nat] :
( ( B
= ( plus_plus_nat @ C @ D ) )
& ~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(927,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( times_times_int @ B @ A ) )
= ( times_times_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(3817,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( times_times_int @ B @ A ) )
= ( times_times_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(106,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_nat__add__left__commute) ).
thf(1500,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1107,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_MultInv__prop4) ).
thf(4330,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( multInv @ B @ ( multInv @ B @ A ) ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(970,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_eq__number__of__Pls__Min) ).
thf(3939,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(141,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(1597,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(898,axiom,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_mult__zero__right) ).
thf(3740,plain,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(524,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_exp__eq__1) ).
thf(2699,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(925,axiom,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( times_times_int @ A @ ( div_mod_int @ B @ C ) ) @ C )
= ( div_mod_int @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1150_zmod__simps_I3_J) ).
thf(3812,plain,
! [A: int,B: int,C: int] :
( ( div_mod_int @ ( times_times_int @ A @ ( div_mod_int @ B @ C ) ) @ C )
= ( div_mod_int @ ( times_times_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(813,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__power2) ).
thf(3494,plain,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1120,axiom,
? [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) ).
thf(4363,plain,
? [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(408,axiom,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_power__eq__0__iff) ).
thf(2372,plain,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_add__is__0) ).
thf(1606,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(974,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_power__0__left__number__of) ).
thf(3950,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1195,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ A ) ) )
& ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_number__of1) ).
thf(4584,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ A ) ) )
& ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(941,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_sum__power2__ge__zero) ).
thf(3854,plain,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(520,axiom,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_mult__eq__0__iff) ).
thf(2690,plain,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(491,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_mult__nonpos__nonneg) ).
thf(2615,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(400,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B )
= ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( B
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_nat__eq__add__iff2) ).
thf(2351,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B )
= ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) )
= ( B
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(891,axiom,
! [A: real,B: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_power2__eq__imp__eq) ).
thf(3721,plain,
! [A: real,B: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(626,axiom,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_eq__number__of) ).
thf(2980,plain,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(1177,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_zadd__zmult__distrib2) ).
thf(4533,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(954,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_power__0) ).
thf(3901,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(827,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_sum__power2__gt__zero__iff) ).
thf(3526,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(976,axiom,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_power3__eq__cube) ).
thf(3960,plain,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(846,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( ( ord_less_int @ C @ E )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ( plus_plus_int @ B @ A )
= one_one_int )
=> ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B @ D ) @ ( times_times_int @ A @ C ) ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_convex__bound__lt) ).
thf(3580,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( ( ord_less_int @ C @ E )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ( plus_plus_int @ B @ A )
= one_one_int )
=> ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B @ D ) @ ( times_times_int @ A @ C ) ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(800,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ A @ B @ C )
=> ( zcong @ ( multInv @ C @ A ) @ ( multInv @ C @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_MultInv__prop1) ).
thf(3461,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ A @ B @ C )
=> ( zcong @ ( multInv @ C @ A ) @ ( multInv @ C @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(46,axiom,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ A @ ( times_times_real @ B @ ( times_times_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1320,plain,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ A @ ( times_times_real @ B @ ( times_times_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1174,axiom,
! [A: int,B: nat,C: int] :
( ( ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_nat__number__of__mult__left) ).
thf(4520,plain,
! [A: int,B: nat,C: int] :
( ( ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1085,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( times_times_int @ ( multInv @ B @ A ) @ A ) @ one_one_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_MultInv__prop2a) ).
thf(4274,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zprime @ B )
=> ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( zcong @ ( times_times_int @ ( multInv @ B @ A ) @ A ) @ one_one_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(964,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_sum__squares__ge__zero) ).
thf(3924,plain,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(590,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ B @ one_one_int ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_zcong__square__zless) ).
thf(2881,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ B @ one_one_int ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(257,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ( dvd_dvd_nat @ C @ A )
& ~ ( dvd_dvd_nat @ A @ C ) )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_dvd_Oord__eq__less__trans) ).
thf(1945,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ( dvd_dvd_nat @ C @ A )
& ~ ( dvd_dvd_nat @ A @ C ) )
=> ( ( dvd_dvd_nat @ B @ A )
& ~ ( dvd_dvd_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(743,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_mult__strict__left__mono) ).
thf(3299,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(1182,axiom,
! [A: int] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of) ).
thf(4547,plain,
! [A: int] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(428,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_add__0__iff) ).
thf(2436,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(434,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_nat__add__left__cancel) ).
thf(2453,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(655,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_zero__neq__one) ).
thf(3052,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(341,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( dvd_dvd_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_dvd_Oless__imp__le) ).
thf(2191,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) )
=> ( dvd_dvd_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_mod__less) ).
thf(1204,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( div_mod_nat @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(88,axiom,
! [A: int,B: int] :
( ( ( standardRes @ A @ B )
= zero_zero_int )
= ( zcong @ B @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1189_StandardRes__eq__zcong) ).
thf(1449,plain,
! [A: int,B: int] :
( ( ( standardRes @ A @ B )
= zero_zero_int )
= ( zcong @ B @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(508,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_mult__nonneg__nonpos) ).
thf(2655,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(991,axiom,
! [A: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_power__m1__even) ).
thf(4002,plain,
! [A: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(231,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ ( div_mod_int @ A @ C ) @ ( div_mod_int @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_zcong__zmod) ).
thf(1870,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ ( div_mod_int @ A @ C ) @ ( div_mod_int @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(874,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( inv @ B @ ( inv @ B @ A ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_inv__inv) ).
thf(3669,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( inv @ B @ ( inv @ B @ A ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(551,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_add__diff__assoc) ).
thf(2771,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(4722,plain,
$false,
inference(cvc4,[status(thm)],[2163,1337,1369,3798,3434,2544,1956,2280,2250,3021,1665,4101,3345,4005,4262,1767,3666,1729,4290,3698,3397,1899,1315,2499,2427,3969,1982,2559,3449,1750,3990,4075,2622,2381,1443,3153,1401,1939,3910,3012,1591,3498,1305,4479,1855,3680,3534,3072,1924,2210,3317,4226,4500,1522,3762,2395,2908,3509,3285,2854,1533,1692,4408,1437,4487,1486,4105,1426,1671,3794,3429,3049,1310,4220,1275,2434,1640,2901,1954,1458,3276,4543,2195,1705,3135,3942,3365,2740,2918,4026,3044,2316,3446,2448,2933,3616,4279,3781,4440,2627,2168,4058,1988,2459,3121,4294,4435,3577,1222,3895,3717,4142,3994,3502,2020,3088,3947,2886,3898,2869,2957,3836,4343,3236,3350,3545,2723,2763,1782,2985,1576,3730,1645,1921,1386,3466,4137,1724,3809,1366,2400,2067,4156,1803,2136,1904,4467,2405,3820,2328,3029,1792,1298,4151,2755,3574,3061,2708,2501,2274,3776,3353,3803,4243,3248,1409,3263,1287,2735,2814,4563,4422,3046,3689,1860,2217,1323,3148,3542,1313,1279,4349,3410,2185,1455,3749,2562,4023,2745,2571,2356,1545,3463,1609,3216,3470,3312,3708,4265,1963,3231,2829,2403,1514,1741,1398,3734,3014,2520,2730,2301,4460,4390,4471,4507,1778,1232,4253,3258,4396,3724,1911,2259,3473,3438,2335,4162,2456,2007,2178,4411,1489,4205,1415,3524,3431,2324,1714,2027,3887,3966,3199,3934,4443,1811,4018,2090,3393,1632,4297,3163,2650,1418,2236,3621,1978,1383,2254,4556,2073,2861,3421,1622,4307,1201,2804,1600,3211,4211,3378,2508,2964,3986,2058,2367,3537,4055,3068,4230,1377,4033,2833,3505,1886,4504,2523,3036,2530,3756,4536,3243,2242,1345,3588,1697,4285,3184,2586,2884,1975,4082,4483,1564,1863,4199,2574,3852,3531,3186,2118,2047,2641,4172,2954,1651,3151,2011,3097,3591,2910,3301,2204,3303,3984,3169,4480,2646,1470,1708,3767,2296,4576,4031,4312,2790,2660,1868,2673,2705,2541,4375,3610,2969,3752,3884,2528,1883,3711,2733,1343,4016,1519,2596,1570,1676,2133,1217,2147,4449,4493,1824,1619,2414,3250,3207,3514,4140,2670,2477,3090,3297,2872,4553,2609,4187,3144,1210,3926,1407,1634,3931,1573,2653,3282,1423,3166,2445,3191,2758,3269,3618,2663,1555,2332,1819,4327,1624,4402,1836,2547,2344,3727,1281,3647,2112,4080,3784,2801,3862,4248,3381,1227,4429,1498,3102,3746,1755,2638,1402,3731,1936,4123,1360,1234,1541,3831,2157,2115,1762,2515,2100,3413,1270,1772,1259,4108,2359,3518,3963,1878,2726,2631,1719,2858,3650,4012,2268,3205,3176,3018,4291,2798,3714,4545,4513,2172,4180,4530,4333,4049,1329,4301,2023,3326,1942,4276,1659,3922,3000,3179,3407,3210,4167,1739,1461,4315,3441,2312,1214,3194,2349,2108,2038,1446,2551,1207,1889,3555,4457,3294,1744,1263,2536,3743,2566,4120,1984,1852,3115,4086,3703,2285,2450,3486,1588,1478,4384,1530,2836,1266,4068,2387,3770,1668,1552,2851,2243,2581,2465,4237,3390,3222,2497,4540,3540,1429,4135,3692,2052,2697,1246,3064,4259,3109,3074,3005,3920,4416,3201,4223,1759,1393,3476,3755,4352,3279,1695,3856,3306,2076,4036,4550,4148,2749,1434,1857,1991,2788,1814,3225,1241,2702,3563,2761,3173,4476,3999,3321,3639,2915,2408,2793,2089,3841,2617,2338,1996,3675,4308,1906,1727,2677,2904,2556,3042,3890,1273,1927,2602,3375,3274,3686,3158,2121,2144,2936,1648,3660,2001,1764,3130,2033,2149,2717,1219,3607,3491,1483,3079,4256,4393,3289,4503,3792,2894,1374,4599,3387,3319,4077,3240,3945,3272,4465,1535,3458,2695,2827,3213,4144,3372,3547,1833,4341,4268,3636,3234,2849,2657,4159,2188,4309,2393,1752,3266,2016,1795,2398,3604,4381,4590,3404,3868,4485,2193,3773,2326,2293,3663,3002,1332,2055,3700,1897,3416,3568,2319,3796,1503,3118,2220,2891,3077,3695,2738,3340,4573,1239,2442,3436,1464,2474,2510,2679,4228,4305,2097,1722,2839,2945,2856,3384,2065,2079,2311,4498,4369,2229,3815,3238,2214,3764,1894,3957,2774,3683,1524,3515,3779,2906,3419,2257,1933,2246,1492,1603,3106,3468,4073,1801,4154,2378,3182,3586,3066,2896,1969,1307,2180,3219,2605,4569,4462,4028,1909,4208,4332,3034,2252,2928,2974,1952,3893,2578,2025,2812,3055,4009,2314,2625,4064,1993,1821,1731,2785,2593,3483,3971,3583,2278,2553,1474,1594,1643,3917,2369,3016,2633,4196,3348,2207,1805,2867,1396,2439,2962,2365,2212,3627,3759,3838,2765,3423,2481,2139,3806,2931,2288,1775,2752,2967,2390,1250,3512,4282,3908,2693,2506,4473,4084,3881,3009,4426,1809,1662,1873,3936,2665,2271,2471,3146,1509,2629,1340,4355,3292,4336,3571,3444,2239,4405,3031,2816,1467,2994,3161,3672,3981,2878,2503,1277,4052,3048,4566,3455,1472,2846,2564,4581,1958,2942,2513,3082,3833,1252,2720,4324,2160,2831,1547,1748,1798,2298,3737,1770,2863,3315,4360,3507,4490,3112,2977,1611,2375,1225,2060,1566,3904,3260,2588,3228,2175,4287,1780,2821,3786,3058,4593,2888,1790,2920,4020,4145,1901,3623,3095,2468,2354,1711,2747,2569,3246,4437,3642,4346,4092,4240,2092,1432,4190,2165,1300,1452,1637,2688,3334,3475,3026,2429,2276,3801,1980,2128,1317,1830,3127,3828,4132,2322,1538,2599,3847,3359,3329,2044,4117,1579,2948,2411,1543,1702,1284,4431,3024,2939,1372,2675,1404,1358,2247,3124,2992,4246,3356,4510,2843,1972,2711,1506,4202,1585,2728,1717,2030,1881,2807,3156,3914,3007,4516,4111,4414,4217,1617,2875,1839,3452,2479,4587,2818,1966,4165,4419,3188,4185,3039,1421,2013,1918,4424,3565,3401,1817,2960,2347,1654,1412,4559,1517,2743,2997,2110,4170,2342,1289,2226,2643,1866,3929,1807,4061,1998,3593,2591,3613,2283,3789,4089,2532,4250,3336,3630,2971,4338,3331,3085,1326,3911,2988,3864,2290,3825,4126,2823,1629,3104,2004,3991,3561,2431,3501,1244,4495,2130,3859,2526,4527,1558,2152,2262,4182,2384,3324,1440,2198,3529,2362,3645,4372,3552,1614,1689,3978,4321,2041,4175,4214,3844,2648,4299,3598,2462,4387,2576,2183,1212,2095,4446,4098,2494,4570,2142,2102,1512,2517,3705,2983,3601,4596,3987,3100,1380,2951,4014,4114,4399,2155,4378,2534,3997,3907,3521,1876,1303,1986,1527,3337,1673,3132,1248,2050,1757,4357,3496,4579,2768,1480,4178,2201,1363,1495,3558,4007,3479,2913,2668,2063,2783,3309,3822,2636,1657,2334,1335,2070,3850,1561,2714,3196,3426,1891,2223,2795,3633,4193,2619,4318,2549,1930,1236,4129,1268,2898,1550,2583,3489,4071,4271,3362,2810,1827,1261,1582,2265,3817,1500,4330,3939,1597,3740,2699,3812,3494,4363,2372,1606,3950,4584,3854,2690,2615,2351,3721,2980,4533,3901,3526,3960,3580,3461,1320,4520,4274,3924,2881,1945,3299,4547,2436,2453,3052,2191,1204,1449,2655,4002,1870,3669,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM926^3 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n023.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 12:12:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.11/1.22 % [INFO] Parsing done (312ms).
% 2.30/1.23 % [INFO] Running in sequential loop mode.
% 2.76/1.45 % [INFO] eprover registered as external prover.
% 2.76/1.45 % [INFO] cvc4 registered as external prover.
% 3.06/1.45 % [INFO] Scanning for conjecture ...
% 3.35/1.58 % [INFO] Found a conjecture and 1198 axioms. Running axiom selection ...
% 3.91/1.75 % [INFO] Axiom selection finished. Selected 1198 axioms (removed 0 axioms).
% 5.06/2.05 % [INFO] Problem is higher-order (TPTP THF).
% 5.06/2.07 % [INFO] Type checking passed.
% 5.39/2.07 % [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 ...
% 24.40/6.42 % External prover 'cvc4' found a proof!
% 24.40/6.42 % [INFO] Killing All external provers ...
% 24.40/6.42 % Time passed: 5885ms (effective reasoning time: 5187ms)
% 24.40/6.42 % 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)>
% 24.40/6.43 % Axioms used in derivation (1198): fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_822_mult__strict__left__mono, fact_269_double__number__of__Bit0, fact_865_real__mult__less__mono2, fact_925_dvd_Oless__irrefl, fact_547_nat__number__of__Pls, fact_999_trans__le__add1, fact_946_eq__diff__iff, fact_78_nat__numeral__1__eq__1, fact_327_zdvd__antisym__nonneg, fact_1168_zmult2__lemma__aux4, fact_997_le__iff__add, fact_47_zpower__zpower, fact_505_int__pos__lt__two__imp__zero__or__one, fact_959_zero__less__diff, fact_559_less__0__number__of, fact_325_power__eq__imp__eq__base, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_1039_dvd__imp__le, fact_598_unique__quotient__lemma__neg, fact_613_number__of__diff, fact_846_mult__pos__pos, fact_454_zero__less__power2, fact_88_zle__add1__eq__le, fact_439_zero__power2, fact_770_split__mult__neg__le, fact_740_mult__dvd__mono, fact_118_mem__def, fact_7_zadd__power2, fact_434_le__special_I1_J, fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_528_rel__simps_I13_J, fact_457_power__commutes, fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_742_dvd__mult, fact_753_dvd__add, fact_1178_mod__less__divisor, fact_296_power__less__power__Suc, fact_329_dvd__power__same, fact_214_semiring__mult__number__of, fact_884_diff__0__eq__0, fact_772_split__mult__neg__le, fact_287_semiring__one__add__one__is__two, fact_763_divides__add__revr, fact_1005_add__leE, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_321_power__le__dvd, fact_136_eq__number__of, fact_152_rel__simps_I4_J, fact_766_nat__mult__eq__one, fact_368_zero__less__power, fact_1117_pow__divides__eq__int, fact_162_less__special_I4_J, fact_678_dvd__refl, fact_1145_zcong__zmod, fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_278_mult__2, fact_928_nat__add__left__commute, fact_139_number__of__reorient, fact_248_add__number__of__eq, fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_395_semiring__numeral__0__eq__0, fact_757_one__dvd, fact_564_zcong__trans, fact_702_no__zero__divisors, fact_799_mult__nonneg__nonpos2, fact_74_less__eq__number__of__int__code, fact_754_dvd__add, fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_201_mult__Pls, fact_363_zero__le__power, fact_164_less__special_I2_J, fact_257_mult__numeral__1, fact_733_dvd__mult__left, fact_365_power__mono, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_355_add__0__iff, fact_393_number__of__Pls, fact_135_eq__number__of, fact_283_mult__2__right, fact_478_sum__power2__le__zero__iff, fact_657_zprime__zdvd__zmult__better, fact_207_zmult__1__right, fact_160_power__even__eq, 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fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_69_rel__simps_I14_J, fact_205_add__Bit0__Bit0, fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest, fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_573_IntPrimes_Ozcong__zero, fact_777_mult__mono, fact_644_zcong__zmult__prop1, fact_827_mult__neg__neg, fact_1031_nat__diff__split, fact_262_semiring__numeral__1__eq__1, fact_802_mult__nonneg__nonpos, fact_161_power__even__eq, fact_844_mult__pos__neg, fact_1004_add__leD1, fact_90_is__mult__sum2sq, fact_1070_Wilson__Russ, fact_633_zle__diff1__eq, fact_340_power__strict__mono, fact_654_zdvd__bounds, fact_933_diff__add__inverse, fact_270_double__number__of__Bit0, fact_1106_d22set__induct__old, fact_170_crossproduct__eq, fact_1115_d22set__mem, fact_240_mult__number__of__left, fact_592_power__0__left__number__of, fact_405_odd__nonzero, fact_660_neg__one__power, 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fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_914_dvd_Oord__le__eq__trans, fact_11_power2__sum, fact_993_dvd__diffD1, fact_581_power__m1__even, fact_485_one__le__power, fact_1174_pos__zmod__mult__2, fact_506_even__power__le__0__imp__0, fact_1027_nat__1__eq__mult__iff, fact_619_zdvd__zdiffD, fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_86_zless__imp__add1__zle, fact_683_dvd__trans, fact_834_zero__less__mult__pos2, fact_527_not__real__square__gt__zero, fact_561_eq__0__number__of, fact_1109_mono__nat__linear__lb, fact_1193_StandardRes__SR__prop, fact_1183_le__mod__geq, fact_483_zero__le__even__power_H, fact_475_sum__power2__ge__zero, fact_181_crossproduct__noteq, fact_60_nat__mult__2, fact_1197_StandardRes__prop2, fact_652_zcong__less__eq, fact_1069_norR__mem__unique__aux, fact_322_power__le__dvd, fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J, fact_627_less__bin__lemma, fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_477_sum__power2__le__zero__iff, fact_431_less__special_I3_J, fact_297_power__gt1__lemma, fact_755_dvd__add, fact_1029_nat__dvd__not__less, fact_693_realpow__minus__mult, fact_195_rel__simps_I39_J, fact_1057_nat__eq__add__iff2, fact_696_power__eq__if, fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_1173_zmod__minus1, fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_279_mult__2, fact_883_real__le__antisym, fact_819_comm__mult__strict__left__mono, fact_411_sum__squares__ge__zero, fact_499_power__less__imp__less__exp, fact_720_combine__common__factor, fact_217_semiring__add__number__of, fact_729_dvd__mult__right, fact_540_power__dvd__imp__le, fact_54_le__number__of, fact_1091_MultInv__zcong__prop3, fact_1189_StandardRes__eq__zcong, fact_546_power__0, fact_204_add__Pls, fact_140_rel__simps_I51_J, fact_1185_mod__mult__distrib, fact_381_power__strict__decreasing, fact_815_mult__strict__left__mono__neg, fact_1149_zmod__zmult1__eq, fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_6_qf1pt, fact_824_mult__strict__right__mono, fact_794_mult__nonpos__nonpos, fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_268_mult__Bit1, fact_968_diff__is__0__eq, fact_826_mult__strict__right__mono, fact_389_add__scale__eq__noteq, fact_628_xzgcda__linear__aux1, fact_482_sum__power2__gt__zero__iff, fact_246_add__number__of__left, fact_985_nat__less__le, fact_983_add__diff__inverse, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_966_less__eq__nat_Osimps_I1_J, fact_364_zero__le__power, fact_250_number__of__add, fact_423_power__one__right, fact_704_mult__eq__0__iff, fact_991_diff__less__mono, fact_1038_mult__eq__self__implies__10, fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_788_mult__left__mono, fact_780_mult__mono_H, fact_490_power__increasing, fact_1159_pos__mod__conj, fact_695_mult__eq__if, fact_728_add__diff__add, fact_36_zle__linear, fact_28_add__special_I2_J, fact_1192_StandardRes__ubound, fact_1108_int__gr__induct, fact_519_rel__simps_I43_J, fact_737_dvdI, fact_816_mult__strict__right__mono__neg, fact_717_one__neq__zero, fact_518_rel__simps_I47_J, fact_923_dvd_Ole__less, fact_1034_mult__less__mono1, fact_210_zadd__zmult__distrib, fact_749_dvd__triv__right, fact_940_le__trans, fact_680_dvd__refl, fact_902_dvd_Oless__imp__triv, fact_169_le__special_I2_J, fact_768_nat__power__eq__0__iff, fact_701_no__zero__divisors, fact_775_mult__mono, fact_493_power__inject__exp, fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_817_mult__strict__right__mono__neg, fact_202_mult__Bit0, fact_521_rel__simps_I37_J, fact_1030_add__gr__0, fact_335_power__0__left, fact_8_zadd__power3, fact_1019_nat__dvd__1__iff__1, fact_316_le__imp__power__dvd, fact_643_zcong__id, fact_1111_ex__least__nat__le, fact_1113_d22set__le__swap, fact_402_int__0__less__1, fact_417_not__sum__squares__lt__zero, fact_1132_mult__left__cancel, fact_300_power__le__imp__le__exp, fact_366_power__mono, fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_758_one__dvd, fact_958_diff__less, fact_973_mult__cancel2, fact_1071_zfact_Osimps, fact_247_add__number__of__eq, fact_242_arith__simps_I32_J, fact_267_one__is__num__one, fact_502_power__strict__increasing, fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_315_le__imp__power__dvd, fact_16_one__power2, fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_369_zero__less__power, fact_299_power__gt1__lemma, fact_1045_nat__mult__eq__cancel__disj, fact_551_pos__zmult__eq__1__iff__lemma, fact_1077_inv__not__1, fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_1046_left__add__mult__distrib, fact_1066_incr__mult__lemma, fact_895_diff__less__mono2, fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_1190_StandardRes__prop3, fact_769_divides__exp, fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_213_semiring__mult__number__of, fact_76_zadd__left__mono, fact_576_zcong__scalar2, fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_292_real__sum__squared__expand, fact_1036_mult__less__cancel1, fact_631_add__number__of__diff1, fact_1100_wset__less, fact_848_mult__pos__pos, fact_698_divisors__zero, fact_241_arith__simps_I32_J, fact_523_rel__simps_I45_J, fact_1099_wset__subset
% 24.40/6.43 % No. of inferences in proof: 2400
% 24.40/6.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5885 ms resp. 5187 ms w/o parsing
% 26.00/6.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.00/6.76 % [INFO] Killing All external provers ...
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