TSTP Solution File: NUM925^3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 08:01:38 EDT 2024
% Result : Theorem 19.48s 5.17s
% Output : Refutation 20.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1258
% Syntax : Number of formulae : 2458 (1481 unt; 60 typ; 0 def)
% Number of atoms : 5755 (2430 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 19986 ( 433 ~; 128 |; 291 &;17436 @)
% ( 0 <=>;1698 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 19 con; 0-3 aty)
% Number of variables : 4973 ( 0 ^4935 !; 38 ?;4973 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(all_type,type,
all: ( nat > $o ) > $o ).
thf(ex_type,type,
ex: ( nat > $o ) > $o ).
thf(abs_abs_int_type,type,
abs_abs_int: int > int ).
thf(abs_abs_real_type,type,
abs_abs_real: real > real ).
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(if_nat_type,type,
if_nat: $o > nat > nat > nat ).
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(nat_1_type,type,
nat_1: int > nat ).
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(succ_type,type,
succ: int > int ).
thf(semiri1621563631at_int_type,type,
semiri1621563631at_int: nat > int ).
thf(semiri984289939at_nat_type,type,
semiri984289939at_nat: nat > nat ).
thf(semiri132038758t_real_type,type,
semiri132038758t_real: nat > 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(legendre_type,type,
legendre: int > int > int ).
thf(quadRes_type,type,
quadRes: int > int > $o ).
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(twoSqu919416604sum2sq_type,type,
twoSqu919416604sum2sq: int > $o ).
thf(m_type,type,
m: int ).
thf(m1_type,type,
m1: int ).
thf(n_type,type,
n: nat ).
thf(s1_type,type,
s1: int ).
thf(s_type,type,
s: int ).
thf(t_type,type,
t: int ).
thf(tn_type,type,
tn: nat ).
thf(x_type,type,
x: int ).
thf(y_type,type,
y: int ).
thf(43,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_942_le__imp__diff__is__add) ).
thf(1322,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)],[43]) ).
thf(1062,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_52_add__nat__number__of) ).
thf(4188,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)],[1062]) ).
thf(970,axiom,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_zcong__1) ).
thf(3944,plain,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(61,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_121_add__number__of__left) ).
thf(1369,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)],[61]) ).
thf(778,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_700_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3399,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)],[778]) ).
thf(999,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_21_quartic__square__square) ).
thf(4022,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)],[999]) ).
thf(983,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_1081_Legendre__1mod4) ).
thf(3979,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)],[983]) ).
thf(229,axiom,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_zero__le__square) ).
thf(1840,plain,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(278,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_1110_dvd_Oless__le__not__le) ).
thf(1982,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(964,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 ) ) ) ) )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A) ).
thf(3927,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 ) ) ) ) )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(405,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_mult__strict__mono_H) ).
thf(2331,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(220,axiom,
ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_zero__less__two) ).
thf(1818,plain,
ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1187,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_281_power__strict__increasing) ).
thf(4560,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)],[1187]) ).
thf(49,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_mult__less__le__imp__less) ).
thf(1337,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(185,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_875_le__neq__implies__less) ).
thf(1718,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)],[185]) ).
thf(506,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_489_mult__left__mono__neg) ).
thf(2612,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)],[506]) ).
thf(1026,axiom,
! [A: nat] : ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( power_power_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_of__nat__less__two__power) ).
thf(4094,plain,
! [A: nat] : ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( power_power_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(96,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ~ ( dvd_dvd_int @ B @ A )
=> ( zcong @ ( power_power_int @ A @ ( nat_1 @ ( minus_minus_int @ B @ one_one_int ) ) ) @ one_one_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_Little__Fermat) ).
thf(1469,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ~ ( dvd_dvd_int @ B @ A )
=> ( zcong @ ( power_power_int @ A @ ( nat_1 @ ( minus_minus_int @ B @ one_one_int ) ) ) @ one_one_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(396,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_1067_zcong__zmult__prop3) ).
thf(2306,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)],[396]) ).
thf(1152,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_1085__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(4450,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)],[1152]) ).
thf(409,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_515_mult__nonneg__nonneg) ).
thf(2341,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)],[409]) ).
thf(407,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_1184_left__add__mult__distrib) ).
thf(2336,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)],[407]) ).
thf(323,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_mult__less__imp__less__left) ).
thf(2109,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(91,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_1113_dvd_Oeq__iff) ).
thf(1454,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)],[91]) ).
thf(310,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_929_real__two__squares__add__zero__iff) ).
thf(2072,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)],[310]) ).
thf(202,axiom,
! [A: nat,B: nat] :
( ( semiri984289939at_nat @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_of__nat__add) ).
thf(1767,plain,
! [A: nat,B: nat] :
( ( semiri984289939at_nat @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(921,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_82_zless__add1__eq) ).
thf(3798,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)],[921]) ).
thf(127,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_273_power__inject__exp) ).
thf(1559,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)],[127]) ).
thf(40,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_649_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1315,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)],[40]) ).
thf(565,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_mult__strict__mono) ).
thf(2787,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(500,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_640_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(2595,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)],[500]) ).
thf(174,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_nat__mult__1) ).
thf(1686,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1053,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Numeral1__eq1__nat) ).
thf(4166,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(374,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_add__less__cancel__right) ).
thf(2250,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(703,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_mult__less__imp__less__left) ).
thf(3185,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(988,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_989__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(3990,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)],[988]) ).
thf(362,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_1191_nat__diff__add__eq1) ).
thf(2210,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)],[362]) ).
thf(73,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_add__le__imp__le__right) ).
thf(1406,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1019,axiom,
! [A: nat,B: nat] :
( ( power_power_int @ ( semiri1621563631at_int @ A ) @ B )
= ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zpower__int) ).
thf(4075,plain,
! [A: nat,B: nat] :
( ( power_power_int @ ( semiri1621563631at_int @ A ) @ B )
= ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(425,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_195_nat__less__cases) ).
thf(2381,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)],[425]) ).
thf(428,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_mult__less__imp__less__left) ).
thf(2395,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(737,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_999_zdvd__period) ).
thf(3285,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)],[737]) ).
thf(671,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_semiring__numeral__0__eq__0) ).
thf(3098,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(959,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_749_convex__bound__lt) ).
thf(3910,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)],[959]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_of__nat__less__imp__less) ).
thf(1728,plain,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(325,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_198_nat__power__less__imp__less) ).
thf(2114,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)],[325]) ).
thf(176,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_897_nat__1__eq__mult__iff) ).
thf(1692,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)],[176]) ).
thf(38,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_706_Nat_Odiff__cancel) ).
thf(1305,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)],[38]) ).
thf(1162,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_71_less__special_I1_J) ).
thf(4487,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)],[1162]) ).
thf(772,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_439_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(3382,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)],[772]) ).
thf(877,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_78_bin__less__0__simps_I4_J) ).
thf(3680,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)],[877]) ).
thf(1,conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1200,plain,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(312,axiom,
! [A: nat,B: nat] :
( ( semiri132038758t_real @ ( times_times_nat @ A @ B ) )
= ( times_times_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_of__nat__mult) ).
thf(2077,plain,
! [A: nat,B: nat] :
( ( semiri132038758t_real @ ( times_times_nat @ A @ B ) )
= ( times_times_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1101,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_840_t) ).
thf(4311,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)],[1101]) ).
thf(113,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_119_power__eq__0__iff__number__of) ).
thf(1522,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)],[113]) ).
thf(517,axiom,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_power__one) ).
thf(2644,plain,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1170,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_1132_zcong__zadd) ).
thf(4515,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)],[1170]) ).
thf(561,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_232_field__power__not__zero) ).
thf(2776,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)],[561]) ).
thf(522,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_335_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2659,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)],[522]) ).
thf(770,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_432_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(3377,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)],[770]) ).
thf(474,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_mult__left__less__imp__less) ).
thf(2527,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(692,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_1105_dvd_Ole__neq__trans) ).
thf(3153,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)],[692]) ).
thf(800,axiom,
! [A: nat] :
( ( abs_abs_int @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_abs__int__eq) ).
thf(3460,plain,
! [A: nat] :
( ( abs_abs_int @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(79,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_64_even__less__0__iff) ).
thf(1422,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)],[79]) ).
thf(621,axiom,
ord_less_real @ zero_zero_real @ one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_zero__less__one) ).
thf(2947,plain,
ord_less_real @ zero_zero_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(264,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_less__not__refl) ).
thf(1939,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(274,axiom,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( minus_minus_int @ B @ D ) ) @ ( times_times_int @ ( minus_minus_int @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_mult__diff__mult) ).
thf(1971,plain,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( minus_minus_int @ B @ D ) ) @ ( times_times_int @ ( minus_minus_int @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(212,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_858_real__mult__le__cancel__iff1) ).
thf(1793,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)],[212]) ).
thf(779,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ C @ zero_zero_int )
=> ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_eq_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_mult__le__cancel__left__neg) ).
thf(3402,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ C @ zero_zero_int )
=> ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_eq_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(919,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_754_le__special_I4_J) ).
thf(3794,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)],[919]) ).
thf(162,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_937_le__add__diff) ).
thf(1655,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)],[162]) ).
thf(679,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_280_power__less__imp__less__exp) ).
thf(3120,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)],[679]) ).
thf(550,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_diff__eq__diff__eq) ).
thf(2740,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(190,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_1031_zprime__power__zdvd__cancel__right) ).
thf(1735,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)],[190]) ).
thf(400,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2316,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(336,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_981_real__le__trans) ).
thf(2141,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)],[336]) ).
thf(240,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_le__add__iff2) ).
thf(1872,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1149,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_58_number__of__reorient) ).
thf(4440,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)],[1149]) ).
thf(200,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_616_no__zero__divisors) ).
thf(1761,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)],[200]) ).
thf(837,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_84_less__special_I4_J) ).
thf(3562,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)],[837]) ).
thf(747,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_479_split__mult__neg__le) ).
thf(3313,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)],[747]) ).
thf(842,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_711_less__eq__int__code_I16_J) ).
thf(3577,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)],[842]) ).
thf(338,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_144_number__of__Bit1) ).
thf(2146,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)],[338]) ).
thf(954,axiom,
! [A: int,B: int] :
( ( ( minus_minus_int @ A @ B )
= zero_zero_int )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_right__minus__eq) ).
thf(3895,plain,
! [A: int,B: int] :
( ( ( minus_minus_int @ A @ B )
= zero_zero_int )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(492,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_491_mult__right__mono__neg) ).
thf(2575,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)],[492]) ).
thf(938,axiom,
! [A: int,B: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_zero__le__zpower__abs) ).
thf(3848,plain,
! [A: int,B: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(357,axiom,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_add__numeral__0) ).
thf(2195,plain,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(644,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( nat_1 @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_Int2_Oaux__2) ).
thf(3017,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( nat_1 @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1181,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_620_divisors__zero) ).
thf(4543,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)],[1181]) ).
thf(715,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_1180_incr__mult__lemma) ).
thf(3217,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)],[715]) ).
thf(827,axiom,
( ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) )
= ( nat_1 @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_transfer__nat__int__numerals_I4_J) ).
thf(3530,plain,
( ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) )
= ( nat_1 @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(654,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_856_mult__le__cancel2) ).
thf(3049,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)],[654]) ).
thf(1141,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_587_power__increasing) ).
thf(4418,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)],[1141]) ).
thf(198,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_341_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1756,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)],[198]) ).
thf(1193,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_910_zpower__zpower) ).
thf(4575,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)],[1193]) ).
thf(639,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_56_eq__number__of) ).
thf(3004,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)],[639]) ).
thf(297,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_mult_Ocomm__neutral) ).
thf(2035,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(866,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rel__simps_I49_J) ).
thf(3648,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1032,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ord_less_int @ ( minus_minus_int @ A @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ one_one_int ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_decr__lemma) ).
thf(4110,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ord_less_int @ ( minus_minus_int @ A @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ one_one_int ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1072,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_69_less__special_I3_J) ).
thf(4220,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)],[1072]) ).
thf(353,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_125_number__of__add) ).
thf(2184,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)],[353]) ).
thf(447,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_503_mult__nonpos__nonneg) ).
thf(2448,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)],[447]) ).
thf(616,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_980_real__mult__assoc) ).
thf(2933,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)],[616]) ).
thf(855,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_diff__add__cancel) ).
thf(3616,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(13,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( C
= ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_eq__add__iff2) ).
thf(1233,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( C
= ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,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_180_nat__add__left__commute) ).
thf(1327,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)],[45]) ).
thf(881,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3693,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(457,axiom,
! [A: real] :
~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_not__square__less__zero) ).
thf(2476,plain,
! [A: real] :
~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(22,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_Nat_Odiff__le__self) ).
thf(1260,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(257,axiom,
! [A: nat] :
~ ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_of__nat__less__0__iff) ).
thf(1919,plain,
! [A: nat] :
~ ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(281,axiom,
! [A: nat] :
~ ( ord_less_real @ ( semiri132038758t_real @ A ) @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_of__nat__less__0__iff) ).
thf(1988,plain,
! [A: nat] :
~ ( ord_less_real @ ( semiri132038758t_real @ A ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1008,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_135_power2__less__0) ).
thf(4047,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)],[1008]) ).
thf(227,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_1048_dvd__diffD) ).
thf(1835,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)],[227]) ).
thf(861,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri1621563631at_int @ ( nat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_nat__0__le) ).
thf(3634,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri1621563631at_int @ ( nat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(816,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) @ one_one_int ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_incr__lemma) ).
thf(3502,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) @ one_one_int ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(820,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_731_le__special_I3_J) ).
thf(3513,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)],[820]) ).
thf(1002,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_semiring__numeral__1__eq__1) ).
thf(4030,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(348,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_1022_zdvd__imp__le) ).
thf(2173,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)],[348]) ).
thf(470,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_87_less__special_I2_J) ).
thf(2516,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)],[470]) ).
thf(948,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_157_one__less__power) ).
thf(3880,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)],[948]) ).
thf(432,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_210_linorder__neqE__linordered__idom) ).
thf(2405,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)],[432]) ).
thf(194,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1746,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(673,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_344_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3103,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)],[673]) ).
thf(934,axiom,
! [A: nat > $o] :
( ( ex @ A )
= ( ? [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( A @ ( nat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_ex__nat) ).
thf(3836,plain,
! [A: nat > $o] :
( ( ex @ A )
= ( ? [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( A @ ( nat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(364,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_277_power__strict__increasing__iff) ).
thf(2216,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)],[364]) ).
thf(720,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_add__less__imp__less__left) ).
thf(3236,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(759,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_894_nat__mult__eq__one) ).
thf(3350,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)],[759]) ).
thf(831,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_add__diff__cancel) ).
thf(3545,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(545,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_209_linorder__neqE__linordered__idom) ).
thf(2723,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)],[545]) ).
thf(908,axiom,
! [A: int > $o] :
( ( ? [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( A @ B ) ) )
= ( ? [B: nat] : ( A @ ( semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_transfer__int__nat__quantifiers_I2_J) ).
thf(3766,plain,
! [A: int > $o] :
( ( ? [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
& ( A @ B ) ) )
= ( ? [B: nat] : ( A @ ( semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(442,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_433_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2432,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)],[442]) ).
thf(255,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_mult__le__less__imp__less) ).
thf(1914,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1165,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_160_power__0__left) ).
thf(4496,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)],[1165]) ).
thf(133,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_435_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1576,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)],[133]) ).
thf(1123,axiom,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ B )
= ( ( abs_abs_int @ A )
= one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_zdvd__mult__cancel1) ).
thf(4371,plain,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ B )
= ( ( abs_abs_int @ A )
= one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(1087,axiom,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_IntPrimes_Ozcong__zero) ).
thf(4266,plain,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(745,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_less__irrefl__nat) ).
thf(3308,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(262,axiom,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_zero__le__square) ).
thf(1935,plain,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1037,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
thf(4124,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(67,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_454_le__number__of) ).
thf(1386,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)],[67]) ).
thf(802,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_835_p0) ).
thf(3466,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)],[802]) ).
thf(1063,axiom,
( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_transfer__int__nat__numerals_I4_J) ).
thf(4198,plain,
( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(955,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_699_power__mult__distrib) ).
thf(3898,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)],[955]) ).
thf(314,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_859_real__mult__le__cancel__iff2) ).
thf(2082,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)],[314]) ).
thf(430,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_883_add__leE) ).
thf(2400,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)],[430]) ).
thf(308,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_1142_zprime__def) ).
thf(2067,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)],[308]) ).
thf(947,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_1151_zcong__zpower__zmult) ).
thf(3878,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)],[947]) ).
thf(334,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_of__nat__le__iff) ).
thf(2136,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(151,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_329_add__right__cancel) ).
thf(1623,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)],[151]) ).
thf(101,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_mult__zero__right) ).
thf(1482,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(849,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).
thf(3597,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(20,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_diff__add__cancel) ).
thf(1254,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(182,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_gr__implies__not0) ).
thf(1709,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(647,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_add__neg__neg) ).
thf(3029,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(549,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_874_less__or__eq__imp__le) ).
thf(2735,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)],[549]) ).
thf(683,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(3131,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(525,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_add__0__left) ).
thf(2667,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(408,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_493_comm__mult__left__mono) ).
thf(2339,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)],[408]) ).
thf(1140,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_zero__less__double__add__iff__zero__less__single__add) ).
thf(4415,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(912,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 @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_add__mono) ).
thf(3776,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 @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(900,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_add__le__cancel__right) ).
thf(3744,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(760,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_511_mult__nonneg__nonpos) ).
thf(3353,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)],[760]) ).
thf(454,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_183_nat__add__right__cancel) ).
thf(2466,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)],[454]) ).
thf(651,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_502_mult__nonpos__nonpos) ).
thf(3043,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)],[651]) ).
thf(951,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_1061_zcong__zpower) ).
thf(3891,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)],[951]) ).
thf(521,axiom,
! [A: int,B: int] :
( ( ( ord_less_int @ zero_zero_int @ B )
| ( ord_less_eq_int @ zero_zero_int @ A ) )
=> ( ( ord_less_eq_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_eq_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_nat__le__eq__zle) ).
thf(2654,plain,
! [A: int,B: int] :
( ( ( ord_less_int @ zero_zero_int @ B )
| ( ord_less_eq_int @ zero_zero_int @ A ) )
=> ( ( ord_less_eq_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_eq_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(725,axiom,
! [A: nat,B: nat] :
( ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
thf(3248,plain,
! [A: nat,B: nat] :
( ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1179,axiom,
! [A: nat] : ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_of__nat__less__two__power) ).
thf(4539,plain,
! [A: nat] : ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(730,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_990_zdvd__zdiffD) ).
thf(3263,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)],[730]) ).
thf(1182,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_651_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(4546,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)],[1182]) ).
thf(982,axiom,
! [A: int] :
( ( ( bit1 @ A )
= min )
= ( A = min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_rel__simps_I47_J) ).
thf(3976,plain,
! [A: int] :
( ( ( bit1 @ A )
= min )
= ( A = min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(404,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2328,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(540,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_182_nat__add__left__cancel) ).
thf(2708,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)],[540]) ).
thf(932,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_6_one__power2) ).
thf(3821,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)],[932]) ).
thf(46,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 @ D @ B ) @ E ) )
= ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_le__add__iff2) ).
thf(1330,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 @ D @ B ) @ E ) )
= ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(236,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1860,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(24,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_885_add__leD2) ).
thf(1264,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)],[24]) ).
thf(108,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_zero__less__one) ).
thf(1511,plain,
ord_less_nat @ zero_zero_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(383,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_add__less__imp__less__right) ).
thf(2274,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(810,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_1118_neg__one__power) ).
thf(3485,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)],[810]) ).
thf(681,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_1181_nat__less__add__iff1) ).
thf(3125,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)],[681]) ).
thf(224,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( dvd_dvd_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_transfer__nat__int__relations_I4_J) ).
thf(1826,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( dvd_dvd_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1039,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_720_zadd__zmult__distrib) ).
thf(4130,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)],[1039]) ).
thf(830,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3542,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1115,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_power__one__right) ).
thf(4349,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(28,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_282_power__strict__increasing) ).
thf(1279,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)],[28]) ).
thf(1090,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_add__strict__left__mono) ).
thf(4275,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(782,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_178_nat__neq__iff) ).
thf(3410,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)],[782]) ).
thf(736,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_1106_dvd_Ole__imp__less__or__eq) ).
thf(3280,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)],[736]) ).
thf(902,axiom,
! [A: int] :
( ( succ @ A )
= ( plus_plus_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_succ__def) ).
thf(3749,plain,
! [A: int] :
( ( succ @ A )
= ( plus_plus_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(937,axiom,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_of__nat__add) ).
thf(3845,plain,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(668,axiom,
! [A: int] :
( ( nat_1 @ ( number_number_of_int @ A ) )
= ( number_number_of_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_nat__number__of) ).
thf(3089,plain,
! [A: int] :
( ( nat_1 @ ( number_number_of_int @ A ) )
= ( number_number_of_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(552,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_1111_dvd_Oless__le) ).
thf(2745,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)],[552]) ).
thf(888,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_3_sum__power2__eq__zero__iff) ).
thf(3713,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)],[888]) ).
thf(258,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_460_mult__number__of__left) ).
thf(1922,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)],[258]) ).
thf(991,axiom,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__numeral__0__right) ).
thf(3998,plain,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(590,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_480_split__mult__pos__le) ).
thf(2857,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)],[590]) ).
thf(180,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_1045_nat__dvd__not__less) ).
thf(1704,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)],[180]) ).
thf(560,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_1175_decr__mult__lemma) ).
thf(2767,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)],[560]) ).
thf(157,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_30_zless__linear) ).
thf(1641,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)],[157]) ).
thf(58,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1362,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(943,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_1120_QuadRes__def) ).
thf(3866,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)],[943]) ).
thf(732,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_698_power__mult__distrib) ).
thf(3268,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)],[732]) ).
thf(121,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_475_diff__commute) ).
thf(1545,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)],[121]) ).
thf(437,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_1095_dvd_Oless__imp__le) ).
thf(2420,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)],[437]) ).
thf(801,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_50_rel__simps_I14_J) ).
thf(3463,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)],[801]) ).
thf(769,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_204_zero__less__power__nat__eq) ).
thf(3374,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)],[769]) ).
thf(773,axiom,
! [A: nat] :
( ( ord_less_real @ zero_zero_real @ ( semiri132038758t_real @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_of__nat__0__less__iff) ).
thf(3385,plain,
! [A: nat] :
( ( ord_less_real @ zero_zero_real @ ( semiri132038758t_real @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(431,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_1128_zcong__zmult__self) ).
thf(2403,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)],[431]) ).
thf(110,axiom,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_one__reorient) ).
thf(1514,plain,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(302,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_345_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2049,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)],[302]) ).
thf(483,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_one__reorient) ).
thf(2552,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
= ( dvd_dvd_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_zdvd__int) ).
thf(1479,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
= ( dvd_dvd_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(146,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_le__square) ).
thf(1609,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(71,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_1109_dvd_Oneq__le__trans) ).
thf(1398,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)],[71]) ).
thf(666,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(3084,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(261,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_298_less__imp__add__positive) ).
thf(1931,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)],[261]) ).
thf(130,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__0) ).
thf(1568,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(897,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_129_odd__nonzero) ).
thf(3734,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)],[897]) ).
thf(643,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_1187_nat__mult__dvd__cancel__disj) ).
thf(3014,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)],[643]) ).
thf(1044,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_1038_s0p) ).
thf(4141,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)],[1044]) ).
thf(1127,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_963_two__realpow__ge__one) ).
thf(4383,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)],[1127]) ).
thf(394,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_751_le__special_I2_J) ).
thf(2301,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)],[394]) ).
thf(219,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_632_comm__semiring__class_Odistrib) ).
thf(1815,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)],[219]) ).
thf(851,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_639_crossproduct__eq) ).
thf(3602,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)],[851]) ).
thf(241,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_zero__neq__one) ).
thf(1875,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(206,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_906_diff__le__mono) ).
thf(1778,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)],[206]) ).
thf(588,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_869_mult__cancel2) ).
thf(2852,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)],[588]) ).
thf(718,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_877_le__eq__less__or__eq) ).
thf(3231,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)],[718]) ).
thf(580,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_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2829,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)],[580]) ).
thf(917,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_rel__simps_I37_J) ).
thf(3788,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(350,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_less__zeroE) ).
thf(2178,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1133,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_231_field__power__not__zero) ).
thf(4396,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)],[1133]) ).
thf(776,axiom,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_double__zero__sym) ).
thf(3393,plain,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(636,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_902_le__diff__iff) ).
thf(2996,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)],[636]) ).
thf(695,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_461_mult__number__of__left) ).
thf(3163,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)],[695]) ).
thf(797,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_46_less__int__code_I16_J) ).
thf(3453,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)],[797]) ).
thf(762,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_575_sum__squares__ge__zero) ).
thf(3357,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)],[762]) ).
thf(840,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nat__number__of__Pls) ).
thf(3569,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1034,axiom,
! [A: int,B: nat] :
( ( ( nat_1 @ A )
= B )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( A
= ( semiri1621563631at_int @ B ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( B = zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_nat__eq__iff) ).
thf(4115,plain,
! [A: int,B: nat] :
( ( ( nat_1 @ A )
= B )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( A
= ( semiri1621563631at_int @ B ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(30,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_458_arith__simps_I32_J) ).
thf(1283,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)],[30]) ).
thf(1146,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
=> ( ord_less_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_add__less__imp__less__left) ).
thf(4432,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
=> ( ord_less_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(450,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_mult__less__le__imp__less) ).
thf(2456,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1066,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_819_le__imp__0__less) ).
thf(4205,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)],[1066]) ).
thf(369,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_944_add__diff__assoc2) ).
thf(2237,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)],[369]) ).
thf(37,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_212_add__is__0) ).
thf(1302,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)],[37]) ).
thf(166,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_348_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1664,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)],[166]) ).
thf(1108,axiom,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(4329,plain,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(294,axiom,
! [A: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ one_one_real ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_abs__add__one__not__less__self) ).
thf(2027,plain,
! [A: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ one_one_real ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1150,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_124_number__of__add) ).
thf(4443,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)],[1150]) ).
thf(663,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_less__add__iff1) ).
thf(3075,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1194,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_141_number__of__Bit0) ).
thf(4578,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)],[1194]) ).
thf(321,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_mult__right__le__imp__le) ).
thf(2105,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(602,axiom,
! [A: int] :
( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ A ) @ one_one_nat )
= one_one_nat ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ A ) @ one_one_nat )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_nat__number__of__add__1) ).
thf(2893,plain,
! [A: int] :
( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ A ) @ one_one_nat )
= one_one_nat ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ A ) @ one_one_nat )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(154,axiom,
! [A: int,B: int] :
( ( ord_less_nat @ ( nat_1 @ A ) @ ( nat_1 @ B ) )
= ( ( ord_less_int @ zero_zero_int @ B )
& ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_zless__nat__conj) ).
thf(1632,plain,
! [A: int,B: int] :
( ( ord_less_nat @ ( nat_1 @ A ) @ ( nat_1 @ B ) )
= ( ( ord_less_int @ zero_zero_int @ B )
& ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(455,axiom,
! [A: int,B: int] :
( ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
= one_one_int )
=> ( ( abs_abs_int @ A )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_abs__zmult__eq__1) ).
thf(2469,plain,
! [A: int,B: int] :
( ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
= one_one_int )
=> ( ( abs_abs_int @ A )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(377,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_723_less__eq__number__of__int__code) ).
thf(2259,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)],[377]) ).
thf(992,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_913_diff__bin__simps_I9_J) ).
thf(4001,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)],[992]) ).
thf(826,axiom,
! [A: int] :
( ( minus_minus_int @ ( times_times_int @ A @ A ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ ( minus_minus_int @ A @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_real__squared__diff__one__factored) ).
thf(3527,plain,
! [A: int] :
( ( minus_minus_int @ ( times_times_int @ A @ A ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ ( minus_minus_int @ A @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(884,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_19_semiring__one__add__one__is__two) ).
thf(3702,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)],[884]) ).
thf(792,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_rel__simps_I29_J) ).
thf(3438,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1046,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rel__simps_I4_J) ).
thf(4147,plain,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(1009,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_721_zadd__left__mono) ).
thf(4050,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)],[1009]) ).
thf(613,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_764_mult__less__cancel__right__disj) ).
thf(2925,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)],[613]) ).
thf(981,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_812_add1__zle__eq) ).
thf(3973,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)],[981]) ).
thf(270,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_500_mult__right__mono) ).
thf(1960,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)],[270]) ).
thf(484,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_1137_zcong__def) ).
thf(2555,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)],[484]) ).
thf(742,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_487_mult__mono_H) ).
thf(3300,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)],[742]) ).
thf(910,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_102_add__Bit0__Bit0) ).
thf(3771,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)],[910]) ).
thf(1051,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_add__less__imp__less__right) ).
thf(4162,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(986,axiom,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_add__neg__neg) ).
thf(3986,plain,
! [A: int,B: int] :
( ( ord_less_int @ B @ zero_zero_int )
=> ( ( ord_less_int @ A @ zero_zero_int )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1011,axiom,
( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_int__0) ).
thf(4055,plain,
( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(386,axiom,
! [A: nat,B: nat] :
( ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_of__nat__less__imp__less) ).
thf(2281,plain,
! [A: nat,B: nat] :
( ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(7,axiom,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_mult__diff__mult) ).
thf(1215,plain,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(320,axiom,
~ ( ord_less_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_rel__simps_I3_J) ).
thf(2103,plain,
~ ( ord_less_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(716,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_451_zmult__assoc) ).
thf(3226,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)],[716]) ).
thf(1068,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_zmult__1__right) ).
thf(4211,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(599,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_diff__self__eq__0) ).
thf(2884,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(558,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 @ A @ one_one_real )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_mult__left__le__one__le) ).
thf(2762,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 @ A @ one_one_real )
=> ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(420,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri984289939at_nat @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_of__nat__0__less__iff) ).
thf(2367,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri984289939at_nat @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(260,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_465_left__diff__distrib__number__of) ).
thf(1928,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)],[260]) ).
thf(355,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_plus__nat_Oadd__0) ).
thf(2190,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(786,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_47_rel__simps_I17_J) ).
thf(3421,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)],[786]) ).
thf(245,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_949_zle__diff1__eq) ).
thf(1886,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)],[245]) ).
thf(1166,axiom,
( ( succ @ pls )
= ( bit1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_succ__Pls) ).
thf(4504,plain,
( ( succ @ pls )
= ( bit1 @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(926,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_153_realpow__two__sum__zero__iff) ).
thf(3808,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)],[926]) ).
thf(213,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_707_diff__cancel2) ).
thf(1796,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)],[213]) ).
thf(764,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_887_add__le__mono1) ).
thf(3361,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)],[764]) ).
thf(1178,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_208_less__nat__number__of) ).
thf(4536,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)],[1178]) ).
thf(974,axiom,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_zcong__id) ).
thf(3955,plain,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(723,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_770_diff__less) ).
thf(3243,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)],[723]) ).
thf(573,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_457_number__of__mult) ).
thf(2809,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)],[573]) ).
thf(388,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_285_power__eq__0__iff) ).
thf(2286,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)],[388]) ).
thf(1005,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_826_int__pos__lt__two__imp__zero__or__one) ).
thf(4038,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)],[1005]) ).
thf(515,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_mult__zero__left) ).
thf(2639,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(571,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_add__left__mono) ).
thf(2804,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1172,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_mult__1__right) ).
thf(4519,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(846,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_rel__simps_I38_J) ).
thf(3588,plain,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(16,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_855_real__le__eq__diff) ).
thf(1242,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)],[16]) ).
thf(836,axiom,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(3559,plain,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(1160,axiom,
! [A: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_zero__zle__int) ).
thf(4483,plain,
! [A: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(819,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_797_eq__number__of__0) ).
thf(3510,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)],[819]) ).
thf(1015,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(4065,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(129,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_less__not__refl3) ).
thf(1564,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(144,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_72_less__special_I1_J) ).
thf(1604,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)],[144]) ).
thf(796,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_14_add__special_I3_J) ).
thf(3450,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)],[796]) ).
thf(847,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_804_mult__Bit1) ).
thf(3591,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)],[847]) ).
thf(360,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_286_power__eq__0__iff) ).
thf(2204,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)],[360]) ).
thf(345,axiom,
! [A: nat,B: nat] :
( ( semiri984289939at_nat @ ( power_power_nat @ A @ B ) )
= ( power_power_nat @ ( semiri984289939at_nat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_of__nat__power) ).
thf(2164,plain,
! [A: nat,B: nat] :
( ( semiri984289939at_nat @ ( power_power_nat @ A @ B ) )
= ( power_power_nat @ ( semiri984289939at_nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(327,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_mult__left__less__imp__less) ).
thf(2118,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(318,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_638_crossproduct__eq) ).
thf(2093,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)],[318]) ).
thf(208,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_619_divisors__zero) ).
thf(1783,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)],[208]) ).
thf(510,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_757_realpow__minus__mult) ).
thf(2621,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)],[510]) ).
thf(306,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_991_zprime__zdvd__zmult__better) ).
thf(2061,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)],[306]) ).
thf(785,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_rel__simps_I28_J) ).
thf(3418,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(188,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1730,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_zmult__int) ).
thf(1863,plain,
! [A: nat,B: nat] :
( ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(791,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_rel__simps_I27_J) ).
thf(3435,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(844,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_add__0__right) ).
thf(3582,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(717,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_972_unique__quotient__lemma) ).
thf(3229,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)],[717]) ).
thf(642,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_615_no__zero__divisors) ).
thf(3011,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)],[642]) ).
thf(4,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_464_right__diff__distrib__number__of) ).
thf(1206,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)],[4]) ).
thf(1198,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_one__is__num__one) ).
thf(4589,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(1137,axiom,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_mult__zero__right) ).
thf(4407,plain,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(456,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_power__0) ).
thf(2473,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(84,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_586_power__increasing) ).
thf(1438,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)],[84]) ).
thf(891,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_add__strict__mono) ).
thf(3720,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(697,axiom,
( ( semiri984289939at_nat @ one_one_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_of__nat__1) ).
thf(3169,plain,
( ( semiri984289939at_nat @ one_one_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(1159,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_346_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(4480,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)],[1159]) ).
thf(731,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_882_add__mult__distrib2) ).
thf(3265,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)],[731]) ).
thf(990,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_805_pos__zmult__eq__1__iff) ).
thf(3995,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)],[990]) ).
thf(301,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_1130_zcong__scalar2) ).
thf(2047,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)],[301]) ).
thf(367,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_790_zpower__zadd__distrib) ).
thf(2232,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)],[367]) ).
thf(656,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_783_zadd__zless__mono) ).
thf(3054,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)],[656]) ).
thf(445,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_1104_dvd_Oord__eq__le__trans) ).
thf(2441,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)],[445]) ).
thf(498,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_879_real__less__def) ).
thf(2589,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)],[498]) ).
thf(539,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_184_nat__add__left__cancel__less) ).
thf(2705,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)],[539]) ).
thf(250,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_less__eq__nat_Osimps_I1_J) ).
thf(1900,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(440,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_283_power__strict__increasing) ).
thf(2428,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)],[440]) ).
thf(479,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_zle__refl) ).
thf(2541,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(112,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_185_linorder__neqE__nat) ).
thf(1519,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)],[112]) ).
thf(56,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_1074_dvd__mult__cancel2) ).
thf(1355,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)],[56]) ).
thf(1147,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_1145_prime__g__5) ).
thf(4434,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)],[1147]) ).
thf(333,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_mult__1) ).
thf(2133,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(196,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_417_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1751,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)],[196]) ).
thf(853,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_709_mult__Bit0) ).
thf(3610,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)],[853]) ).
thf(504,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_mult__1__right) ).
thf(2606,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(223,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_964_Euler_Oaux2) ).
thf(1824,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)],[223]) ).
thf(296,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_637_crossproduct__eq) ).
thf(2032,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)],[296]) ).
thf(913,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_682_add__left__mono) ).
thf(3778,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)],[913]) ).
thf(1007,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_mult__1) ).
thf(4044,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(52,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_1107_dvd_Oantisym__conv) ).
thf(1343,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)],[52]) ).
thf(997,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_617_no__zero__divisors) ).
thf(4016,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)],[997]) ).
thf(628,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_194_add__lessD1) ).
thf(2969,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)],[628]) ).
thf(1113,axiom,
! [A: int] :
( ( abs_abs_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ ( abs_abs_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_abs__power2__distrib) ).
thf(4344,plain,
! [A: int] :
( ( abs_abs_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ ( abs_abs_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1025,axiom,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri1621563631at_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_of__nat__power) ).
thf(4091,plain,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri1621563631at_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(903,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_813_zless__imp__add1__zle) ).
thf(3752,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)],[903]) ).
thf(661,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_1131_zcong__zmult) ).
thf(3069,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)],[661]) ).
thf(684,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_438_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(3134,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)],[684]) ).
thf(1164,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_337_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(4493,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)],[1164]) ).
thf(601,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_402_nat__power__eq__0__iff) ).
thf(2890,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)],[601]) ).
thf(435,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2414,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(626,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_429_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(2958,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)],[626]) ).
thf(273,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_900_diff__mult__distrib2) ).
thf(1968,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)],[273]) ).
thf(92,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_427_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1457,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)],[92]) ).
thf(505,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_123_add__number__of__eq) ).
thf(2609,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)],[505]) ).
thf(363,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ C @ zero_zero_real )
=> ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_eq_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_mult__le__cancel__left__neg) ).
thf(2213,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ C @ zero_zero_real )
=> ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_eq_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(411,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_1129_zcong__scalar) ).
thf(2345,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)],[411]) ).
thf(69,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_1188_nat__mult__dvd__cancel1) ).
thf(1392,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)],[69]) ).
thf(1103,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_51_zadd__strict__right__mono) ).
thf(4316,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)],[1103]) ).
thf(1014,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_bin__less__0__simps_I1_J) ).
thf(4063,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(733,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_nat__add__commute) ).
thf(3271,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(696,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_neq0__conv) ).
thf(3166,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(446,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_1115_divides__antisym) ).
thf(2445,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)],[446]) ).
thf(1098,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_1039__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4) ).
thf(4295,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)],[1098]) ).
thf(453,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_483_mult__mono) ).
thf(2464,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)],[453]) ).
thf(1092,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add__numeral__0) ).
thf(4280,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(228,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_mult__1__right) ).
thf(1837,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(143,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_993_zdvd__bounds) ).
thf(1602,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)],[143]) ).
thf(59,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_mult__left__le__imp__le) ).
thf(1365,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(526,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_less__imp__of__nat__less) ).
thf(2670,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(125,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_189_trans__less__add1) ).
thf(1555,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)],[125]) ).
thf(1050,axiom,
! [A: nat,B: nat,C: $o] :
( ( C
=> ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) )
& ( ~ C
=> ( ( semiri1621563631at_int @ B )
= ( semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_int__if__cong) ).
thf(4155,plain,
! [A: nat,B: nat,C: $o] :
( ( C
=> ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) )
& ( ~ C
=> ( ( semiri1621563631at_int @ B )
= ( semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(741,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(3297,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(685,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_1096_dvd_Oless__not__sym) ).
thf(3137,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)],[685]) ).
thf(815,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_86_less__special_I2_J) ).
thf(3499,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)],[815]) ).
thf(835,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_rel__simps_I40_J) ).
thf(3556,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(595,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_434_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2872,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)],[595]) ).
thf(1128,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_double__eq__0__iff) ).
thf(4385,plain,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(268,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_403_realpow__pos__nth__unique) ).
thf(1951,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)],[268]) ).
thf(953,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_841_p) ).
thf(3894,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)],[953]) ).
thf(221,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_1071_zcong__zprime__prod__zero__contra) ).
thf(1819,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)],[221]) ).
thf(1107,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_8_zero__power2) ).
thf(4327,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)],[1107]) ).
thf(1135,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
= ( ? [C: nat] :
( B
= ( plus_plus_int @ A @ ( semiri1621563631at_int @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_zle__iff__zadd) ).
thf(4402,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
= ( ? [C: nat] :
( B
= ( plus_plus_int @ A @ ( semiri1621563631at_int @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(351,axiom,
ord_less_eq_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_rel__simps_I23_J) ).
thf(2181,plain,
ord_less_eq_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(907,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_74_less__int__code_I15_J) ).
thf(3763,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)],[907]) ).
thf(461,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_le0) ).
thf(2492,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1030,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_1116_neg__one__power__eq__mod__m) ).
thf(4104,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)],[1030]) ).
thf(894,axiom,
~ ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_nQ1) ).
thf(3727,plain,
~ ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(29,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_real @ ( plus_plus_real @ B @ A ) @ ( plus_plus_real @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_add__strict__right__mono) ).
thf(1281,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_real @ ( plus_plus_real @ B @ A ) @ ( plus_plus_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(649,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_957_power__eq__if) ).
thf(3033,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)],[649]) ).
thf(781,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_739_power__le__imp__le__exp) ).
thf(3408,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)],[781]) ).
thf(192,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_940_le__diff__conv2) ).
thf(1740,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)],[192]) ).
thf(896,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_122_add__number__of__eq) ).
thf(3731,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)],[896]) ).
thf(979,axiom,
( ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) )
= ( nat_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_transfer__nat__int__numerals_I3_J) ).
thf(3968,plain,
( ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) )
= ( nat_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(915,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_10_zero__eq__power2) ).
thf(3782,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)],[915]) ).
thf(279,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_add__0) ).
thf(1983,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1081,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_rel__simps_I21_J) ).
thf(4248,plain,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(584,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_1063_zcong__not__zero) ).
thf(2841,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)],[584]) ).
thf(493,axiom,
~ ( ord_less_real @ one_one_real @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_not__one__less__zero) ).
thf(2577,plain,
~ ( ord_less_real @ one_one_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(11,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_diff__0__right) ).
thf(1227,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1145,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_967_zdiff__power3) ).
thf(4429,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)],[1145]) ).
thf(107,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_1179_ex__least__nat__less) ).
thf(1498,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)],[107]) ).
thf(977,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_semiring__numeral__0__eq__0) ).
thf(3963,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1075,axiom,
~ ( ord_less_int @ one_one_int @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_not__one__less__zero) ).
thf(4227,plain,
~ ( ord_less_int @ one_one_int @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(664,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_769_zero__less__diff) ).
thf(3078,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)],[664]) ).
thf(961,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_984_Int2_Oaux1) ).
thf(3916,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)],[961]) ).
thf(380,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_1133_zcong__zdiff) ).
thf(2268,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)],[380]) ).
thf(638,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_880_less__eq__real__def) ).
thf(3001,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)],[638]) ).
thf(803,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_1117_one__not__neg__one__mod__m) ).
thf(3467,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)],[803]) ).
thf(883,axiom,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_mult__Pls) ).
thf(3699,plain,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(139,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_847_nat__le__linear) ).
thf(1592,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)],[139]) ).
thf(393,axiom,
ord_less_nat @ zero_zero_nat @ tn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_tn0) ).
thf(2300,plain,
ord_less_nat @ zero_zero_nat @ tn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(808,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_782_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(3482,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)],[808]) ).
thf(727,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_mult_Ocomm__neutral) ).
thf(3254,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(783,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_267_zero__less__power) ).
thf(3413,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)],[783]) ).
thf(233,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_426_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1851,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)],[233]) ).
thf(204,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_int @ A @ B )
= ( ord_less_int @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_diff__eq__diff__less) ).
thf(1772,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_int @ A @ B )
= ( ord_less_int @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(680,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_327_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(3122,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)],[680]) ).
thf(634,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_936_le__diff__conv) ).
thf(2990,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)],[634]) ).
thf(423,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_585_power__increasing) ).
thf(2377,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)],[423]) ).
thf(570,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_647_crossproduct__noteq) ).
thf(2801,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)],[570]) ).
thf(117,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_926_mult__eq__self__implies__10) ).
thf(1534,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)],[117]) ).
thf(1169,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_602_add__diff__add) ).
thf(4512,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)],[1169]) ).
thf(417,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_nat__dvd__1__iff__1) ).
thf(2359,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(63,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1375,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1174,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_Bit1__Min) ).
thf(4525,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(80,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_904_eq__diff__iff) ).
thf(1425,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)],[80]) ).
thf(169,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_687_add__le__cancel__left) ).
thf(1672,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)],[169]) ).
thf(885,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_rel__simps_I51_J) ).
thf(3704,plain,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(242,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1878,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(546,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_927_diff__is__0__eq) ).
thf(2726,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)],[546]) ).
thf(514,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_955_mult__eq__if) ).
thf(2631,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)],[514]) ).
thf(658,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( ( nat_1 @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_nat @ ( nat_1 @ A ) @ ( nat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_nat__diff__distrib) ).
thf(3060,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( ( nat_1 @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_nat @ ( nat_1 @ A ) @ ( nat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(667,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 @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_add__mono) ).
thf(3087,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 @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1086,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_rel__simps_I22_J) ).
thf(4263,plain,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(1096,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ? [C: int] : ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ ( times_times_int @ C @ B ) ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_best__division__abs) ).
thf(4291,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ? [C: int] : ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ ( times_times_int @ C @ B ) ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1100,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_1119_Legendre__def) ).
thf(4301,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)],[1100]) ).
thf(688,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_306_double__add__less__zero__iff__single__add__less__zero) ).
thf(3143,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)],[688]) ).
thf(265,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_nat__mult__commute) ).
thf(1942,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(486,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_mult__le__less__imp__less) ).
thf(2561,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(1130,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_75_rel__simps_I16_J) ).
thf(4389,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)],[1130]) ).
thf(793,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_add__right__cancel) ).
thf(3441,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(313,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_385_add__strict__mono) ).
thf(2080,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)],[313]) ).
thf(263,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_mult__right__le__imp__le) ).
thf(1937,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(211,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_845_le__cube) ).
thf(1791,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)],[211]) ).
thf(298,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_394_add__less__cancel__left) ).
thf(2038,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)],[298]) ).
thf(519,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_336_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2649,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)],[519]) ).
thf(740,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_868_mult__cancel1) ).
thf(3294,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)],[740]) ).
thf(105,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_488_mult__left__mono__neg) ).
thf(1493,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)],[105]) ).
thf(569,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_736_power__increasing__iff) ).
thf(2798,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)],[569]) ).
thf(687,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_mult__less__imp__less__right) ).
thf(3141,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(973,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_32_plus__numeral__code_I9_J) ).
thf(3952,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)],[973]) ).
thf(746,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_mult__le__less__imp__less) ).
thf(3311,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(597,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_1103_dvd_Oord__le__eq__trans) ).
thf(2877,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)],[597]) ).
thf(33,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ ( plus_plus_real @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_add__right__mono) ).
thf(1292,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ ( plus_plus_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(857,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_127_add__Bit0__Bit1) ).
thf(3622,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)],[857]) ).
thf(370,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_864_zdiff__zmult__distrib2) ).
thf(2240,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)],[370]) ).
thf(230,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_real__zero__not__eq__one) ).
thf(1842,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(707,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_463_right__diff__distrib__number__of) ).
thf(3194,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)],[707]) ).
thf(413,axiom,
( ( semiri132038758t_real @ one_one_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_of__nat__1) ).
thf(2349,plain,
( ( semiri132038758t_real @ one_one_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(874,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_829_self__quotient__aux1) ).
thf(3671,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)],[874]) ).
thf(315,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( power_power_int @ A @ ( nat_1 @ B ) )
= ( times_times_int @ A @ ( power_power_int @ A @ ( minus_minus_nat @ ( nat_1 @ B ) @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_Euler_Oaux__1) ).
thf(2085,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( power_power_int @ A @ ( nat_1 @ B ) )
= ( times_times_int @ A @ ( power_power_int @ A @ ( minus_minus_nat @ ( nat_1 @ B ) @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(246,axiom,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_zcong__refl) ).
thf(1889,plain,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(158,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_379_add__less__imp__less__left) ).
thf(1644,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)],[158]) ).
thf(563,axiom,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( nat_1 @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_zero__less__nat__eq) ).
thf(2781,plain,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( nat_1 @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1176,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_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(4530,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)],[1176]) ).
thf(966,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_zero__less__one) ).
thf(3935,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(78,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_996_zdvd__mult__cancel) ).
thf(1419,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)],[78]) ).
thf(466,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_899_diff__mult__distrib) ).
thf(2504,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)],[466]) ).
thf(471,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_1190_nat__le__add__iff1) ).
thf(2519,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)],[471]) ).
thf(119,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_941_le__add__diff__inverse2) ).
thf(1539,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)],[119]) ).
thf(501,axiom,
( ( semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_of__nat__0) ).
thf(2598,plain,
( ( semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(275,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_1076_power__dvd__imp__le) ).
thf(1974,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)],[275]) ).
thf(859,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_257_pos__add__strict) ).
thf(3628,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)],[859]) ).
thf(906,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_rel__simps_I44_J) ).
thf(3760,plain,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1048,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_1037_s1) ).
thf(4152,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)],[1048]) ).
thf(1023,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_add__less__cancel__left) ).
thf(4086,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(448,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_873_real__mult__right__cancel) ).
thf(2450,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)],[448]) ).
thf(330,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_1136_zcong__iff__lin) ).
thf(2125,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)],[330]) ).
thf(137,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_545_mult__right__le__imp__le) ).
thf(1588,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)],[137]) ).
thf(477,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 @ ( plus_plus_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_add__pos__pos) ).
thf(2536,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 @ ( plus_plus_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(35,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_911_real__add__left__mono) ).
thf(1297,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)],[35]) ).
thf(530,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_1193_nat__le__add__iff2) ).
thf(2681,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)],[530]) ).
thf(829,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(3541,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(90,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_1065_zcong__zmult__prop2) ).
thf(1451,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)],[90]) ).
thf(395,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_less__imp__of__nat__less) ).
thf(2304,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(25,axiom,
! [A: real,B: real] :
( ( ord_less_real @ B @ zero_zero_real )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ B @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_add__neg__neg) ).
thf(1266,plain,
! [A: real,B: real] :
( ( ord_less_real @ B @ zero_zero_real )
=> ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ B @ A ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1016,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_mult__1__left) ).
thf(4068,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(341,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_326_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(2153,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)],[341]) ).
thf(603,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_mult__right__less__imp__less) ).
thf(2900,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(124,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_less__add__iff1) ).
thf(1552,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(371,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ A @ A )
& ~ ( dvd_dvd_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_dvd_Oless__irrefl) ).
thf(2243,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(931,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_7_zero__power2) ).
thf(3819,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)],[931]) ).
thf(775,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_530_zero__le__mult__iff) ).
thf(3390,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)],[775]) ).
thf(288,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_274_power__inject__exp) ).
thf(2006,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)],[288]) ).
thf(463,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_1183_nat__mult__eq__cancel__disj) ).
thf(2497,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)],[463]) ).
thf(488,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_684_add__right__mono) ).
thf(2566,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)],[488]) ).
thf(214,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_1051_divides__exp2) ).
thf(1799,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)],[214]) ).
thf(968,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_800_rel__simps_I15_J) ).
thf(3937,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)],[968]) ).
thf(1077,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_1147_imp__le__cong) ).
thf(4231,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)],[1077]) ).
thf(1114,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
=> ( ord_less_eq_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_add__le__imp__le__left) ).
thf(4347,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
=> ( ord_less_eq_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(303,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_le__refl) ).
thf(2052,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(142,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_31_less__number__of__int__code) ).
thf(1599,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)],[142]) ).
thf(675,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_181_nat__add__assoc) ).
thf(3109,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)],[675]) ).
thf(277,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_1194_nat__diff__add__eq2) ).
thf(1979,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)],[277]) ).
thf(962,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rel__simps_I50_J) ).
thf(3920,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(382,axiom,
! [A: int,B: int] :
( ( twoSqu919416604sum2sq @ B )
=> ( ( twoSqu919416604sum2sq @ A )
=> ( twoSqu919416604sum2sq @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_is__mult__sum2sq) ).
thf(2272,plain,
! [A: int,B: int] :
( ( twoSqu919416604sum2sq @ B )
=> ( ( twoSqu919416604sum2sq @ A )
=> ( twoSqu919416604sum2sq @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1073,axiom,
! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_less__add__one) ).
thf(4223,plain,
! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(199,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_678_add__mono) ).
thf(1759,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)],[199]) ).
thf(421,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_1093_dvd_Oless__imp__not__eq) ).
thf(2370,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)],[421]) ).
thf(714,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_492_comm__mult__left__mono) ).
thf(3215,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)],[714]) ).
thf(114,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
= ( ord_less_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_rel__simps_I13_J) ).
thf(1525,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
= ( ord_less_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(690,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_982_real__le__antisym) ).
thf(3147,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)],[690]) ).
thf(47,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_490_mult__right__mono__neg) ).
thf(1333,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)],[47]) ).
thf(923,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_rel__simps_I46_J) ).
thf(3802,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(1116,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_add__right__mono) ).
thf(4352,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(702,axiom,
( tn
= ( minus_minus_nat @ ( nat_1 @ t ) @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_tn) ).
thf(3183,plain,
( tn
= ( minus_minus_nat @ ( nat_1 @ t ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(177,axiom,
! [A: int,B: int] :
( ( nat_1 @ ( abs_abs_int @ ( times_times_int @ A @ B ) ) )
= ( times_times_nat @ ( nat_1 @ ( abs_abs_int @ A ) ) @ ( nat_1 @ ( abs_abs_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_nat__abs__mult__distrib) ).
thf(1695,plain,
! [A: int,B: int] :
( ( nat_1 @ ( abs_abs_int @ ( times_times_int @ A @ B ) ) )
= ( times_times_nat @ ( nat_1 @ ( abs_abs_int @ A ) ) @ ( nat_1 @ ( abs_abs_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(941,axiom,
! [A: int] :
( ( zero_zero_int
= ( plus_plus_int @ A @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_double__zero__sym) ).
thf(3856,plain,
! [A: int] :
( ( zero_zero_int
= ( plus_plus_int @ A @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(305,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_320_add__imp__eq) ).
thf(2057,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)],[305]) ).
thf(553,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_142_number__of__Bit0) ).
thf(2748,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)],[553]) ).
thf(95,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_rel__simps_I9_J) ).
thf(1466,plain,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(508,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_mult__strict__mono) ).
thf(2617,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(523,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_499_mult__right__mono) ).
thf(2662,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)],[523]) ).
thf(475,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_759_less__iff__diff__less__0) ).
thf(2529,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)],[475]) ).
thf(235,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_765_mult__less__cancel__right__disj) ).
thf(1857,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)],[235]) ).
thf(1060,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_semiring__norm_I110_J) ).
thf(4184,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(282,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_494_comm__mult__left__mono) ).
thf(1991,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)],[282]) ).
thf(41,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_1042_dvd__diff__nat) ).
thf(1318,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)],[41]) ).
thf(538,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_748_convex__bound__lt) ).
thf(2702,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)],[538]) ).
thf(481,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ? [B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
& ( A
= ( semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_zero__less__imp__eq__int) ).
thf(2546,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ? [B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
& ( A
= ( semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1190,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_986_real__sum__squared__expand) ).
thf(4567,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)],[1190]) ).
thf(1021,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_semiring__norm_I110_J) ).
thf(4081,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(31,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_909_real__add__mult__distrib) ).
thf(1286,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)],[31]) ).
thf(750,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_930_diff__less__mono) ).
thf(3321,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)],[750]) ).
thf(433,axiom,
! [A: nat,B: nat] :
( ( semiri984289939at_nat @ ( times_times_nat @ A @ B ) )
= ( times_times_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_of__nat__mult) ).
thf(2408,plain,
! [A: nat,B: nat] :
( ( semiri984289939at_nat @ ( times_times_nat @ A @ B ) )
= ( times_times_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(705,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_165_power__strict__decreasing) ).
thf(3190,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)],[705]) ).
thf(993,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_696_power__commutes) ).
thf(4004,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)],[993]) ).
thf(284,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_mult__right__less__imp__less) ).
thf(1996,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(607,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_add__right__cancel) ).
thf(2909,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(925,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_1082__096_091s_____A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_) ).
thf(3807,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)],[925]) ).
thf(368,axiom,
~ ( ord_less_int @ min @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_rel__simps_I7_J) ).
thf(2235,plain,
~ ( ord_less_int @ min @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(886,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_340_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3707,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)],[886]) ).
thf(812,axiom,
! [A: int] :
( ( ord_less_int @ ( abs_abs_int @ A ) @ one_one_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_zabs__less__one__iff) ).
thf(3491,plain,
! [A: int] :
( ( ord_less_int @ ( abs_abs_int @ A ) @ one_one_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1188,axiom,
! [A: nat] :
( ( number_number_of_int @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_number__of__int) ).
thf(4562,plain,
! [A: nat] :
( ( number_number_of_int @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(734,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_436_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(3274,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)],[734]) ).
thf(1088,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_133_zero__less__power2) ).
thf(4269,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)],[1088]) ).
thf(882,axiom,
! [A: nat > $o,B: int] :
( ( A @ ( nat_1 @ B ) )
= ( ! [C: nat] :
( ( B
= ( semiri1621563631at_int @ C ) )
=> ( A @ C ) )
& ( ( ord_less_int @ B @ zero_zero_int )
=> ( A @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_split__nat) ).
thf(3696,plain,
! [A: nat > $o,B: int] :
( ( A @ ( nat_1 @ B ) )
= ( ! [C: nat] :
( ( B
= ( semiri1621563631at_int @ C ) )
=> ( A @ C ) )
& ( ( ord_less_int @ B @ zero_zero_int )
=> ( A @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(777,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_477_split__mult__neg__le) ).
thf(3396,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)],[777]) ).
thf(617,axiom,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_int__mult) ).
thf(2936,plain,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(547,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_1062_zcong__less__eq) ).
thf(2729,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)],[547]) ).
thf(870,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zadd__0) ).
thf(3660,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(286,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_516_mult__nonneg__nonneg) ).
thf(2001,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)],[286]) ).
thf(19,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_468_number__of__diff) ).
thf(1251,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)],[19]) ).
thf(201,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_613_mult__eq__0__iff) ).
thf(1764,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)],[201]) ).
thf(1157,axiom,
! [A: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri1621563631at_int @ ( nat_1 @ A ) )
= A ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri1621563631at_int @ ( nat_1 @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_int__nat__eq) ).
thf(4470,plain,
! [A: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri1621563631at_int @ ( nat_1 @ A ) )
= A ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( semiri1621563631at_int @ ( nat_1 @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(197,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_1033_zpower__zdvd__prop2) ).
thf(1754,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)],[197]) ).
thf(390,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_1057_divides__add__revr) ).
thf(2292,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)],[390]) ).
thf(1126,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_120_add__number__of__left) ).
thf(4380,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)],[1126]) ).
thf(426,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_504_mult__nonpos__nonneg) ).
thf(2391,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)],[426]) ).
thf(605,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_891_le__iff__add) ).
thf(2904,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)],[605]) ).
thf(178,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1698,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1117,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_272_power__inject__exp) ).
thf(4354,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)],[1117]) ).
thf(375,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_1030_pos__zmult__eq__1__iff__lemma) ).
thf(2253,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)],[375]) ).
thf(339,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_1068_dvd__imp__le) ).
thf(2149,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)],[339]) ).
thf(728,axiom,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_of__nat__less__iff) ).
thf(3257,plain,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(543,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ D @ E )
=> ( ( ord_less_eq_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_eq_real @ ( plus_plus_real @ ( times_times_real @ B @ D ) @ ( times_times_real @ A @ C ) ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_convex__bound__le) ).
thf(2717,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ D @ E )
=> ( ( ord_less_eq_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_eq_real @ ( plus_plus_real @ ( times_times_real @ B @ D ) @ ( times_times_real @ A @ C ) ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1139,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_965_zspecial__product) ).
thf(4412,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)],[1139]) ).
thf(490,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ ( nat_1 @ B ) @ A )
= ( ord_less_int @ B @ ( semiri1621563631at_int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_nat__less__iff) ).
thf(2570,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ ( nat_1 @ B ) @ A )
= ( ord_less_int @ B @ ( semiri1621563631at_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(122,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_1138_norR__mem__unique__aux) ).
thf(1548,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)],[122]) ).
thf(985,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(3985,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(898,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ( ( minus_minus_nat @ ( nat_1 @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( nat_1 @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_Int2_Oaux__1) ).
thf(3738,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ( ( minus_minus_nat @ ( nat_1 @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( nat_1 @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(935,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_1036__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_) ).
thf(3839,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)],[935]) ).
thf(824,axiom,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add__Pls__right) ).
thf(3523,plain,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(758,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_1090_dvd_Oord__less__eq__trans) ).
thf(3343,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)],[758]) ).
thf(693,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_1087_dvd_Oless__trans) ).
thf(3158,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)],[693]) ).
thf(704,axiom,
! [A: int] :
( ( minus_minus_int @ A @ min )
= ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_diff__bin__simps_I2_J) ).
thf(3187,plain,
! [A: int] :
( ( minus_minus_int @ A @ min )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1112,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(4341,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(749,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_924_real__mult__order) ).
thf(3319,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)],[749]) ).
thf(256,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_add__le__cancel__right) ).
thf(1916,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(719,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_le__add2) ).
thf(3234,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(427,axiom,
( ( semiri132038758t_real @ zero_zero_nat )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_of__nat__0) ).
thf(2393,plain,
( ( semiri132038758t_real @ zero_zero_nat )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(1003,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_eq_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_add__le__cancel__left) ).
thf(4032,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_eq_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1155,axiom,
! [A: int,B: int] :
( ( A = B )
= ( ( minus_minus_int @ A @ B )
= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_eq__iff__diff__eq__0) ).
thf(4465,plain,
! [A: int,B: int] :
( ( A = B )
= ( ( minus_minus_int @ A @ B )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(572,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_753_le__special_I4_J) ).
thf(2806,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)],[572]) ).
thf(179,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_minus__nat_Odiff__0) ).
thf(1701,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(272,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_mult__1) ).
thf(1965,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1006,axiom,
! [A: nat,B: nat] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zadd__int) ).
thf(4041,plain,
! [A: nat,B: nat] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(768,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_979_real__le__linear) ).
thf(3372,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)],[768]) ).
thf(899,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_126_add__Bit1__Bit0) ).
thf(3741,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)],[899]) ).
thf(226,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_918_mult__less__mono1) ).
thf(1833,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)],[226]) ).
thf(366,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_961_mult__nat__number__of) ).
thf(2225,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)],[366]) ).
thf(817,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_633_comm__semiring__class_Odistrib) ).
thf(3504,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)],[817]) ).
thf(244,axiom,
! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_less__add__one) ).
thf(1884,plain,
! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1093,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_137_sum__power2__gt__zero__iff) ).
thf(4283,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)],[1093]) ).
thf(68,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_422_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1389,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)],[68]) ).
thf(927,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_zero__less__two) ).
thf(3811,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(722,axiom,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_of__nat__mult) ).
thf(3240,plain,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(566,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_mult__0__right) ).
thf(2789,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(822,axiom,
ord_less_int @ m1 @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_mn) ).
thf(3519,plain,
ord_less_int @ m1 @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(473,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_158_one__less__power) ).
thf(2525,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)],[473]) ).
thf(587,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_1195_nat__eq__add__iff2) ).
thf(2849,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)],[587]) ).
thf(150,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_794_nat__diff__split__asm) ).
thf(1620,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)],[150]) ).
thf(805,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_802_rel__simps_I33_J) ).
thf(3472,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)],[805]) ).
thf(460,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_730_le__special_I3_J) ).
thf(2489,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)],[460]) ).
thf(161,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_299_exp__eq__1) ).
thf(1652,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)],[161]) ).
thf(665,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_zcong__eq__zdvd__prop) ).
thf(3081,plain,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(290,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_755_realpow__minus__mult) ).
thf(2016,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)],[290]) ).
thf(489,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_mult__strict__mono_H) ).
thf(2568,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(72,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_diff__0__eq__0) ).
thf(1403,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(799,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_734_power__decreasing) ).
thf(3458,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)],[799]) ).
thf(535,axiom,
ord_less_int @ min @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_bin__less__0__simps_I2_J) ).
thf(2695,plain,
ord_less_int @ min @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(103,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_1086_dvd_Oless__asym) ).
thf(1488,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)],[103]) ).
thf(579,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_852_le__trans) ).
thf(2827,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)],[579]) ).
thf(850,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_add__left__cancel) ).
thf(3599,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1161,axiom,
! [A: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(4485,plain,
! [A: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1038,axiom,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri1621563631at_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_int__power) ).
thf(4127,plain,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri1621563631at_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1033,axiom,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_diff__bin__simps_I1_J) ).
thf(4112,plain,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1028,axiom,
( ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_IH) ).
thf(4099,plain,
( ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1013,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_zmult__1) ).
thf(4060,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(856,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( nat_1 @ ( power_power_int @ B @ A ) )
= ( power_power_nat @ ( nat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_nat__power__eq) ).
thf(3619,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( nat_1 @ ( power_power_int @ B @ A ) )
= ( power_power_nat @ ( nat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(249,axiom,
! [A: nat,B: nat] :
( ( ( semiri984289939at_nat @ A )
= ( semiri984289939at_nat @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_of__nat__eq__iff) ).
thf(1897,plain,
! [A: nat,B: nat] :
( ( ( semiri984289939at_nat @ A )
= ( semiri984289939at_nat @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(439,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_872_real__mult__left__cancel) ).
thf(2425,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)],[439]) ).
thf(170,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_529_zero__le__mult__iff) ).
thf(1675,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)],[170]) ).
thf(828,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_1146_conj__le__cong) ).
thf(3532,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)],[828]) ).
thf(81,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_1097_dvd_Oless__imp__neq) ).
thf(1428,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)],[81]) ).
thf(344,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_power__one__right) ).
thf(2161,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1082,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_334_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(4251,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)],[1082]) ).
thf(1186,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_semiring__numeral__1__eq__1) ).
thf(4558,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(356,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_832_q__neg__lemma) ).
thf(2193,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)],[356]) ).
thf(209,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_less__add__iff2) ).
thf(1786,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1061,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_add__le__imp__le__right) ).
thf(4186,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(1027,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_diff__bin__simps_I4_J) ).
thf(4096,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(893,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_int__0__less__1) ).
thf(3726,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(27,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_162_power__0__left) ).
thf(1271,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)],[27]) ).
thf(397,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_332_add__left__cancel) ).
thf(2308,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)],[397]) ).
thf(1055,axiom,
! [A: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_int__less__0__conv) ).
thf(4171,plain,
! [A: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(871,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_16_one__add__one__is__two) ).
thf(3663,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)],[871]) ).
thf(1071,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_266_zero__less__power) ).
thf(4218,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)],[1071]) ).
thf(155,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_one__neq__zero) ).
thf(1635,plain,
one_one_real != zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(189,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_970_unique__quotient__lemma__neg) ).
thf(1733,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)],[189]) ).
thf(1192,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I2_J) ).
thf(4573,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(15,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_eq__add__iff1) ).
thf(1239,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(757,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_eq_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_transfer__nat__int__relations_I3_J) ).
thf(3340,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_eq_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(848,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_diff__bin__simps_I3_J) ).
thf(3594,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(743,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_zero__reorient) ).
thf(3302,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(839,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_837_qf1pt) ).
thf(3568,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)],[839]) ).
thf(156,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_34_less__number__of) ).
thf(1638,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)],[156]) ).
thf(761,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_831_q__pos__lemma) ).
thf(3355,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)],[761]) ).
thf(1080,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rel__simps_I10_J) ).
thf(4245,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(10,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_real @ A @ B )
= ( ord_less_real @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_diff__eq__diff__less) ).
thf(1224,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_real @ A @ B )
= ( ord_less_real @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(401,axiom,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__numeral__0__right) ).
thf(2319,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(491,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_693_diff__less__mono2) ).
thf(2573,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)],[491]) ).
thf(890,axiom,
ord_less_int @ one_one_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
thf(3719,plain,
ord_less_int @ one_one_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(468,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_zero__less__double__add__iff__zero__less__single__add) ).
thf(2510,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(398,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_nat__mult__1__right) ).
thf(2311,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(5,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_diff__eq__diff__eq) ).
thf(1209,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(132,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_542_mult__left__le__imp__le) ).
thf(1574,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)],[132]) ).
thf(376,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_680_add__left__mono) ).
thf(2257,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)],[376]) ).
thf(625,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_467_number__of__diff) ).
thf(2955,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)],[625]) ).
thf(1043,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
thf(4139,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(708,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ( nat_1 @ B )
= ( nat_1 @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_eq__nat__nat__iff) ).
thf(3197,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ( nat_1 @ B )
= ( nat_1 @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(1129,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(4388,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(478,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_add__0__left) ).
thf(2538,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(74,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_501_mult__nonpos__nonpos) ).
thf(1408,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)],[74]) ).
thf(726,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_921_nat__0__less__mult__iff) ).
thf(3251,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)],[726]) ).
thf(1122,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_number__of__Pls) ).
thf(4369,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(340,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_509_mult__nonneg__nonpos) ).
thf(2151,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)],[340]) ).
thf(516,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_507_mult__nonneg__nonpos2) ).
thf(2642,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)],[516]) ).
thf(929,axiom,
( ( plus_plus_int @ ( power_power_int @ x @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_xy) ).
thf(3815,plain,
( ( plus_plus_int @ ( power_power_int @ x @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(721,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_le__add1) ).
thf(3238,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(511,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_1041_divides__mul__l) ).
thf(2624,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)],[511]) ).
thf(248,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_998_zdvd__reduce) ).
thf(1894,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)],[248]) ).
thf(633,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_1047_nat__mult__dvd__cancel__disj_H) ).
thf(2987,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)],[633]) ).
thf(833,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zero__is__num__zero) ).
thf(3551,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(438,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_695_power__commutes) ).
thf(2422,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)],[438]) ).
thf(975,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_968_zdiff__power2) ).
thf(3957,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)],[975]) ).
thf(878,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_add__right__imp__eq) ).
thf(3683,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(674,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_1102_dvd__antisym) ).
thf(3106,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)],[674]) ).
thf(120,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_447_semiring__mult__number__of) ).
thf(1542,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)],[120]) ).
thf(1197,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_702_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(4586,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)],[1197]) ).
thf(326,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_add__strict__mono) ).
thf(2116,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(887,axiom,
! [A: nat > $o] :
( ( all @ A )
= ( ! [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A @ ( nat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_all__nat) ).
thf(3710,plain,
! [A: nat > $o] :
( ( all @ A )
= ( ! [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A @ ( nat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(620,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_738_power__le__imp__le__exp) ).
thf(2945,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)],[620]) ).
thf(1124,axiom,
! [A: nat,B: nat] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(4374,plain,
! [A: nat,B: nat] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(660,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_905_diff__diff__cancel) ).
thf(3066,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)],[660]) ).
thf(131,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_rel__simps_I30_J) ).
thf(1571,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1168,axiom,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
=> ( ( abs_abs_int @ A )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_power2__eq1__iff) ).
thf(4509,plain,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
=> ( ( abs_abs_int @ A )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1158,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_88_odd__less__0) ).
thf(4477,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)],[1158]) ).
thf(1031,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_80_bin__less__0__simps_I3_J) ).
thf(4107,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)],[1031]) ).
thf(352,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_907_diff__le__mono2) ).
thf(2182,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)],[352]) ).
thf(1180,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_278_power__less__imp__less__exp) ).
thf(4541,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)],[1180]) ).
thf(126,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_513_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(1557,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)],[126]) ).
thf(283,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_add_Ocomm__neutral) ).
thf(1993,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1001,axiom,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_transfer__int__nat__numerals_I3_J) ).
thf(4028,plain,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(222,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_573_mult__le__cancel__left__pos) ).
thf(1821,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)],[222]) ).
thf(965,axiom,
! [A: nat,B: nat,C: int] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( plus_plus_int @ ( semiri1621563631at_int @ B ) @ C ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zadd__int__left) ).
thf(3932,plain,
! [A: nat,B: nat,C: int] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( plus_plus_int @ ( semiri1621563631at_int @ B ) @ C ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1059,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_811_zle__add1__eq__le) ).
thf(4181,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)],[1059]) ).
thf(524,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_339_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2664,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)],[524]) ).
thf(691,axiom,
! [A: int] :
( ( ( abs_abs_int @ A )
= one_one_int )
= ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_abs__eq__1__iff) ).
thf(3150,plain,
! [A: int] :
( ( ( abs_abs_int @ A )
= one_one_int )
= ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(952,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_zprime__2) ).
thf(3893,plain,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(798,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_one__add__one__is__two) ).
thf(3456,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(167,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_644_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1667,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)],[167]) ).
thf(578,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_338_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2824,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)],[578]) ).
thf(1065,axiom,
( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
thf(4203,plain,
( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(97,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_add__less__cancel__left) ).
thf(1471,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(901,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_1079_Euler_Oaux____1) ).
thf(3747,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)],[901]) ).
thf(293,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_less__imp__le__nat) ).
thf(2025,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(574,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_756_realpow__minus__mult) ).
thf(2812,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)],[574]) ).
thf(50,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_391_add__strict__right__mono) ).
thf(1339,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)],[50]) ).
thf(1142,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_add__0) ).
thf(4420,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
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_505_mult__nonpos__nonneg) ).
thf(2314,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(410,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_850_mult__le__mono1) ).
thf(2343,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)],[410]) ).
thf(873,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_66_zadd__left__commute) ).
thf(3668,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)],[873]) ).
thf(1154,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_13_add__special_I2_J) ).
thf(4462,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)],[1154]) ).
thf(324,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 @ D @ B ) @ E ) )
= ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_le__add__iff1) ).
thf(2111,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 @ D @ B ) @ E ) )
= ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1091,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_138_sum__power2__gt__zero__iff) ).
thf(4277,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)],[1091]) ).
thf(556,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2757,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1109,axiom,
! [A: int] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_diff__self) ).
thf(4332,plain,
! [A: int] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(706,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_1069_dvd__mult__cancel) ).
thf(3192,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)],[706]) ).
thf(612,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_1032_zprime__power__zdvd__cancel__left) ).
thf(2923,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)],[612]) ).
thf(44,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_508_mult__nonneg__nonpos2) ).
thf(1325,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)],[44]) ).
thf(93,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_add__0__right) ).
thf(1460,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(389,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_276_power__strict__increasing__iff) ).
thf(2289,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)],[389]) ).
thf(518,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_672_add__le__imp__le__left) ).
thf(2647,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)],[518]) ).
thf(614,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_add__le__imp__le__right) ).
thf(2928,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(65,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_mult__zero__left) ).
thf(1381,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(452,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_mult__1__left) ).
thf(2461,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(630,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_919_mult__less__cancel2) ).
thf(2974,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)],[630]) ).
thf(311,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_497_mult__left__mono) ).
thf(2075,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)],[311]) ).
thf(419,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_780_zmult__zless__mono2) ).
thf(2365,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)],[419]) ).
thf(98,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_1029_zmult__eq__1__iff) ).
thf(1474,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)],[98]) ).
thf(140,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_1089_dvd_Oless__le__trans) ).
thf(1594,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)],[140]) ).
thf(582,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_add__0__right) ).
thf(2835,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(875,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_134_zero__less__power2) ).
thf(3674,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)],[875]) ).
thf(361,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2207,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(534,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_506_mult__nonneg__nonpos2) ).
thf(2693,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)],[534]) ).
thf(482,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_191_add__less__mono1) ).
thf(2550,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)],[482]) ).
thf(17,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_466_left__diff__distrib__number__of) ).
thf(1245,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)],[17]) ).
thf(87,axiom,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_number__of__is__id) ).
thf(1445,plain,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(115,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_one__neq__zero) ).
thf(1528,plain,
one_one_nat != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(335,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_1134_zcong__not) ).
thf(2139,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)],[335]) ).
thf(879,axiom,
! [A: nat,B: int] :
( ( A
= ( nat_1 @ B ) )
= ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( B
= ( semiri1621563631at_int @ A ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_nat__eq__iff2) ).
thf(3687,plain,
! [A: nat,B: int] :
( ( A
= ( nat_1 @ B ) )
= ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( B
= ( semiri1621563631at_int @ A ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(924,axiom,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_pos2) ).
thf(3806,plain,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(372,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_zmult__commute) ).
thf(2244,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(83,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_863_zdiff__zmult__distrib) ).
thf(1435,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)],[83]) ).
thf(205,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_real__mult__commute) ).
thf(1775,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(499,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(2592,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(292,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_of__nat__le__iff) ).
thf(2022,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(765,axiom,
! [A: nat] :
( ( ord_less_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_of__nat__0__less__iff) ).
thf(3363,plain,
! [A: nat] :
( ( ord_less_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(99,axiom,
! [A: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_abs__add__one__gt__zero) ).
thf(1477,plain,
! [A: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(752,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_857_mult__le__cancel1) ).
thf(3325,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)],[752]) ).
thf(637,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_923_real__mult__less__mono2) ).
thf(2999,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)],[637]) ).
thf(342,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_zero__reorient) ).
thf(2156,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(632,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_922_not__real__square__gt__zero) ).
thf(2984,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)],[632]) ).
thf(216,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_add__left__imp__eq) ).
thf(1805,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(771,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_732_power__decreasing) ).
thf(3380,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)],[771]) ).
thf(128,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_514_mult__nonneg__nonneg) ).
thf(1562,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)],[128]) ).
thf(76,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_223_less__0__number__of) ).
thf(1413,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)],[76]) ).
thf(794,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_710_rel__simps_I34_J) ).
thf(3444,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)],[794]) ).
thf(3,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
= ( ord_less_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_less__iff__diff__less__0) ).
thf(1203,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
= ( ord_less_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1085,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_305_double__add__less__zero__iff__single__add__less__zero) ).
thf(4260,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)],[1085]) ).
thf(520,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_pos__add__strict) ).
thf(2652,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1010,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_446_semiring__mult__number__of) ).
thf(4052,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)],[1010]) ).
thf(689,axiom,
ord_less_int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_rel__simps_I6_J) ).
thf(3146,plain,
ord_less_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(531,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_795_nat__diff__split) ).
thf(2684,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)],[531]) ).
thf(152,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_1056_dvd__reduce) ).
thf(1626,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)],[152]) ).
thf(641,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_159_one__less__power) ).
thf(3009,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)],[641]) ).
thf(304,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_421_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(2054,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)],[304]) ).
thf(1144,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_642_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(4426,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)],[1144]) ).
thf(1067,axiom,
! [A: int] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_rel__simps_I42_J) ).
thf(4207,plain,
! [A: int] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(267,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_459_arith__simps_I32_J) ).
thf(1948,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)],[267]) ).
thf(1136,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_45_nat__1__add__1) ).
thf(4405,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)],[1136]) ).
thf(609,axiom,
! [A: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( nat_1 @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_nat__le__0) ).
thf(2914,plain,
! [A: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( nat_1 @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(648,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_279_power__less__imp__less__exp) ).
thf(3031,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)],[648]) ).
thf(217,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_1064_zcong__zmult__prop1) ).
thf(1809,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)],[217]) ).
thf(624,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_eq__number__of__Pls__Min) ).
thf(2952,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1132,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_740_power__le__imp__le__exp) ).
thf(4394,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)],[1132]) ).
thf(1041,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 @ A @ one_one_int )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_mult__right__le__one__le) ).
thf(4136,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 @ A @ one_one_int )
=> ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(507,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_le__add__iff1) ).
thf(2614,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(319,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_1099_dvd_Oord__eq__less__trans) ).
thf(2096,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)],[319]) ).
thf(788,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__0__right) ).
thf(3427,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(996,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(4013,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(967,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_988__0964_A_K_Am_A_L_A1_Advd_As_____A_094_A2_A_N_A_N1_096) ).
thf(3936,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)],[967]) ).
thf(322,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_482_mult__mono) ).
thf(2107,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)],[322]) ).
thf(564,axiom,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_eq__number__of) ).
thf(2784,plain,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1153,axiom,
~ ! [A: int,B: int] :
~ ( ( B
= ( minus_minus_int @ y @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) )
& ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153__096_B_Bthesis_O_A_I_B_Bs_Aw_O_Aw_A_061_Ay_A_N_As_A_K_A_I1_A_L_Aint_An) ).
thf(4456,plain,
~ ! [A: int,B: int] :
~ ( ( B
= ( minus_minus_int @ y @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) )
& ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(711,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_456_number__of__mult) ).
thf(3206,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)],[711]) ).
thf(694,axiom,
~ ( ord_less_eq_int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_rel__simps_I20_J) ).
thf(3161,plain,
~ ( ord_less_eq_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(252,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_200_nat__zero__less__power__iff) ).
thf(1905,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)],[252]) ).
thf(465,axiom,
ord_less_nat @ zero_zero_nat @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_n0) ).
thf(2503,plain,
ord_less_nat @ zero_zero_nat @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(173,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_add__strict__left__mono) ).
thf(1684,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1057,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_836_t__l__p) ).
thf(4177,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)],[1057]) ).
thf(513,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_1088_dvd_Oless__asym_H) ).
thf(2629,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)],[513]) ).
thf(406,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2333,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(586,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_718_zless__le) ).
thf(2846,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)],[586]) ).
thf(1195,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_add_Ocomm__neutral) ).
thf(4581,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(269,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_mult__less__le__imp__less) ).
thf(1958,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1054,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_862_diff__bin__simps_I7_J) ).
thf(4168,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)],[1054]) ).
thf(495,axiom,
! [A: nat,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( times_times_int @ ( semiri1621563631at_int @ A ) @ B ) @ ( times_times_int @ ( semiri1621563631at_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_zmult__zless__mono2__lemma) ).
thf(2582,plain,
! [A: nat,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( times_times_int @ ( semiri1621563631at_int @ A ) @ B ) @ ( times_times_int @ ( semiri1621563631at_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(841,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_1083__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s) ).
thf(3571,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)],[841]) ).
thf(619,axiom,
! [A: nat] :
( ( ord_less_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_zero__less__int__conv) ).
thf(2942,plain,
! [A: nat] :
( ( ord_less_int @ zero_zero_int @ ( semiri1621563631at_int @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(203,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_1094_dvd_Oless__imp__not__less) ).
thf(1770,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)],[203]) ).
thf(1004,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_15_add__special_I3_J) ).
thf(4035,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)],[1004]) ).
thf(960,axiom,
! [A: nat] :
( ( ( semiri1621563631at_int @ A )
= zero_zero_int )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_int__eq__0__conv) ).
thf(3913,plain,
! [A: nat] :
( ( ( semiri1621563631at_int @ A )
= zero_zero_int )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(972,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_power__0) ).
thf(3949,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(529,axiom,
! [A: nat,B: int] :
( ( dvd_dvd_int @ ( semiri1621563631at_int @ A ) @ B )
= ( dvd_dvd_nat @ A @ ( nat_1 @ ( abs_abs_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_int__dvd__iff) ).
thf(2678,plain,
! [A: nat,B: int] :
( ( dvd_dvd_int @ ( semiri1621563631at_int @ A ) @ B )
= ( dvd_dvd_nat @ A @ ( nat_1 @ ( abs_abs_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(12,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_add__diff__cancel) ).
thf(1230,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(987,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_987__096s_____A_094_A2_A_N_A_N1_A_061_As_____A_094_A2_A_L_A1_096) ).
thf(3988,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)],[987]) ).
thf(469,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_641_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(2513,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)],[469]) ).
thf(231,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_mult__le__cancel__left__pos) ).
thf(1845,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
= ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(863,axiom,
( zero_zero_int
= ( semiri1621563631at_int @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_transfer__int__nat__numerals_I1_J) ).
thf(3640,plain,
( zero_zero_int
= ( semiri1621563631at_int @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(592,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_445_semiring__mult__number__of) ).
thf(2863,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)],[592]) ).
thf(818,axiom,
! [A: int] :
( ( one_one_int = A )
= ( A = one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_one__reorient) ).
thf(3507,plain,
! [A: int] :
( ( one_one_int = A )
= ( A = one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1119,axiom,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_of__nat__eq__iff) ).
thf(4360,plain,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(429,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_895_nat__mult__eq__1__iff) ).
thf(2397,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)],[429]) ).
thf(936,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_645_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3842,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)],[936]) ).
thf(1163,axiom,
! [A: int] :
( ( succ @ ( bit0 @ A ) )
= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_succ__Bit0) ).
thf(4490,plain,
! [A: int] :
( ( succ @ ( bit0 @ A ) )
= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(676,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_semiring__norm_I112_J) ).
thf(3112,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(631,axiom,
! [A: int] :
( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_nat__1__add__number__of) ).
thf(2977,plain,
! [A: int] :
( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(147,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_118_power__eq__0__iff__number__of) ).
thf(1611,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)],[147]) ).
thf(1089,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_add__0__iff) ).
thf(4272,plain,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(193,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_le__0__eq) ).
thf(1743,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1121,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_636_combine__common__factor) ).
thf(4366,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)],[1121]) ).
thf(337,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_add__le__cancel__left) ).
thf(2143,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(957,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ D @ E )
=> ( ( ord_less_eq_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_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ D ) @ ( times_times_int @ A @ C ) ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_convex__bound__le) ).
thf(3904,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ D @ E )
=> ( ( ord_less_eq_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_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ D ) @ ( times_times_int @ A @ C ) ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(729,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_848_nat__mult__assoc) ).
thf(3260,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)],[729]) ).
thf(904,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_zero__neq__one) ).
thf(3754,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(548,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_916_less__bin__lemma) ).
thf(2732,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)],[548]) ).
thf(1064,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_one__neq__zero) ).
thf(4200,plain,
one_one_int != zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1171,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_9_zero__power2) ).
thf(4517,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)],[1171]) ).
thf(349,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_1185_nat__mult__less__cancel1) ).
thf(2175,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)],[349]) ).
thf(207,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_1073_dvd__mult__cancel1) ).
thf(1780,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)],[207]) ).
thf(577,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_not__add__less2) ).
thf(2821,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(712,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_735_power__increasing__iff) ).
thf(3209,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)],[712]) ).
thf(544,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2720,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(945,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_796_eq__0__number__of) ).
thf(3872,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)],[945]) ).
thf(1125,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_rel__simps_I5_J) ).
thf(4377,plain,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(116,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_969_zdiv__mono2__neg__lemma) ).
thf(1531,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)],[116]) ).
thf(1106,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_803_less__eq__int__code_I15_J) ).
thf(4324,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)],[1106]) ).
thf(645,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_24_power__0__left__number__of) ).
thf(3019,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)],[645]) ).
thf(1148,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_2_sum__power2__eq__zero__iff) ).
thf(4437,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)],[1148]) ).
thf(1173,axiom,
! [A: nat,B: int] :
( ( ( semiri1621563631at_int @ A )
= B )
= ( ( A
= ( nat_1 @ B ) )
& ( ord_less_eq_int @ zero_zero_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_int__eq__iff) ).
thf(4522,plain,
! [A: nat,B: int] :
( ( ( semiri1621563631at_int @ A )
= B )
= ( ( A
= ( nat_1 @ B ) )
& ( ord_less_eq_int @ zero_zero_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(864,axiom,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_power__one) ).
thf(3642,plain,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1078,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_1059_zcong__shift) ).
thf(4240,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)],[1078]) ).
thf(892,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_rel__simps_I39_J) ).
thf(3722,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1183,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_775_rel__simps_I32_J) ).
thf(4549,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)],[1183]) ).
thf(239,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_701_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1869,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)],[239]) ).
thf(911,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_5_one__power2) ).
thf(3774,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)],[911]) ).
thf(459,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_zle__int) ).
thf(2486,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(134,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_455_le__number__of) ).
thf(1579,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)],[134]) ).
thf(909,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_576_sum__squares__ge__zero) ).
thf(3769,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)],[909]) ).
thf(184,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_496_mult__left__mono) ).
thf(1716,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)],[184]) ).
thf(969,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_add__imp__eq) ).
thf(3940,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(744,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_481_split__mult__pos__le) ).
thf(3305,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)],[744]) ).
thf(82,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
= ( ord_less_eq_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_rel__simps_I26_J) ).
thf(1432,plain,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
= ( ord_less_eq_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(950,axiom,
~ ! [A: int,B: int] :
~ ( ( B
= ( minus_minus_int @ x @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) )
& ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154__096_B_Bthesis_O_A_I_B_Br_Av_O_Av_A_061_Ax_A_N_Ar_A_K_A_I1_A_L_Aint_An) ).
thf(3885,plain,
~ ! [A: int,B: int] :
~ ( ( B
= ( minus_minus_int @ x @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) )
& ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(677,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_1182_nat__less__add__iff2) ).
thf(3114,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)],[677]) ).
thf(755,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_1192_nat__eq__add__iff1) ).
thf(3334,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)],[755]) ).
thf(918,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(3791,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(659,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_add__0__iff) ).
thf(3063,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(611,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_440_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2920,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)],[611]) ).
thf(806,axiom,
~ ( ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
=> ~ ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_smaller_I2_J) ).
thf(3475,plain,
~ ( ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
=> ~ ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(646,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_418_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(3026,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)],[646]) ).
thf(868,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_275_power__strict__increasing__iff) ).
thf(3655,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)],[868]) ).
thf(23,axiom,
( zero_zero_nat
= ( nat_1 @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_transfer__nat__int__numerals_I1_J) ).
thf(1262,plain,
( zero_zero_nat
= ( nat_1 @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1045,axiom,
( ( semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_of__nat__1) ).
thf(4145,plain,
( ( semiri1621563631at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(933,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_169_int__gr__induct) ).
thf(3823,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)],[933]) ).
thf(384,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_650_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(2276,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)],[384]) ).
thf(922,axiom,
ord_less_eq_int @ one_one_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_tpos) ).
thf(3801,plain,
ord_less_eq_int @ one_one_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(365,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_1091_dvd_Oless__imp__triv) ).
thf(2219,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)],[365]) ).
thf(331,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_1141_zprime__zdvd__zmult) ).
thf(2128,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)],[331]) ).
thf(164,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_935_diff__diff__right) ).
thf(1658,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)],[164]) ).
thf(402,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_add_Ocomm__neutral) ).
thf(2322,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(763,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_258_pos__add__strict) ).
thf(3359,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)],[763]) ).
thf(699,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_less__nat__zero__code) ).
thf(3174,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
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_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_971_zdiv__mono2__lemma) ).
thf(2044,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)],[300]) ).
thf(8,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_diff__self) ).
thf(1218,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(650,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_add__less__imp__less__right) ).
thf(3041,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(670,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_772_less__diff__conv) ).
thf(3095,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)],[670]) ).
thf(940,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_408_zadd__power3) ).
thf(3853,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)],[940]) ).
thf(1052,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_18_semiring__one__add__one__is__two) ).
thf(4164,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)],[1052]) ).
thf(415,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ( nat_1 @ B )
= ( nat_1 @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_transfer__nat__int__relations_I1_J) ).
thf(2354,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ( nat_1 @ B )
= ( nat_1 @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(622,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_881_add__mult__distrib) ).
thf(2948,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)],[622]) ).
thf(1040,axiom,
! [A: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_of__nat__less__0__iff) ).
thf(4133,plain,
! [A: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(215,axiom,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
= ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_number__of__reorient) ).
thf(1802,plain,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
= ( B
= ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(424,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_452_zle__trans) ).
thf(2379,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)],[424]) ).
thf(480,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_le__iff__diff__le__0) ).
thf(2543,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(9,axiom,
! [A: real,B: real] :
( ( ( minus_minus_real @ A @ B )
= zero_zero_real )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_right__minus__eq) ).
thf(1221,plain,
! [A: real,B: real] :
( ( ( minus_minus_real @ A @ B )
= zero_zero_real )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(494,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_add__less__cancel__right) ).
thf(2579,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(195,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_less__add__one) ).
thf(1749,plain,
! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(774,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_495_mult__left__mono) ).
thf(3388,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)],[774]) ).
thf(136,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_33_less__number__of) ).
thf(1585,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)],[136]) ).
thf(168,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_less__imp__of__nat__less) ).
thf(1670,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(618,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_diff__eq__diff__less__eq) ).
thf(2939,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(662,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_less__not__refl2) ).
thf(3071,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(62,axiom,
! [A: int] :
( ( number_number_of_nat @ A )
= ( nat_1 @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_nat__number__of__def) ).
thf(1372,plain,
! [A: int] :
( ( number_number_of_nat @ A )
= ( nat_1 @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(243,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_mult__zero__right) ).
thf(1881,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(528,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_of__nat__le__iff) ).
thf(2675,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( dvd_dvd_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_dvd_Oeq__refl) ).
thf(1358,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( dvd_dvd_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(373,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_577_sum__squares__le__zero__iff) ).
thf(2247,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)],[373]) ).
thf(434,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_add__le__cancel__right) ).
thf(2411,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(811,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_49_less__int__code_I13_J) ).
thf(3488,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)],[811]) ).
thf(464,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_1122_zcong__square__zless) ).
thf(2500,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)],[464]) ).
thf(1012,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ ( succ @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_add__Bit1__Bit1) ).
thf(4057,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ ( succ @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(867,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_776_less__eq__int__code_I14_J) ).
thf(3652,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)],[867]) ).
thf(21,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_413_le__iff__diff__le__0) ).
thf(1257,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)],[21]) ).
thf(583,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_643_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2838,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)],[583]) ).
thf(485,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_428_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2558,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)],[485]) ).
thf(980,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( plus_plus_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( nat_1 @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
thf(3970,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( plus_plus_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( nat_1 @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(784,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_728_le__special_I1_J) ).
thf(3415,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)],[784]) ).
thf(385,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_268_zero__less__power) ).
thf(2279,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)],[385]) ).
thf(416,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_498_mult__right__mono) ).
thf(2357,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)],[416]) ).
thf(585,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_925_real__mult__less__iff1) ).
thf(2843,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)],[585]) ).
thf(102,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_not__add__less1) ).
thf(1485,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(541,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2711,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(678,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_1098_dvd_Ole__less__trans) ).
thf(3117,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)],[678]) ).
thf(591,axiom,
! [A: int] :
( ( ( nat_1 @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_nat__0__iff) ).
thf(2860,plain,
! [A: int] :
( ( ( nat_1 @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(295,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_886_add__le__mono) ).
thf(2030,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)],[295]) ).
thf(1074,axiom,
( ( succ @ min )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_succ__Min) ).
thf(4225,plain,
( ( succ @ min )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(823,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_mult_Ocomm__neutral) ).
thf(3520,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(766,axiom,
! [A: nat,B: nat] :
( ( ( semiri132038758t_real @ A )
= ( semiri132038758t_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_of__nat__eq__iff) ).
thf(3366,plain,
! [A: nat,B: nat] :
( ( ( semiri132038758t_real @ A )
= ( semiri132038758t_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(640,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_854_mult__le__mono) ).
thf(3007,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)],[640]) ).
thf(1047,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_numeral__1__eq__1) ).
thf(4150,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(496,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_430_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(2584,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)],[496]) ).
thf(1084,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_950_le__nat__number__of) ).
thf(4257,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)],[1084]) ).
thf(1131,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 @ A @ one_one_int )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_mult__left__le__one__le) ).
thf(4392,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 @ A @ one_one_int )
=> ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(738,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_528_mult__le__0__iff) ).
thf(3288,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)],[738]) ).
thf(1070,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_1034__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(4217,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)],[1070]) ).
thf(149,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_705_diff__diff__left) ).
thf(1617,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)],[149]) ).
thf(596,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_1100_dvd_Oorder__trans) ).
thf(2875,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)],[596]) ).
thf(686,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_mult__less__imp__less__right) ).
thf(3139,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(451,axiom,
! [A: int] :
( ( dvd_dvd_int @ A @ one_one_int )
= ( ( abs_abs_int @ A )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1158_zdvd1__eq) ).
thf(2458,plain,
! [A: int] :
( ( dvd_dvd_int @ A @ one_one_int )
= ( ( abs_abs_int @ A )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(669,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_add__left__cancel) ).
thf(3092,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(576,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_transfer__nat__int__relations_I2_J) ).
thf(2818,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(536,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_201_add__gr__0) ).
thf(2696,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)],[536]) ).
thf(594,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_164_power__strict__decreasing) ).
thf(2870,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)],[594]) ).
thf(698,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_zero__neq__one) ).
thf(3171,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(795,axiom,
! [A: int] :
( ( succ @ ( bit1 @ A ) )
= ( bit0 @ ( succ @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_succ__Bit1) ).
thf(3447,plain,
! [A: int] :
( ( succ @ ( bit1 @ A ) )
= ( bit0 @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(832,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_diff__bin__simps_I5_J) ).
thf(3548,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(412,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_mult__strict__mono_H) ).
thf(2347,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(111,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_mult__left__le__imp__le) ).
thf(1517,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(403,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_power__one__right) ).
thf(2325,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(238,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_power__0) ).
thf(1866,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(872,axiom,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_zero__reorient) ).
thf(3665,plain,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(443,axiom,
! [A: nat,B: nat] :
( ( semiri132038758t_real @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_of__nat__add) ).
thf(2435,plain,
! [A: nat,B: nat] :
( ( semiri132038758t_real @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(557,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_1143_zcong__square) ).
thf(2760,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)],[557]) ).
thf(790,axiom,
( one_one_int
= ( semiri1621563631at_int @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_transfer__int__nat__numerals_I2_J) ).
thf(3433,plain,
( one_one_int
= ( semiri1621563631at_int @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(971,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(3946,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1095,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_390_add__strict__right__mono) ).
thf(4289,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)],[1095]) ).
thf(512,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_938_le__add__diff__inverse) ).
thf(2626,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)],[512]) ).
thf(1042,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(4138,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(160,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_1140_zcong__zless__imp__eq) ).
thf(1649,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)],[160]) ).
thf(905,axiom,
! [A: nat] :
( ( number267125858f_real @ ( semiri1621563631at_int @ A ) )
= ( semiri132038758t_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_number__of__int) ).
thf(3757,plain,
! [A: nat] :
( ( number267125858f_real @ ( semiri1621563631at_int @ A ) )
= ( semiri132038758t_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(458,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_23_power__0__left__number__of) ).
thf(2479,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)],[458]) ).
thf(838,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_117_power__eq__0__iff__number__of) ).
thf(3565,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)],[838]) ).
thf(316,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_1189_nat__mult__le__cancel1) ).
thf(2088,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)],[316]) ).
thf(858,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( nat_1 @ ( plus_plus_int @ B @ A ) )
= ( plus_plus_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_nat__add__distrib) ).
thf(3625,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( nat_1 @ ( plus_plus_int @ B @ A ) )
= ( plus_plus_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1020,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_11_zero__eq__power2) ).
thf(4078,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)],[1020]) ).
thf(551,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_733_power__decreasing) ).
thf(2743,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)],[551]) ).
thf(88,axiom,
ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( nat_1 @ t ) @ one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411__096_B_Bthesis_O_A_I_B_Btn_O_A_091_124_Atn_A_061_Anat_At_A_N_A1_059_A0_) ).
thf(1448,plain,
ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( nat_1 @ t ) @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1029,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_788_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(4102,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)],[1029]) ).
thf(354,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_eq__add__iff1) ).
thf(2187,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(32,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_70_less__special_I3_J) ).
thf(1289,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)],[32]) ).
thf(657,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_1060_zcong__eq__trans) ).
thf(3056,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)],[657]) ).
thf(567,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_867_mult__is__0) ).
thf(2792,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)],[567]) ).
thf(606,axiom,
~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_not__one__less__zero) ).
thf(2907,plain,
~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(285,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_722_times__numeral__code_I5_J) ).
thf(1998,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)],[285]) ).
thf(920,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_number__of2) ).
thf(3797,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(138,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_510_mult__nonneg__nonpos) ).
thf(1590,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)],[138]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( dvd_dvd_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_Nat__Transfer_Otransfer__int__nat__relations_I4_J) ).
thf(1646,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( dvd_dvd_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(854,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_1080_divides__cases) ).
thf(3613,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)],[854]) ).
thf(186,axiom,
! [A: int,B: nat > int,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( B @ D ) ) ) @ one_one_int ) )
=> ( ( ord_less_eq_int @ ( B @ zero_zero_nat ) @ A )
=> ( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ? [D: nat] :
( ( ord_less_eq_nat @ D @ C )
& ( ( B @ D )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_int__val__lemma) ).
thf(1721,plain,
! [A: int,B: nat > int,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( B @ D ) ) ) @ one_one_int ) )
=> ( ( ord_less_eq_int @ ( B @ zero_zero_nat ) @ A )
=> ( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ? [D: nat] :
( ( ord_less_eq_nat @ D @ C )
& ( ( B @ D )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(346,axiom,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(2167,plain,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(387,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_of__nat__less__iff) ).
thf(2283,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(589,axiom,
( one_one_nat
= ( nat_1 @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_transfer__nat__int__numerals_I2_J) ).
thf(2855,plain,
( one_one_nat
= ( nat_1 @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(476,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_add__imp__eq) ).
thf(2532,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(767,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_419_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(3369,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)],[767]) ).
thf(153,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_771_diff__add__0) ).
thf(1629,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)],[153]) ).
thf(860,axiom,
! [A: int] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_rel__simps_I45_J) ).
thf(3630,plain,
! [A: int] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(629,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_add__eq__self__zero) ).
thf(2971,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(559,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_1050_divides__rev) ).
thf(2764,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)],[559]) ).
thf(754,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3331,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(378,axiom,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( dvd_dvd_int @ A @ B )
=> ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_dvd__imp__le__int) ).
thf(2262,plain,
! [A: int,B: int] :
( ( B != zero_zero_int )
=> ( ( dvd_dvd_int @ A @ B )
=> ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(895,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_semiring__numeral__0__eq__0) ).
thf(3729,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1036,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_648_crossproduct__noteq) ).
thf(4121,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)],[1036]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_add__strict__left__mono) ).
thf(1341,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(809,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_781_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(3484,plain,
ord_less_eq_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1024,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_semiring__one__add__one__is__two) ).
thf(4089,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1156,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_semiring__numeral__1__eq__1) ).
thf(4468,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(234,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_double__eq__0__iff) ).
thf(1854,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1111,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rel__simps_I48_J) ).
thf(4338,plain,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(995,axiom,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_mult__zero__left) ).
thf(4010,plain,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(821,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rel__simps_I12_J) ).
thf(3516,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(332,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_1148_zdvd__mono) ).
thf(2130,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)],[332]) ).
thf(942,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_22_power__0__left__number__of) ).
thf(3859,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)],[942]) ).
thf(1175,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_801_less__int__code_I14_J) ).
thf(4527,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)],[1175]) ).
thf(914,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_nat__numeral__1__eq__1) ).
thf(3780,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(289,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_960_nat__number__of__mult__left) ).
thf(2009,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)],[289]) ).
thf(175,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_425_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(1689,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)],[175]) ).
thf(701,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_of__nat__less__imp__less) ).
thf(3181,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri984289939at_nat @ A ) @ ( semiri984289939at_nat @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(1097,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 @ ( plus_plus_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_add__pos__pos) ).
thf(4293,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 @ ( plus_plus_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(85,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_851_mult__le__mono2) ).
thf(1440,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)],[85]) ).
thf(181,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_423_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(1706,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)],[181]) ).
thf(6,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_diff__eq__diff__less__eq) ).
thf(1212,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(145,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_995_zdvd__not__zless) ).
thf(1607,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)],[145]) ).
thf(165,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_85_less__special_I4_J) ).
thf(1661,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)],[165]) ).
thf(610,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_1101_dvd_Oantisym) ).
thf(2917,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)],[610]) ).
thf(148,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_420_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1614,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)],[148]) ).
thf(608,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_692_less__imp__diff__less) ).
thf(2912,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)],[608]) ).
thf(1105,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_12_add__special_I2_J) ).
thf(4321,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)],[1105]) ).
thf(299,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_gr0I) ).
thf(2041,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1049,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_1078_zcong__neg__1__impl__ne__1) ).
thf(4153,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)],[1049]) ).
thf(1069,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_284_power__eq__0__iff) ).
thf(4214,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)],[1069]) ).
thf(845,axiom,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_diff__0__right) ).
thf(3585,plain,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(789,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_959_nat__mult__2__right) ).
thf(3430,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)],[789]) ).
thf(1199,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_985__0964_A_K_Am_A_L_A1_Advd_As_____A_094_A2_A_L_A1_096) ).
thf(4591,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)],[1199]) ).
thf(1099,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_4_one__power2) ).
thf(4299,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)],[1099]) ).
thf(34,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Nat_Oadd__0__right) ).
thf(1294,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(39,axiom,
! [A: int,B: nat > int,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( B @ D ) ) ) @ one_one_int ) )
=> ( ( ord_less_eq_int @ ( B @ zero_zero_nat ) @ A )
=> ( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ? [D: nat] :
( ( ord_less_eq_nat @ D @ C )
& ( ( B @ D )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_nat0__intermed__int__val) ).
thf(1308,plain,
! [A: int,B: nat > int,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( B @ D ) ) ) @ one_one_int ) )
=> ( ( ord_less_eq_int @ ( B @ zero_zero_nat ) @ A )
=> ( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ? [D: nat] :
( ( ord_less_eq_nat @ D @ C )
& ( ( B @ D )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(358,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_939_add__diff__assoc) ).
thf(2198,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)],[358]) ).
thf(876,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_143_number__of__Bit1) ).
thf(3677,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)],[876]) ).
thf(418,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_not__less0) ).
thf(2362,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(604,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_484_mult__mono) ).
thf(2902,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)],[604]) ).
thf(328,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_773_add__diff__inverse) ).
thf(2120,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)],[328]) ).
thf(1018,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_rel__simps_I19_J) ).
thf(4074,plain,
ord_less_eq_int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1151,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_add__left__imp__eq) ).
thf(4446,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(391,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2294,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(865,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_65_zadd__assoc) ).
thf(3645,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)],[865]) ).
thf(462,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_193_less__add__eq__less) ).
thf(2494,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)],[462]) ).
thf(1191,axiom,
! [A: nat] :
( ( number_number_of_nat @ ( semiri1621563631at_int @ A ) )
= ( semiri984289939at_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_number__of__int) ).
thf(4570,plain,
! [A: nat] :
( ( number_number_of_nat @ ( semiri1621563631at_int @ A ) )
= ( semiri984289939at_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(86,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_1139_zcong__zless__0) ).
thf(1442,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)],[86]) ).
thf(1000,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_diff__bin__simps_I6_J) ).
thf(4025,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(562,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_dvd_Oorder__refl) ).
thf(2779,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(291,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( times_times_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( nat_1 @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
thf(2019,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( times_times_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( nat_1 @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(109,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 @ A @ one_one_real )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_mult__right__le__one__le) ).
thf(1512,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 @ A @ one_one_real )
=> ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1134,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_add__0__left) ).
thf(4399,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(503,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_486_mult__mono_H) ).
thf(2604,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)],[503]) ).
thf(623,axiom,
ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_zero__less__two) ).
thf(2951,plain,
ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(756,axiom,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_zless__int) ).
thf(3337,plain,
! [A: nat,B: nat] :
( ( ord_less_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(18,axiom,
! [A: real,B: real] :
( ( A = B )
= ( ( minus_minus_real @ A @ B )
= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_eq__iff__diff__eq__0) ).
thf(1248,plain,
! [A: real,B: real] :
( ( A = B )
= ( ( minus_minus_real @ A @ B )
= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(880,axiom,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_int__int__eq) ).
thf(3690,plain,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(710,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_931_less__diff__iff) ).
thf(3203,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)],[710]) ).
thf(804,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_719_zadd__zmult__distrib2) ).
thf(3469,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)],[804]) ).
thf(287,axiom,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_real__squared__diff__one__factored) ).
thf(2003,plain,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(989,axiom,
! [A: nat,B: nat] :
( ( power_power_int @ ( semiri1621563631at_int @ A ) @ B )
= ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(3992,plain,
! [A: nat,B: nat] :
( ( power_power_int @ ( semiri1621563631at_int @ A ) @ B )
= ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(253,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_eq__imp__le) ).
thf(1908,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(869,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_numeral__1__eq__1) ).
thf(3658,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(615,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_206_zero__less__power__nat__eq__number__of) ).
thf(2930,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)],[615]) ).
thf(329,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_1070_zcong__zprime__prod__zero) ).
thf(2123,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)],[329]) ).
thf(422,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_527_mult__le__0__iff) ).
thf(2374,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)],[422]) ).
thf(54,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_1092_dvd_Oless__imp__not__eq2) ).
thf(1348,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)],[54]) ).
thf(171,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_diff__add__inverse) ).
thf(1678,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(916,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_806_int__one__le__iff__zero__less) ).
thf(3785,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)],[916]) ).
thf(739,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_int @ ( semiri1621563631at_int @ B ) @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_zdiff__int) ).
thf(3291,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_int @ ( semiri1621563631at_int @ B ) @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(958,axiom,
! [A: int > $o] :
( ( ! [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A @ B ) ) )
= ( ! [B: nat] : ( A @ ( semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_transfer__int__nat__quantifiers_I1_J) ).
thf(3907,plain,
! [A: int > $o] :
( ( ! [B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A @ B ) ) )
= ( ! [B: nat] : ( A @ ( semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1083,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
thf(4254,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(497,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_1023_zpower__zdvd__prop1) ).
thf(2587,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)],[497]) ).
thf(949,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_139_not__sum__power2__lt__zero) ).
thf(3882,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)],[949]) ).
thf(70,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_347_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1395,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)],[70]) ).
thf(472,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_920_mult__less__cancel1) ).
thf(2522,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)],[472]) ).
thf(672,axiom,
! [A: int,B: nat] :
( ( dvd_dvd_nat @ ( nat_1 @ A ) @ B )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( dvd_dvd_int @ A @ ( semiri1621563631at_int @ B ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( B = zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_nat__dvd__iff) ).
thf(3100,plain,
! [A: int,B: nat] :
( ( dvd_dvd_nat @ ( nat_1 @ A ) @ B )
= ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( dvd_dvd_int @ A @ ( semiri1621563631at_int @ B ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(575,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_634_combine__common__factor) ).
thf(2815,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)],[575]) ).
thf(280,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_779_pos__zmult__pos) ).
thf(1986,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)],[280]) ).
thf(1118,axiom,
! [A: int] :
( ( min
= ( bit1 @ A ) )
= ( min = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_rel__simps_I43_J) ).
thf(4357,plain,
! [A: int] :
( ( min
= ( bit1 @ A ) )
= ( min = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(814,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_409_zadd__power2) ).
thf(3496,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)],[814]) ).
thf(984,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_824_cube__square) ).
thf(3982,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)],[984]) ).
thf(554,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( C
= ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_eq__add__iff2) ).
thf(2751,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( C
= ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(106,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_618_divisors__zero) ).
thf(1495,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)],[106]) ).
thf(163,axiom,
ord_less_eq_int @ min @ min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_rel__simps_I24_J) ).
thf(1657,plain,
ord_less_eq_int @ min @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(700,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_add__right__imp__eq) ).
thf(3177,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(946,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_842__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_) ).
thf(3875,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)],[946]) ).
thf(994,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_136_power2__less__0) ).
thf(4007,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)],[994]) ).
thf(939,axiom,
! [A: int] :
( ( abs_abs_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ ( abs_abs_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_abs__power3__distrib) ).
thf(3850,plain,
! [A: int] :
( ( abs_abs_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ ( abs_abs_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(210,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 @ ( plus_plus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_add__pos__pos) ).
thf(1789,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 @ ( plus_plus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(627,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_161_power__0__left) ).
thf(2961,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)],[627]) ).
thf(568,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_697_power__mult__distrib) ).
thf(2795,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)],[568]) ).
thf(652,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_number__of__Pls) ).
thf(3045,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1104,axiom,
! [A: nat] :
( ( nat_1 @ ( semiri1621563631at_int @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_nat__int) ).
thf(4318,plain,
! [A: nat] :
( ( nat_1 @ ( semiri1621563631at_int @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(1058,axiom,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(4178,plain,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(753,axiom,
! [A: int > $o,B: nat,C: nat] :
( ( A @ ( semiri1621563631at_int @ ( minus_minus_nat @ B @ C ) ) )
= ( ( ( ord_less_eq_nat @ C @ B )
=> ( A @ ( minus_minus_int @ ( semiri1621563631at_int @ B ) @ ( semiri1621563631at_int @ C ) ) ) )
& ( ( ord_less_nat @ B @ C )
=> ( A @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_zdiff__int__split) ).
thf(3328,plain,
! [A: int > $o,B: nat,C: nat] :
( ( A @ ( semiri1621563631at_int @ ( minus_minus_nat @ B @ C ) ) )
= ( ( ( ord_less_eq_nat @ C @ B )
=> ( A @ ( minus_minus_int @ ( semiri1621563631at_int @ B ) @ ( semiri1621563631at_int @ C ) ) ) )
& ( ( ord_less_nat @ B @ C )
=> ( A @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(359,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_diff__add__inverse2) ).
thf(2201,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1189,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_semiring__norm_I113_J) ).
thf(4565,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1094,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_140_not__sum__power2__lt__zero) ).
thf(4286,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)],[1094]) ).
thf(735,axiom,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_power__one) ).
thf(3277,plain,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(48,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_mult__left__less__imp__less) ).
thf(1335,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1022,axiom,
! [A: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_int__le__0__conv) ).
thf(4083,plain,
! [A: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(309,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_1049_dvd__diffD1) ).
thf(2070,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)],[309]) ).
thf(889,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_737_power__increasing__iff) ).
thf(3716,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)],[889]) ).
thf(807,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_713_rel__simps_I31_J) ).
thf(3479,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)],[807]) ).
thf(75,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_1066_Int2_Ozcong__zero) ).
thf(1410,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)],[75]) ).
thf(436,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ ( nat_1 @ A ) @ ( nat_1 @ B ) )
= ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_nat__mono__iff) ).
thf(2417,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ ( nat_1 @ A ) @ ( nat_1 @ B ) )
= ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(317,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_884_add__leD1) ).
thf(2091,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)],[317]) ).
thf(751,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_mult__right__less__imp__less) ).
thf(3323,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(542,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_478_split__mult__neg__le) ).
thf(2714,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)],[542]) ).
thf(247,axiom,
! [A: nat,B: nat] :
( ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_of__nat__less__iff) ).
thf(1891,plain,
! [A: nat,B: nat] :
( ( ord_less_real @ ( semiri132038758t_real @ A ) @ ( semiri132038758t_real @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(509,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_1054_divides__exp) ).
thf(2619,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)],[509]) ).
thf(787,axiom,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__Pls) ).
thf(3424,plain,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(53,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_192_add__less__mono) ).
thf(1346,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)],[53]) ).
thf(307,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_323_add__left__imp__eq) ).
thf(2063,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)],[307]) ).
thf(14,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_601_add__diff__add) ).
thf(1236,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)],[14]) ).
thf(1079,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_828_self__quotient__aux2) ).
thf(4242,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)],[1079]) ).
thf(64,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_rel__simps_I8_J) ).
thf(1378,plain,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1167,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_966_diff__square) ).
thf(4506,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)],[1167]) ).
thf(467,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_646_crossproduct__noteq) ).
thf(2507,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)],[467]) ).
thf(1076,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_825_power2__ge__self) ).
thf(4229,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)],[1076]) ).
thf(259,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_real__mult__1) ).
thf(1925,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(183,axiom,
! [A: int,B: nat] :
( ( dvd_dvd_int @ A @ ( semiri1621563631at_int @ B ) )
= ( dvd_dvd_nat @ ( nat_1 @ ( abs_abs_int @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_dvd__int__iff) ).
thf(1713,plain,
! [A: int,B: nat] :
( ( dvd_dvd_int @ A @ ( semiri1621563631at_int @ B ) )
= ( dvd_dvd_nat @ ( nat_1 @ ( abs_abs_int @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(381,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_real__le__refl) ).
thf(2270,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1120,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_915_Euler_Oaux1) ).
thf(4363,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)],[1120]) ).
thf(343,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_eq_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_add__le__imp__le__left) ).
thf(2159,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_eq_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(55,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_878_nat__less__le) ).
thf(1352,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)],[55]) ).
thf(682,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_928_diff__is__0__eq_H) ).
thf(3128,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)],[682]) ).
thf(225,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_404_realpow__pos__nth) ).
thf(1829,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)],[225]) ).
thf(441,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_190_trans__less__add2) ).
thf(2430,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)],[441]) ).
thf(26,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_rel__simps_I11_J) ).
thf(1268,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(502,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_1072_divides__div__not) ).
thf(2600,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)],[502]) ).
thf(118,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_1040_divides__mul__r) ).
thf(1537,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)],[118]) ).
thf(66,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_450_zle__linear) ).
thf(1384,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)],[66]) ).
thf(852,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_976__096_B_Bthesis_O_A_I_B_Bt_O_As_____A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_) ).
thf(3605,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)],[852]) ).
thf(135,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_1046_divides__ge) ).
thf(1582,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)],[135]) ).
thf(379,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_903_Nat_Odiff__diff__eq) ).
thf(2265,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)],[379]) ).
thf(1035,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_912_diff__bin__simps_I10_J) ).
thf(4118,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)],[1035]) ).
thf(944,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_63_even__less__0__iff) ).
thf(3869,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)],[944]) ).
thf(276,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_635_combine__common__factor) ).
thf(1976,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)],[276]) ).
thf(123,axiom,
( ( nat_1 @ zero_zero_int )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_nat__0) ).
thf(1550,plain,
( ( nat_1 @ zero_zero_int )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(930,axiom,
! [A: real] :
( ( ord_less_real @ ( abs_abs_real @ A ) @ one_one_real )
=> ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_less__one__imp__sqr__less__one) ).
thf(3817,plain,
! [A: real] :
( ( ord_less_real @ ( abs_abs_real @ A ) @ one_one_real )
=> ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(978,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_int__0__neq__1) ).
thf(3965,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(724,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_943_diff__add__assoc) ).
thf(3245,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)],[724]) ).
thf(1138,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pls__def) ).
thf(4410,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(141,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_mult__strict__mono) ).
thf(1597,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(532,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_59_number__of__reorient) ).
thf(2687,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)],[532]) ).
thf(998,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_add__less__cancel__right) ).
thf(4019,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(36,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_853_le__antisym) ).
thf(1299,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)],[36]) ).
thf(1017,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_958_nat__mult__2) ).
thf(4071,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)],[1017]) ).
thf(251,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_mult__0) ).
thf(1902,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(537,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_627_diffs0__imp__equal) ).
thf(2699,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)],[537]) ).
thf(928,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_1152_number__of1) ).
thf(3812,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)],[928]) ).
thf(813,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_994_zprime__zdvd__power) ).
thf(3494,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)],[813]) ).
thf(527,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_890_nat__add__left__cancel__le) ).
thf(2672,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)],[527]) ).
thf(60,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_485_mult__mono_H) ).
thf(1367,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)],[60]) ).
thf(232,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_add__0__iff) ).
thf(1848,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(77,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_997_zdvd__antisym__nonneg) ).
thf(1416,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)],[77]) ).
thf(1143,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_752_le__special_I2_J) ).
thf(4423,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)],[1143]) ).
thf(834,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 ) ) ) ) )
= ( ( abs_abs_int @ A )
= ( abs_abs_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_power2__eq__iff__abs__eq) ).
thf(3553,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 ) ) ) ) )
= ( ( abs_abs_int @ A )
= ( abs_abs_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(653,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_mult__less__imp__less__right) ).
thf(3047,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1056,axiom,
! [A: nat,B: int] :
( ( ( semiri1621563631at_int @ A )
= ( number_number_of_int @ B ) )
= ( ( A
= ( nat_1 @ ( number_number_of_int @ B ) ) )
& ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_int__eq__iff__number__of) ).
thf(4174,plain,
! [A: nat,B: int] :
( ( ( semiri1621563631at_int @ A )
= ( number_number_of_int @ B ) )
= ( ( A
= ( nat_1 @ ( number_number_of_int @ B ) ) )
& ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(254,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_917_mult__less__mono2) ).
thf(1912,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)],[254]) ).
thf(1184,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
thf(4552,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1177,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_325_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(4533,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)],[1177]) ).
thf(956,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( power_power_nat @ ( nat_1 @ B ) @ A )
= ( nat_1 @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
thf(3901,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( power_power_nat @ ( nat_1 @ B ) @ A )
= ( nat_1 @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(825,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_1035_s) ).
thf(3526,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)],[825]) ).
thf(976,axiom,
! [A: int,B: nat] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ B ) )
= ( ( A != zero_zero_int )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_zero__less__zpower__abs__iff) ).
thf(3960,plain,
! [A: int,B: nat] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ B ) )
= ( ( A != zero_zero_int )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(555,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_431_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(2754,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)],[555]) ).
thf(1110,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_578_sum__squares__le__zero__iff) ).
thf(4335,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)],[1110]) ).
thf(843,axiom,
( ( semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_int__1) ).
thf(3580,plain,
( ( semiri1621563631at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(42,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_889_trans__le__add1) ).
thf(1320,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)],[42]) ).
thf(1196,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_163_power__strict__decreasing) ).
thf(4584,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)],[1196]) ).
thf(271,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_1135_xzgcda__linear__aux1) ).
thf(1962,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)],[271]) ).
thf(487,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
thf(2563,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(963,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_714_less__eq__int__code_I13_J) ).
thf(3924,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)],[963]) ).
thf(598,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_nat__less__eq__zless) ).
thf(2881,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) )
= ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(266,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_rel__simps_I25_J) ).
thf(1945,plain,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(713,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( abs_abs_int @ A )
= ( abs_abs_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_zdvd__antisym__abs) ).
thf(3212,plain,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( abs_abs_int @ A )
= ( abs_abs_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1185,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_614_mult__eq__0__iff) ).
thf(4555,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)],[1185]) ).
thf(191,axiom,
! [A: nat,B: int] :
( ( ord_less_nat @ A @ ( nat_1 @ B ) )
= ( ord_less_int @ ( semiri1621563631at_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_zless__nat__eq__int__zless) ).
thf(1737,plain,
! [A: nat,B: int] :
( ( ord_less_nat @ A @ ( nat_1 @ B ) )
= ( ord_less_int @ ( semiri1621563631at_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(172,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_945_diff__add__assoc2) ).
thf(1681,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)],[172]) ).
thf(600,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_mult__1__left) ).
thf(2887,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(780,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_zcong__zero__equiv__div) ).
thf(3405,plain,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(533,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( nat_1 @ ( times_times_int @ B @ A ) )
= ( times_times_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_nat__mult__distrib) ).
thf(2690,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( nat_1 @ ( times_times_int @ B @ A ) )
= ( times_times_nat @ ( nat_1 @ B ) @ ( nat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(94,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_437_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1463,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)],[94]) ).
thf(593,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_317_add__right__imp__eq) ).
thf(2866,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)],[593]) ).
thf(581,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_1186_nat__mult__eq__cancel1) ).
thf(2832,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)],[581]) ).
thf(444,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_453_zle__antisym) ).
thf(2438,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)],[444]) ).
thf(104,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_631_comm__semiring__class_Odistrib) ).
thf(1490,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)],[104]) ).
thf(392,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_424_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(2297,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)],[392]) ).
thf(1102,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_962_four__x__squared) ).
thf(4313,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)],[1102]) ).
thf(449,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_1112_dvd_Ole__less) ).
thf(2453,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)],[449]) ).
thf(655,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_1123_zcong__trans) ).
thf(3052,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)],[655]) ).
thf(862,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_729_le__special_I1_J) ).
thf(3637,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)],[862]) ).
thf(748,axiom,
! [A: nat,B: nat] :
( ( semiri132038758t_real @ ( power_power_nat @ A @ B ) )
= ( power_power_real @ ( semiri132038758t_real @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_of__nat__power) ).
thf(3316,plain,
! [A: nat,B: nat] :
( ( semiri132038758t_real @ ( power_power_nat @ A @ B ) )
= ( power_power_real @ ( semiri132038758t_real @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(347,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_zcong__sym) ).
thf(2170,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(414,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_694_power__commutes) ).
thf(2351,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)],[414]) ).
thf(635,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_less__add__iff2) ).
thf(2993,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(709,axiom,
! [A: int] :
~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_not__square__less__zero) ).
thf(3200,plain,
! [A: int] :
~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(89,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_888_trans__le__add2) ).
thf(1449,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)],[89]) ).
thf(218,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_1150_inv__not__p__minus__1__aux) ).
thf(1812,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)],[218]) ).
thf(4678,plain,
$false,
inference(cvc4,[status(thm)],[1322,4188,3944,1369,3399,4022,3979,1840,1982,3927,2331,1818,4560,1337,1718,2612,4094,1469,2306,4450,2341,2336,2109,1454,2072,1767,3798,1559,1315,2787,2595,1686,4166,2250,3185,3990,2210,1406,4075,2381,2395,3285,3098,3910,1728,2114,1692,1305,4487,3382,3680,1200,2077,4311,1522,2644,4515,2776,2659,3377,2527,3153,3460,1422,2947,1939,1971,1793,3402,3794,1655,3120,2740,1735,2316,2141,1872,4440,1761,3562,3313,3577,2146,3895,2575,3848,2195,3017,4543,3217,3530,3049,4418,1756,4575,3004,2035,3648,4110,4220,2184,2448,2933,3616,1233,1327,3693,2476,1260,1919,1988,4047,1835,3634,3502,3513,4030,2173,2516,3880,2405,1746,3103,3836,2216,3236,3350,3545,2723,3766,2432,1914,4496,1576,4371,4266,3308,1935,4124,1386,3466,4198,3898,2082,2400,2067,3878,2136,1623,1482,3597,1254,1709,3029,2735,3131,2667,2339,4415,3776,3744,3353,2466,3043,3891,2654,3248,4539,3263,4546,3976,2328,2708,3821,1330,1860,1264,1511,2274,3485,3125,1826,4130,3542,4349,1279,4275,3410,3280,3749,3845,3089,2745,3713,1922,3998,2857,1704,2767,1641,1362,3866,3268,1545,2420,3463,3374,3385,2403,1514,2049,2552,1479,1609,1398,3084,1931,1568,3734,3014,4141,4383,2301,1815,3602,1875,1778,2852,3231,2829,3788,2178,4396,3393,2996,3163,3453,3357,3569,4115,1283,4432,2456,4205,2237,1302,1664,4329,2027,4443,3075,4578,2105,2893,1632,2469,2259,4001,3527,3702,3438,4147,4050,2925,3973,1960,2555,3300,3771,4162,3986,4055,2281,1215,2103,3226,4211,2884,2762,2367,1928,2190,3421,1886,4504,3808,1796,3361,4536,3955,3243,2809,2286,4038,2639,2804,4519,3588,1242,3559,4483,3510,4065,1564,1604,3450,3591,2204,2164,2118,2093,1783,2621,2061,3418,1730,1863,3435,3582,3229,3011,1206,4589,4407,2473,1438,3720,3169,4480,3265,3995,2047,2232,3054,2441,2589,2705,1900,2428,2541,1519,1355,4434,2133,1751,3610,2606,1824,2032,3778,4044,1343,4016,2969,4344,4091,3752,3069,3134,4493,2890,2414,2958,1968,1457,2609,2213,2345,1392,4316,4063,3271,3166,2445,4295,2464,4280,1837,1602,1365,2670,1555,4155,3297,3137,3499,3556,2872,4385,1951,3894,1819,4327,4402,2181,3763,2492,4104,3727,1281,3033,3408,1740,3731,3968,3782,1983,4248,2841,2577,1227,4429,1498,3963,4227,3078,3916,2268,3001,3467,3699,1592,2300,3482,3254,3413,1851,1772,3122,2990,2377,2801,1534,4512,2359,1375,4525,1425,1672,3704,1878,2726,2631,3060,3087,4263,4291,4301,3143,1942,2561,4389,3441,2080,1937,1791,2038,2649,3294,1493,2798,3141,3952,3311,2877,1292,3622,2240,1842,3194,2349,3671,2085,1889,1644,2781,4530,3935,1419,2504,2519,1539,2598,1974,3628,3760,4152,4086,2450,2125,1588,2536,1297,2681,3541,1451,2304,1266,4068,2153,2900,1552,2243,3819,3390,2006,2497,2566,1799,3937,4231,4347,2052,1599,3109,1979,3920,2272,4223,1759,2370,3215,1525,3147,1333,3802,4352,3183,1695,3856,2057,2748,1466,2617,2662,2529,1857,4184,1991,1318,2702,2546,4567,4081,1286,3321,2408,3190,4004,1996,2909,3807,2235,3707,3491,4562,3274,4269,3696,3396,2936,2729,3660,2001,1251,1764,4470,1754,2292,4380,2391,2904,1698,4354,2253,2149,3257,2717,4412,2570,1548,3985,3738,3839,3523,3343,3158,3187,4341,3319,1916,3234,2393,4032,4465,2806,1701,1965,4041,3372,3741,1833,2225,3504,1884,4283,1389,3811,3240,2789,3519,2525,2849,1620,3472,2489,1652,3081,2016,2568,1403,3458,2695,1488,2827,3599,4485,4127,4112,4099,4060,3619,1897,2425,1675,3532,1428,2161,4251,4558,2193,1786,4186,4096,3726,1271,2308,4171,3663,4218,1635,1733,4573,1239,3340,3594,3302,3568,1638,3355,4245,1224,2319,2573,3719,2510,2311,1209,1574,2257,2955,4139,3197,4388,2538,1408,3251,4369,2151,2642,3815,3238,2624,1894,2987,3551,2422,3957,3683,3106,1542,4586,2116,3710,2945,4374,3066,1571,4509,4477,4107,2182,4541,1557,1993,4028,1821,3932,4181,2664,3150,3893,3456,1667,2824,4203,1471,3747,2025,2812,1339,4420,2314,2343,3668,4462,2111,4277,2757,4332,3192,2923,1325,1460,2289,2647,2928,1381,2461,2974,2075,2365,1474,1594,2835,3674,2207,2693,2550,1245,1445,1528,2139,3687,3806,2244,1435,1775,2592,2022,3363,1477,3325,2999,2156,2984,1805,3380,1562,1413,3444,1203,4260,2652,4052,3146,2684,1626,3009,2054,4426,4207,1948,4405,2914,3031,1809,2952,4394,4136,2614,2096,3427,4013,3936,2107,2784,4456,3206,3161,1905,2503,1684,4177,2629,2333,2846,4581,1958,4168,2582,3571,2942,1770,4035,3913,3949,2678,1230,3988,2513,1845,3640,2863,3507,4360,2397,3842,4490,3112,2977,1611,4272,1743,4366,2143,3904,3260,3754,2732,4200,4517,2175,1780,2821,3209,2720,3872,4377,1531,4324,3019,4437,4522,3642,4240,3722,4549,1869,3774,2486,1579,3769,1716,3940,3305,1432,3885,3114,3334,3791,3063,2920,3475,3026,3655,1262,4145,3823,2276,3801,2219,2128,1658,2322,3359,3174,2044,1218,3041,3095,3853,4164,2354,2948,4133,1802,2379,2543,1221,2579,1749,3388,1585,1670,2939,3071,1372,1881,2675,1358,2247,2411,3488,2500,4057,3652,1257,2838,2558,3970,3415,2279,2357,2843,1485,2711,3117,2860,2030,4225,3520,3366,3007,4150,2584,4257,4392,3288,4217,1617,2875,3139,2458,3092,2818,2696,2870,3171,3447,3548,2347,1517,2325,1866,3665,2435,2760,3433,3946,4289,2626,4138,1649,3757,2479,3565,2088,3625,4078,2743,1448,4102,2187,1289,3056,2792,2907,1998,3797,1590,1646,3613,1721,2167,2283,2855,2532,3369,1629,3630,2971,2764,3331,2262,3729,4121,1341,3484,4089,4468,1854,4338,4010,3516,2130,3859,4527,3780,2009,1689,3181,4293,1440,1706,1212,1607,1661,2917,1614,2912,4321,2041,4153,4214,3585,3430,4591,4299,1294,1308,2198,3677,2362,2902,2120,4074,4446,2294,3645,2494,4570,1442,4025,2779,2019,1512,4399,2604,2951,3337,1248,3690,3203,3469,2003,3992,1908,3658,2930,2123,2374,1348,1678,3785,3291,3907,4254,2587,3882,1395,2522,3100,2815,1986,4357,3496,3982,2751,1495,1657,3177,3875,4007,3850,1789,2961,2795,3045,4318,4178,3328,2201,4565,4286,3277,1335,4083,2070,3716,3479,1410,2417,2091,3323,2714,1891,2619,3424,1346,2063,1236,4242,1378,4506,2507,4229,1925,1713,2270,4363,2159,1352,3128,1829,2430,1268,2600,1537,1384,3605,1582,2265,4118,3869,1976,1550,3817,3965,3245,4410,1597,2687,4019,1299,4071,1902,2699,3812,3494,2672,1367,1848,1416,4423,3553,3047,4174,1912,4552,4533,3901,3526,3960,2754,4335,3580,1320,4584,1962,2563,3924,2881,1945,3212,4555,1737,1681,2887,3405,2690,1463,2866,2832,2438,1490,2297,4313,2453,3052,3637,3316,2170,2351,2993,3200,1449,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.12 % Command : run_Leo-III %s %d
% 0.10/0.32 % Computer : n032.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon May 6 12:28:09 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.75/0.73 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.79/1.03 % [INFO] Parsing done (295ms).
% 1.79/1.04 % [INFO] Running in sequential loop mode.
% 2.57/1.25 % [INFO] eprover registered as external prover.
% 2.57/1.25 % [INFO] cvc4 registered as external prover.
% 2.57/1.26 % [INFO] Scanning for conjecture ...
% 2.86/1.37 % [INFO] Found a conjecture and 1204 axioms. Running axiom selection ...
% 3.75/1.54 % [INFO] Axiom selection finished. Selected 1197 axioms (removed 7 axioms).
% 4.78/1.83 % [INFO] Problem is higher-order (TPTP THF).
% 4.78/1.86 % [INFO] Type checking passed.
% 4.78/1.86 % [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 ...
% 19.48/5.16 % External prover 'cvc4' found a proof!
% 19.48/5.16 % [INFO] Killing All external provers ...
% 19.48/5.16 % Time passed: 4714ms (effective reasoning time: 4122ms)
% 19.48/5.16 % 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)>
% 19.48/5.17 % Axioms used in derivation (1197): fact_664_mult__1, fact_259_pos__add__strict, fact_726_transfer__nat__int__relations_I2_J, fact_458_arith__simps_I32_J, fact_367_double__zero__sym, fact_280_power__less__imp__less__exp, fact_443_diff__eq__diff__less__eq, fact_97_Bit0__Pls, fact_719_zadd__zmult__distrib2, fact_424_ab__semigroup__mult__class_Omult__ac_I1_J, fact_716_zmult__1, fact_987__096s_____A_094_A2_A_N_A_N1_A_061_As_____A_094_A2_A_L_A1_096, fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_1073_dvd__mult__cancel1, fact_728_le__special_I1_J, fact_761_nat__0, fact_1135_xzgcda__linear__aux1, fact_2_sum__power2__eq__zero__iff, fact_261_not__one__less__zero, fact_3_sum__power2__eq__zero__iff, fact_600_diff__eq__diff__less, fact_957_power__eq__if, fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_1032_zprime__power__zdvd__cancel__left, fact_570_mult__strict__mono, fact_1164_abs__power3__distrib, fact_850_mult__le__mono1, fact_288_of__nat__less__0__iff, fact_241_less__imp__of__nat__less, fact_378_add__less__imp__less__left, fact_872_real__mult__left__cancel, fact_159_one__less__power, fact_771_diff__add__0, fact_918_mult__less__mono1, fact_774_rel__simps_I22_J, fact_844_le__square, fact_474_of__nat__le__iff, fact_469_of__nat__mult, fact_214_plus__nat_Oadd__0, fact_21_quartic__square__square, fact_789_zle__iff__zadd, fact_910_zpower__zpower, fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_967_zdiff__power3, fact_355_add__0__iff, fact_891_le__iff__add, fact_735_power__increasing__iff, fact_369_add__0, fact_526_mult__diff__mult, fact_1189_nat__mult__le__cancel1, fact_48_rel__simps_I2_J, fact_411__096_B_Bthesis_O_A_I_B_Btn_O_A_091_124_Atn_A_061_Anat_At_A_N_A1_059_A0_, fact_1013_rel__simps_I42_J, fact_29_n0, fact_305_double__add__less__zero__iff__single__add__less__zero, fact_270_less__add__one, fact_919_mult__less__cancel2, fact_1070_zcong__zprime__prod__zero, fact_465_left__diff__distrib__number__of, fact_777_rel__simps_I21_J, fact_24_power__0__left__number__of, fact_883_add__leE, fact_236_of__nat__less__iff, fact_543_mult__left__le__imp__le, fact_554_mult__less__imp__less__right, fact_1181_nat__less__add__iff1, fact_1089_dvd_Oless__le__trans, fact_1129_zcong__scalar, fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_110_number__of__Pls, fact_730_le__special_I3_J, fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_674_add__le__imp__le__right, fact_693_diff__less__mono2, fact_1190_nat__le__add__iff1, fact_63_even__less__0__iff, fact_703_diff__add__inverse2, fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_753_le__special_I4_J, fact_619_divisors__zero, fact_1022_zdvd__imp__le, fact_636_combine__common__factor, fact_1112_dvd_Ole__less, fact_948_is__mult__sum2sq, fact_103_Bit0__def, fact_385_add__strict__mono, fact_738_power__le__imp__le__exp, fact_744_nat__add__distrib, fact_737_power__increasing__iff, fact_512_transfer__nat__int__relations_I1_J, fact_41_nat__number__of__Pls, fact_932_Nat__Transfer_Otransfer__int__nat__functions_I2_J, fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_1176_abs__add__one__not__less__self, fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_733_power__decreasing, fact_915_Euler_Oaux1, fact_1137_zcong__def, fact_116_add__numeral__0__right, fact_884_add__leD1, fact_4_one__power2, fact_696_power__commutes, fact_65_zadd__assoc, fact_773_add__diff__inverse, fact_410_tn, fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_187_less__not__refl2, fact_204_zero__less__power__nat__eq, fact_1148_zdvd__mono, fact_1060_zcong__eq__trans, fact_32_plus__numeral__code_I9_J, fact_1115_divides__antisym, fact_61_rel__simps_I51_J, fact_210_linorder__neqE__linordered__idom, fact_749_convex__bound__lt, fact_461_mult__number__of__left, fact_811_zle__add1__eq__le, fact_791_nat__mono__iff, fact_821_add__Bit1__Bit1, fact_190_trans__less__add2, fact_865_mult__0, fact_1105_dvd_Ole__neq__trans, fact_889_trans__le__add1, fact_635_combine__common__factor, fact_464_right__diff__distrib__number__of, fact_740_power__le__imp__le__exp, fact_407_nat__1__add__number__of, fact_527_mult__le__0__iff, fact_708_mult__Pls, fact_467_number__of__diff, fact_338_ab__semigroup__add__class_Oadd__ac_I1_J, fact_129_odd__nonzero, fact_1167_int__dvd__iff, fact_423_ab__semigroup__mult__class_Omult__ac_I1_J, fact_466_left__diff__distrib__number__of, fact_30_zless__linear, fact_562_mult__less__le__imp__less, fact_725_convex__bound__le, fact_923_real__mult__less__mono2, fact_1054_divides__exp, fact_1075_transfer__nat__int__relations_I4_J, fact_293_of__nat__0, fact_36_zpower__int, fact_584_nat__0__iff, fact_383_add__less__imp__less__right, fact_927_diff__is__0__eq, fact_272_power__inject__exp, fact_1042_dvd__diff__nat, fact_576_sum__squares__ge__zero, fact_599_diff__eq__diff__less, fact_15_add__special_I3_J, fact_710_rel__simps_I34_J, fact_511_mult__nonneg__nonpos, fact_181_nat__add__assoc, fact_111_semiring__norm_I112_J, fact_283_power__strict__increasing, fact_370_add__0, fact_591_right__minus__eq, fact_704_diff__add__inverse, fact_169_int__gr__induct, fact_132_number__of__int, fact_522_le__add__iff2, fact_1007_bin__less__0__simps_I2_J, fact_606_diff__add__cancel, fact_79_bin__less__0__simps_I1_J, fact_440_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_279_power__less__imp__less__exp, fact_453_zle__antisym, fact_489_mult__left__mono__neg, fact_145_semiring__numeral__1__eq__1, fact_157_one__less__power, fact_676_add__le__imp__le__right, fact_140_not__sum__power2__lt__zero, fact_83_int__less__0__conv, fact_1125_zcong__sym, fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_39_zadd__int, fact_386_add__strict__mono, fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_447_semiring__mult__number__of, fact_78_bin__less__0__simps_I4_J, fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_1046_divides__ge, fact_227_one__neq__zero, fact_902_le__diff__iff, fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_1134_zcong__not, fact_724_convex__bound__le, fact_277_power__strict__increasing__iff, fact_804_mult__Bit1, fact_1180_incr__mult__lemma, fact_683_add__right__mono, fact_368_double__zero__sym, fact_698_power__mult__distrib, fact_176_not__add__less2, fact_590_nat__0__le, fact_40_int__1, fact_1131_zcong__zmult, fact_608_mult__zero__left, fact_318_add__right__imp__eq, fact_324_add__left__imp__eq, fact_908_Nat_Odiff__le__self, fact_22_power__0__left__number__of, fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_930_diff__less__mono, fact_594_eq__iff__diff__eq__0, fact_396_add__less__cancel__right, fact_251_of__nat__power, fact_1004_rel__simps_I8_J, fact_471_of__nat__mult, fact_353_one__reorient, fact_477_split__mult__neg__le, fact_1019_rel__simps_I47_J, fact_952_nat__diff__distrib, fact_578_sum__squares__le__zero__iff, fact_1008_rel__simps_I23_J, fact_392_add__strict__right__mono, fact_1122_zcong__square__zless, fact_339_ab__semigroup__add__class_Oadd__ac_I1_J, fact_895_nat__mult__eq__1__iff, fact_766_nat__number__of, fact_265_zero__less__one, fact_308_add__pos__pos, fact_100_add__Pls__right, fact_586_power__increasing, fact_384_add__strict__mono, fact_1171_power2__eq1__iff, fact_1132_zcong__zadd, fact_1027_diff__bin__simps_I6_J, fact_292_power__0, fact_1068_dvd__imp__le, fact_854_mult__le__mono, fact_748_convex__bound__lt, fact_653_mult_Ocomm__neutral, fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_1067_zcong__zmult__prop3, fact_14_add__special_I3_J, fact_1010_rel__simps_I28_J, fact_88_odd__less__0, fact_52_add__nat__number__of, fact_945_diff__add__assoc2, fact_647_crossproduct__noteq, fact_866_mult__0__right, fact_798_rel__simps_I5_J, fact_601_add__diff__add, fact_281_power__strict__increasing, fact_475_diff__commute, fact_6_one__power2, fact_720_zadd__zmult__distrib, fact_317_add__right__imp__eq, fact_993_zdvd__bounds, fact_964_Euler_Oaux2, fact_54_nat__numeral__1__eq__1, fact_1048_dvd__diffD, fact_20_semiring__one__add__one__is__two, fact_371_add__0, fact_459_arith__simps_I32_J, fact_1037_s1, fact_763_not__square__less__zero, fact_514_mult__nonneg__nonneg, fact_463_right__diff__distrib__number__of, fact_158_one__less__power, fact_71_less__special_I1_J, fact_551_mult__left__less__imp__less, fact_890_nat__add__left__cancel__le, fact_652_nat__int, fact_912_diff__bin__simps_I10_J, fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_11_zero__eq__power2, fact_965_zspecial__product, fact_289_of__nat__less__0__iff, fact_558_mult__right__less__imp__less, fact_802_rel__simps_I33_J, fact_315_zero__reorient, fact_460_mult__number__of__left, fact_904_eq__diff__iff, fact_365_add__0__right, fact_220_of__nat__eq__iff, fact_480_split__mult__pos__le, fact_618_divisors__zero, fact_587_power__increasing, fact_707_diff__cancel2, fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_625_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_978_real__mult__commute, fact_1117_one__not__neg__one__mod__m, fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A, fact_25_semiring__norm_I110_J, fact_337_ab__semigroup__add__class_Oadd__ac_I1_J, fact_202_neq0__conv, fact_213_Nat_Oadd__0__right, fact_237_of__nat__less__iff, fact_358_add_Ocomm__neutral, fact_1175_decr__mult__lemma, fact_501_mult__nonpos__nonpos, fact_868_mult__cancel1, fact_195_nat__less__cases, fact_1099_dvd_Oord__eq__less__trans, fact_583_nat__le__0, fact_871_le__0__eq, fact_409_zadd__power2, fact_174_less__not__refl, fact_1002_rel__simps_I6_J, fact_772_less__diff__conv, fact_382_add__less__imp__less__right, fact_655_mult_Ocomm__neutral, fact_954_Nat__Transfer_Otransfer__nat__int__functions_I2_J, fact_72_less__special_I1_J, fact_1090_dvd_Oord__less__eq__trans, fact_596_diff__self, fact_1123_zcong__trans, fact_1107_dvd_Oantisym__conv, fact_553_mult__less__imp__less__right, fact_936_le__diff__conv, fact_125_number__of__add, fact_1009_rel__simps_I20_J, fact_106_semiring__numeral__0__eq__0, fact_510_mult__nonneg__nonpos, fact_762_not__square__less__zero, fact_112_semiring__norm_I112_J, fact_99_int__0__neq__1, fact_376_add__0__left, fact_531_all__nat, fact_491_mult__right__mono__neg, fact_1086_dvd_Oless__asym, fact_319_add__imp__eq, fact_1138_norR__mem__unique__aux, fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_1161_zero__le__zpower__abs, fact_831_q__pos__lemma, fact_982_real__le__antisym, fact_405_tpos, fact_1155_dvd__imp__le__int, fact_490_mult__right__mono__neg, fact_787_zero__zle__int, fact_185_linorder__neqE__nat, fact_605_diff__add__cancel, fact_1047_nat__mult__dvd__cancel__disj_H, fact_581_mult__left__le__one__le, fact_328_add__right__cancel, fact_815_zero__less__nat__eq, fact_686_add__le__cancel__left, fact_793_zless__nat__eq__int__zless, fact_419_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_200_nat__zero__less__power__iff, fact_1030_pos__zmult__eq__1__iff__lemma, fact_506_mult__nonneg__nonpos2, fact_846_nat__mult__commute, fact_329_add__right__cancel, fact_767_nat__number__of__def, fact_285_power__eq__0__iff, fact_962_four__x__squared, fact_525_mult__diff__mult, fact_1017_Bit1__Min, fact_113_add__numeral__0, fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_809_succ__Bit0, fact_637_crossproduct__eq, fact_1197_int__val__lemma, fact_239_less__imp__of__nat__less, fact_718_zless__le, fact_741_nat__eq__iff2, fact_1151_zcong__zpower__zmult, fact_933_zmult__int, fact_135_power2__less__0, fact_356_add__0__iff, fact_252_of__nat__power, fact_282_power__strict__increasing, fact_610_mult__zero__right, fact_244_of__nat__less__imp__less, fact_49_less__int__code_I13_J, fact_717_zmult__1__right, fact_505_mult__nonpos__nonneg, fact_800_rel__simps_I15_J, fact_406_nat__number__of__add__1, fact_1153__096_B_Bthesis_O_A_I_B_Bs_Aw_O_Aw_A_061_Ay_A_N_As_A_K_A_I1_A_L_Aint_An, fact_897_nat__1__eq__mult__iff, fact_1040_divides__mul__r, fact_542_mult__left__le__imp__le, fact_867_mult__is__0, fact_878_nat__less__le, fact_182_nat__add__left__cancel, fact_188_less__not__refl3, fact_711_less__eq__int__code_I16_J, fact_1145_prime__g__5, fact_1016_rel__simps_I37_J, fact_572_mult__le__cancel__left__neg, fact_1157_zdvd__antisym__abs, fact_173_real__zero__not__eq__one, fact_359_add_Ocomm__neutral, fact_389_add__strict__left__mono, fact_150_of__nat__less__two__power, fact_266_zero__less__power, fact_161_power__0__left, fact_667_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_1188_nat__mult__dvd__cancel1, fact_765_mult__less__cancel__right__disj, fact_287_of__nat__less__0__iff, fact_801_less__int__code_I14_J, fact_330_add__right__cancel, fact_974_Int2_Oaux__1, fact_483_mult__mono, fact_568_mult__strict__mono, fact_8_zero__power2, fact_246_of__nat__add, fact_271_less__add__one, fact_1163_abs__eq__1__iff, fact_519_eq__add__iff1, fact_524_eq__add__iff2, fact_452_zle__trans, fact_509_mult__nonneg__nonpos, fact_540_real__squared__diff__one__factored, fact_825_power2__ge__self, fact_66_zadd__left__commute, fact_93_rel__simps_I50_J, fact_191_add__less__mono1, fact_1111_dvd_Oless__le, fact_870_less__eq__nat_Osimps_I1_J, fact_852_le__trans, fact_226_one__neq__zero, fact_832_q__neg__lemma, fact_94_rel__simps_I49_J, fact_806_int__one__le__iff__zero__less, fact_1035_s, fact_1114_dvd_Oless__irrefl, fact_420_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_520_eq__add__iff1, fact_783_zadd__zless__mono, fact_876_less__imp__le__nat, fact_745_int__eq__iff__number__of, fact_504_mult__nonpos__nonneg, fact_701_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_486_mult__mono_H, fact_607_mult__zero__left, fact_242_of__nat__less__imp__less, fact_253_of__nat__power, fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_966_diff__square, fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_1066_Int2_Ozcong__zero, fact_117_power__eq__0__iff__number__of, fact_834_le0, fact_603_add__diff__cancel, fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_62_rel__simps_I48_J, fact_630_diff__0__eq__0, fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_1196_nat0__intermed__int__val, fact_513_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_757_realpow__minus__mult, fact_1_t1, fact_224_zero__less__int__conv, fact_849_eq__imp__le, fact_668_mult__1__left, fact_89_double__eq__0__iff, fact_56_eq__number__of, fact_638_crossproduct__eq, fact_960_nat__number__of__mult__left, fact_616_no__zero__divisors, fact_898_nat__mult__1, fact_118_power__eq__0__iff__number__of, fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J, fact_547_mult__less__imp__less__left, fact_446_semiring__mult__number__of, fact_989__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_391_add__strict__right__mono, fact_609_mult__zero__left, fact_1052_Nat__Transfer_Otransfer__int__nat__relations_I4_J, fact_96_rel__simps_I38_J, fact_303_zero__less__double__add__iff__zero__less__single__add, fact_546_mult__right__le__imp__le, fact_53_one__is__num__one, fact_785_transfer__int__nat__quantifiers_I2_J, fact_911_real__add__left__mono, fact_997_zdvd__antisym__nonneg, fact_857_mult__le__cancel1, fact_855_real__le__eq__diff, fact_567_mult__strict__mono_H, fact_885_add__leD2, fact_760_transfer__nat__int__numerals_I1_J, fact_134_zero__less__power2, fact_972_unique__quotient__lemma, fact_879_real__less__def, fact_731_le__special_I3_J, fact_851_mult__le__mono2, fact_1069_dvd__mult__cancel, fact_824_cube__square, fact_862_diff__bin__simps_I7_J, fact_959_nat__mult__2__right, fact_628_diff__self__eq__0, fact_624_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_1041_divides__mul__l, fact_1029_zmult__eq__1__iff, fact_924_real__mult__order, fact_532_ex__nat, fact_147_semiring__numeral__1__eq__1, fact_255_Nat__Transfer_Otransfer__int__nat__functions_I1_J, fact_5_one__power2, fact_387_add__strict__left__mono, fact_694_power__commutes, fact_120_add__number__of__left, fact_375_add__0__left, fact_154_of__nat__0__less__iff, fact_1001_rel__simps_I13_J, fact_321_add__imp__eq, fact_59_number__of__reorient, fact_874_less__or__eq__imp__le, fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_216_power__one__right, fact_102_add__Bit0__Bit0, fact_114_add__numeral__0, fact_971_zdiv__mono2__lemma, fact_67_zadd__commute, fact_914_diff__bin__simps_I3_J, fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_435_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_931_less__diff__iff, fact_148_mn, fact_193_less__add__eq__less, fact_1014_rel__simps_I45_J, fact_654_mult_Ocomm__neutral, fact_425_ab__semigroup__mult__class_Omult__ac_I1_J, fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_263_zero__less__one, fact_153_realpow__two__sum__zero__iff, fact_1020_succ__Min, fact_149_of__nat__less__two__power, fact_995_zdvd__not__zless, fact_597_diff__0__right, fact_899_diff__mult__distrib, fact_268_zero__less__power, fact_759_less__iff__diff__less__0, fact_82_zless__add1__eq, fact_472_of__nat__le__iff, fact_859_real__mult__le__cancel__iff2, fact_175_not__add__less1, fact_449_zmult__commute, fact_979_real__le__linear, fact_91_rel__simps_I46_J, fact_813_zless__imp__add1__zle, fact_968_zdiff__power2, fact_320_add__imp__eq, fact_291_power__0, fact_685_add__right__mono, fact_31_less__number__of__int__code, fact_549_mult__less__imp__less__left, fact_37_int__power, fact_413_le__iff__diff__le__0, fact_920_mult__less__cancel1, fact_1038_s0p, fact_826_int__pos__lt__two__imp__zero__or__one, fact_934_int__mult, fact_225_one__neq__zero, fact_539_real__squared__diff__one__factored, fact_940_le__diff__conv2, fact_840_t, fact_533_zero__le__square, fact_713_rel__simps_I31_J, fact_1074_dvd__mult__cancel2, fact_928_diff__is__0__eq_H, fact_892_le__add1, fact_518_le__add__iff1, fact_678_add__mono, fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_18_semiring__one__add__one__is__two, fact_23_power__0__left__number__of, fact_295_of__nat__0, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_500_mult__right__mono, fact_1165_zero__less__zpower__abs__iff, fact_495_mult__left__mono, fact_602_add__diff__add, fact_1184_left__add__mult__distrib, fact_352_one__reorient, fact_1156_nat__abs__mult__distrib, fact_659_mult__1__right, fact_12_add__special_I2_J, fact_201_add__gr__0, fact_81_int__0__less__1, fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_916_less__bin__lemma, fact_629_minus__nat_Odiff__0, fact_1116_neg__one__power__eq__mod__m, fact_598_diff__0__right, fact_755_realpow__minus__mult, fact_1101_dvd_Oantisym, fact_1098_dvd_Ole__less__trans, fact_1091_dvd_Oless__imp__triv, fact_521_le__add__iff2, fact_211_add__eq__self__zero, fact_901_real__mult__1, fact_163_power__strict__decreasing, fact_45_nat__1__add__1, fact_941_le__add__diff__inverse2, fact_1000_rel__simps_I9_J, fact_304_zero__less__double__add__iff__zero__less__single__add, fact_951_transfer__nat__int__relations_I3_J, fact_442_diff__eq__diff__eq, fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_819_le__imp__0__less, fact_73_rel__simps_I12_J, fact_538_less__add__iff2, fact_448_zle__refl, fact_497_mult__left__mono, fact_223_less__0__number__of, fact_662_mult__1, fact_556_mult__right__less__imp__less, fact_856_mult__le__cancel2, fact_92_rel__simps_I39_J, fact_795_nat__diff__split, fact_105_zadd__0, fact_126_add__Bit1__Bit0, fact_1130_zcong__scalar2, fact_669_mult__1__left, fact_1128_zcong__zmult__self, fact_1050_divides__rev, fact_128_Bit1__def, fact_1158_zdvd1__eq, fact_842__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_, fact_977_real__le__refl, fact_847_nat__le__linear, fact_1185_nat__mult__less__cancel1, fact_397_add__less__cancel__right, fact_123_add__number__of__eq, fact_751_le__special_I2_J, fact_592_right__minus__eq, fact_973_xy, fact_877_le__eq__less__or__eq, fact_909_real__add__mult__distrib, fact_90_double__eq__0__iff, fact_632_comm__semiring__class_Odistrib, fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_233_power__one, fact_171_tn0, fact_313_zero__reorient, fact_816_transfer__nat__int__numerals_I4_J, fact_170_transfer__int__nat__numerals_I1_J, fact_38_zadd__int__left, fact_1166_zdvd__mult__cancel1, fact_87_less__special_I2_J, fact_121_add__number__of__left, fact_108_semiring__numeral__0__eq__0, fact_688_add__le__cancel__left, fact_1033_zpower__zdvd__prop2, fact_492_comm__mult__left__mono, fact_1012_rel__simps_I7_J, fact_422_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_468_number__of__diff, fact_660_mult__1__right, fact_1104_dvd_Oord__eq__le__trans, fact_1193_nat__le__add__iff2, fact_1127_zcong__1, fact_1081_Legendre__1mod4, fact_894_nat__mult__eq__one, fact_264_zero__less__one, fact_573_mult__le__cancel__left__pos, fact_758_less__iff__diff__less__0, fact_119_power__eq__0__iff__number__of, fact_28_numeral__1__eq__1, fact_1034__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_180_nat__add__left__commute, fact_943_diff__add__assoc, fact_229_zero__neq__one, fact_1177_abs__add__one__gt__zero, fact_663_mult__1, fact_564_mult__less__le__imp__less, fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_101_add__Pls, fact_922_not__real__square__gt__zero, fact_580_mult__right__le__one__le, fact_955_mult__eq__if, fact_565_mult__strict__mono_H, fact_794_nat__diff__split__asm, fact_1064_zcong__zmult__prop1, fact_186_less__irrefl__nat, fact_535_less__add__iff1, fact_1028_diff__bin__simps_I5_J, fact_1142_zprime__def, fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_939_add__diff__assoc, fact_992_rel__simps_I24_J, fact_786_transfer__int__nat__quantifiers_I1_J, fact_19_semiring__one__add__one__is__two, fact_1170_power2__eq__iff__abs__eq, fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_1024_rel__simps_I25_J, fact_184_nat__add__left__cancel__less, fact_687_add__le__cancel__left, fact_55_Numeral1__eq1__nat, fact_1174_best__division__abs, fact_35_zero__is__num__zero, fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_7_zero__power2, fact_217_power__one__right, fact_95_rel__simps_I44_J, fact_487_mult__mono_H, fact_681_add__left__mono, fact_1102_dvd__antisym, fact_1059_zcong__shift, fact_1021_diff__bin__simps_I2_J, fact_926_mult__eq__self__implies__10, fact_456_number__of__mult, fact_1093_dvd_Oless__imp__not__eq, fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_222_int__if__cong, fact_257_pos__add__strict, fact_230_zero__neq__one, fact_267_zero__less__power, fact_528_mult__le__0__iff, fact_1092_dvd_Oless__imp__not__eq2, fact_817_split__nat, fact_980_real__mult__assoc, fact_1144_zdiff__int__split, fact_331_add__left__cancel, fact_482_mult__mono, fact_830_smaller_I2_J, fact_70_less__special_I3_J, fact_684_add__right__mono, fact_146_semiring__numeral__1__eq__1, fact_488_mult__left__mono__neg, fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_612_mult__zero__right, fact_323_add__left__imp__eq, fact_888_trans__le__add2, fact_999_zdvd__period, fact_727_nat__less__eq__zless, fact_836_t__l__p, fact_582_mult__left__le__one__le, fact_1043_zcong__eq__zdvd__prop, fact_144_number__of__Bit1, fact_243_of__nat__less__imp__less, fact_142_number__of__Bit0, fact_451_zmult__assoc, fact_810_succ__Bit1, fact_829_self__quotient__aux1, fact_1186_nat__mult__eq__cancel1, fact_249_of__nat__1, fact_143_number__of__Bit1, fact_981_real__le__trans, fact_611_mult__zero__right, fact_961_mult__nat__number__of, fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_869_mult__cancel2, fact_168_zero__less__two, fact_863_zdiff__zmult__distrib, fact_827_Euler_Oaux__1, fact_561_mult__le__less__imp__less, fact_133_zero__less__power2, fact_545_mult__right__le__imp__le, fact_183_nat__add__right__cancel, fact_633_comm__semiring__class_Odistrib, fact_138_sum__power2__gt__zero__iff, fact_715_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_311_add__neg__neg, fact_882_add__mult__distrib2, fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_575_sum__squares__ge__zero, fact_481_split__mult__pos__le, fact_807_int__le__0__conv, fact_1055_nat__dvd__1__iff__1, fact_516_mult__nonneg__nonneg, fact_788_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_17_one__add__one__is__two, fact_354_one__reorient, fact_550_mult__left__less__imp__less, fact_260_not__one__less__zero, fact_769_zero__less__diff, fact_691_add__le__cancel__right, fact_1085__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L, fact_1063_zcong__not__zero, fact_881_add__mult__distrib, fact_541_mult__left__le__imp__le, fact_623_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_515_mult__nonneg__nonneg, fact_953_nat__mult__distrib, fact_574_mult__le__cancel__left__pos, fact_776_less__eq__int__code_I14_J, fact_944_add__diff__assoc2, fact_837_qf1pt, fact_57_eq__number__of, fact_994_zprime__zdvd__power, fact_426_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_507_mult__nonneg__nonpos2, fact_585_power__increasing, fact_595_diff__self, fact_13_add__special_I2_J, fact_473_of__nat__le__iff, fact_269_less__add__one, 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% 19.48/5.17 % No. of inferences in proof: 2398
% 19.48/5.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4714 ms resp. 4122 ms w/o parsing
% 20.56/5.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.56/5.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------