TSTP Solution File: NUM925+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 : Fri May 19 11:43:03 EDT 2023
% Result : Theorem 41.48s 10.02s
% Output : Refutation 42.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1287
% Syntax : Number of formulae : 2509 ( 898 unt; 67 typ; 0 def)
% Number of atoms : 6390 (2049 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 36797 ( 474 ~; 162 |; 805 &;32375 @)
% ( 335 <=>;2646 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 67 usr; 32 con; 0-3 aty)
% Number of variables : 5029 ( 0 ^;4980 !; 49 ?;5029 :)
% Comments :
%------------------------------------------------------------------------------
thf(hAPP_nat_int_type,type,
hAPP_nat_int: $i > $i > $i ).
thf(power_power_int_type,type,
power_power_int: $i > $i ).
thf(plus_plus_int_type,type,
plus_plus_int: $i > $i > $i ).
thf(one_one_int_type,type,
one_one_int: $i ).
thf(semiri1621563631at_int_type,type,
semiri1621563631at_int: $i ).
thf(n_type,type,
n: $i ).
thf(number_number_of_nat_type,type,
number_number_of_nat: $i > $i ).
thf(bit0_type,type,
bit0: $i > $i ).
thf(bit1_type,type,
bit1: $i > $i ).
thf(pls_type,type,
pls: $i ).
thf(zero_zero_int_type,type,
zero_zero_int: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_real_bool_type,type,
hAPP_real_bool: $i > $i > $i ).
thf(hAPP_r1134773055l_bool_type,type,
hAPP_r1134773055l_bool: $i > $i > $i ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: $i ).
thf(plus_plus_real_type,type,
plus_plus_real: $i > $i > $i ).
thf(times_times_real_type,type,
times_times_real: $i > $i > $i ).
thf(minus_minus_real_type,type,
minus_minus_real: $i > $i > $i ).
thf(ord_less_real_type,type,
ord_less_real: $i ).
thf(zero_zero_real_type,type,
zero_zero_real: $i ).
thf(number267125858f_real_type,type,
number267125858f_real: $i > $i ).
thf(hAPP_int_bool_type,type,
hAPP_int_bool: $i > $i > $i ).
thf(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: $i > $i > $i ).
thf(ord_less_int_type,type,
ord_less_int: $i ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: $i ).
thf(hAPP_nat_real_type,type,
hAPP_nat_real: $i > $i > $i ).
thf(semiri132038758t_real_type,type,
semiri132038758t_real: $i ).
thf(hAPP_nat_bool_type,type,
hAPP_nat_bool: $i > $i > $i ).
thf(hAPP_n1699378549t_bool_type,type,
hAPP_n1699378549t_bool: $i > $i > $i ).
thf(ord_less_nat_type,type,
ord_less_nat: $i ).
thf(abs_abs_real_type,type,
abs_abs_real: $i > $i ).
thf(one_one_real_type,type,
one_one_real: $i ).
thf(power_power_real_type,type,
power_power_real: $i > $i ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: $i ).
thf(minus_minus_int_type,type,
minus_minus_int: $i > $i > $i ).
thf(dvd_dvd_nat_type,type,
dvd_dvd_nat: $i ).
thf(minus_minus_nat_type,type,
minus_minus_nat: $i > $i > $i ).
thf(zero_zero_nat_type,type,
zero_zero_nat: $i ).
thf(plus_plus_nat_type,type,
plus_plus_nat: $i > $i > $i ).
thf(times_times_nat_type,type,
times_times_nat: $i > $i > $i ).
thf(number_number_of_int_type,type,
number_number_of_int: $i > $i ).
thf(times_times_int_type,type,
times_times_int: $i > $i > $i ).
thf(is_int_type,type,
is_int: $i > $o ).
thf(zcong_type,type,
zcong: $i > $i > $i ).
thf(hAPP_nat_nat_type,type,
hAPP_nat_nat: $i > $i > $i ).
thf(power_power_nat_type,type,
power_power_nat: $i > $i ).
thf(nat_type,type,
nat: $i > $i ).
thf(zprime_type,type,
zprime: $i ).
thf(dvd_dvd_int_type,type,
dvd_dvd_int: $i ).
thf(abs_abs_int_type,type,
abs_abs_int: $i > $i ).
thf(one_one_nat_type,type,
one_one_nat: $i ).
thf(legendre_type,type,
legendre: $i > $i > $i ).
thf(quadRes_type,type,
quadRes: $i > $i ).
thf(min_type,type,
min: $i ).
thf(m_type,type,
m: $i ).
thf(s1_type,type,
s1: $i ).
thf(tn_type,type,
tn: $i ).
thf(t_type,type,
t: $i ).
thf(semiri984289939at_nat_type,type,
semiri984289939at_nat: $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(if_int_type,type,
if_int: $i > $i > $i > $i ).
thf(twoSqu1154269391sum2sq_type,type,
twoSqu1154269391sum2sq: $i ).
thf(s_type,type,
s: $i ).
thf(m1_type,type,
m1: $i ).
thf(if_nat_type,type,
if_nat: $i > $i > $i > $i ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( 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(4201,plain,
! [A: $i,B: $i] :
( ( A
= ( times_times_nat @ A @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( minus_minus_nat @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_le__diff__conv2) ).
thf(1767,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( minus_minus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( minus_minus_nat @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(677,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( plus_plus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_le__add2) ).
thf(3798,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( plus_plus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4852,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ C @ A ) ) @ ( plus_plus_int @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(590,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3449,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ B @ A ) ) @ B ) )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ B @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_dvd_Ole__less__trans) ).
thf(2544,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(616,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( times_times_nat @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_le__square) ).
thf(3566,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( times_times_nat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
& ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( 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(3021,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
& ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1125,axiom,
! [A: $i,B: $i] :
( ( 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(5437,plain,
! [A: $i,B: $i] :
( ( 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)],[1125]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( nat @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( nat @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_nat__power__eq) ).
thf(4447,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( nat @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( nat @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(1879,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[192]) ).
thf(1120,axiom,
hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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(5422,plain,
hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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)],[1120]) ).
thf(1014,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( 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(5088,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( ( plus_plus_int @ A @ A )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1369,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ B @ A ) ) @ ( plus_plus_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_nat__less__cases) ).
thf(4835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_nat__power__less__imp__less) ).
thf(1823,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(850,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_zero__less__int__conv) ).
thf(4450,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(557,axiom,
! [A: $i] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__0) ).
thf(3345,plain,
! [A: $i] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ A ) @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_zcong__square) ).
thf(2336,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ A ) @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3008,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ C ) ) @ ( times_times_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_zdiv__mono2__lemma) ).
thf(2109,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(437,axiom,
( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_of__nat__0) ).
thf(2876,plain,
( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ B @ A ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_add__neg__neg) ).
thf(1237,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ B @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) ) @ ( plus_plus_nat @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(598,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( plus_plus_nat @ A @ one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_less__add__one) ).
thf(3477,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( plus_plus_nat @ A @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_one__less__power) ).
thf(3830,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2595,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[362]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1850,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ B @ A ) ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rel__simps_I16_J) ).
thf(2331,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ( 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(4682,plain,
! [A: $i,B: $i] :
( ( B != zero_zero_nat )
=> ( ( A != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1215,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_int__power) ).
thf(5733,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1026,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_semiring__norm_I110_J) ).
thf(5131,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(1549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[98]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2210,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ B @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( A
= ( plus_plus_real @ A @ B ) )
<=> ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_add__0__iff) ).
thf(2231,plain,
! [A: $i,B: $i] :
( ( ( A
= ( plus_plus_real @ A @ B ) )
=> ( B = zero_zero_real ) )
& ( ( B = zero_zero_real )
=> ( A
= ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zpower__int) ).
thf(5292,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(1061,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_rel__simps_I40_J) ).
thf(5242,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_776_less__eq__int__code_I14_J) ).
thf(2590,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ B )
<=> ( hBOOL @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ B ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_conj__le__cong) ).
thf(4697,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) ) )
=> ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ A ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
& ( hBOOL @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( ( B != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_divides__rev) ).
thf(3912,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( ( B != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(149,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1728,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(428,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_bin__less__0__simps_I4_J) ).
thf(2837,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1095,axiom,
! [A: $i] :
( ( 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(5348,plain,
! [A: $i] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(924,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_of__nat__less__0__iff) ).
thf(4747,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(569,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3382,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(1855,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[183]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( 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(3680,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( A = B )
=> ( ( minus_minus_int @ A @ B )
= zero_zero_int ) )
& ( ( ( minus_minus_int @ A @ B )
= zero_zero_int )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(967,axiom,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_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(4931,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(735,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__special_I4_J) ).
thf(4037,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ one_one_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_power__le__imp__le__exp) ).
thf(4376,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_Int2_Oaux1) ).
thf(2117,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(240,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__special_I3_J) ).
thf(2104,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1056,axiom,
! [A: $i] :
( ( abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_abs__int__eq) ).
thf(5225,plain,
! [A: $i] :
( ( abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(746,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_rel__simps_I33_J) ).
thf(4075,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1882,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1203,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
thf(5696,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(665,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ B @ A ) ) @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_add__neg__neg) ).
thf(3762,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ B @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1008,axiom,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_rel__simps_I46_J) ).
thf(5069,plain,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(1186,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(5644,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)],[1186]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_mult__less__imp__less__right) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(990,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_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 @ ( hAPP_nat_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 ) ) ) @ ( hAPP_nat_int @ ( 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 ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_zadd__power3) ).
thf(5000,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_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 @ ( hAPP_nat_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 ) ) ) @ ( hAPP_nat_int @ ( 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 ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2776,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3377,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[567]) ).
thf(344,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2527,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( ( 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(3153,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) )
=> ( ( plus_plus_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(382,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ A @ zero_zero_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_diff__0__right) ).
thf(2671,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ A @ zero_zero_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( ( plus_plus_real @ B @ A )
= one_one_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1544,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( ( plus_plus_real @ B @ A )
= one_one_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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)],[96]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4711,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3012,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[473]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__int__code_I15_J) ).
thf(2099,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2282,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( minus_minus_int @ A @ B ) ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( minus_minus_int @ A @ B ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(110,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1591,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ one_one_real ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) @ one_one_int ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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(5669,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) @ one_one_int ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( times_times_nat @ C @ A ) ) @ one_one_int ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(1137,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_zspecial__product) ).
thf(5501,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1033_zpower__zdvd__prop2) ).
thf(4105,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(3439,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5589,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1166]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3648,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ B @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1069_dvd__mult__cancel) ).
thf(4110,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(454,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_bin__less__0__simps_I3_J) ).
thf(2933,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1327,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_mult__right__less__imp__less) ).
thf(1354,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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(2575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( 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 ) ) ) )
& ( ( ( 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 ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( 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(2195,plain,
! [A: $i,B: $i] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1154,axiom,
! [A: $i] :
( ( 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(5550,plain,
! [A: $i] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_power__increasing__iff) ).
thf(1426,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_add__le__cancel__left) ).
thf(3530,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_mult__le__cancel__left__pos) ).
thf(3942,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_nat )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_divides__exp2) ).
thf(4011,plain,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_nat )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(501,axiom,
! [A: $i] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_mult__0) ).
thf(3135,plain,
! [A: $i] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(751,axiom,
! [A: $i] :
( ( hAPP_nat_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(4097,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1067,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(5257,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(2434,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(1872,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[189]) ).
thf(1206,axiom,
~ ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_smaller_I2_J) ).
thf(5701,plain,
~ ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(803,axiom,
! [A: $i] :
( ( 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(4279,plain,
! [A: $i] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2627,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_real__le__antisym) ).
thf(1260,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1195,axiom,
! [A: $i,B: $i] :
( ( 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(5674,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(527,axiom,
! [A: $i] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_diff__self__eq__0) ).
thf(3253,plain,
! [A: $i] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(445,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_semiring__numeral__0__eq__0) ).
thf(2901,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3313,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[545]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5178,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1040]) ).
thf(1208,axiom,
! [A: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_power__0) ).
thf(5708,plain,
! [A: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(1182,axiom,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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(5636,plain,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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)],[1182]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_real__le__trans) ).
thf(1507,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1,conjecture,
( ( hAPP_nat_int @ ( power_power_int @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_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,
( ( hAPP_nat_int @ ( power_power_int @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1222,plain,
( ( hAPP_nat_int @ ( power_power_int @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[654]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_zdvd__not__zless) ).
thf(4941,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(737,axiom,
( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_of__nat__1) ).
thf(4047,plain,
( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(153,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( 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(1746,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ one_one_int @ ( number_number_of_int @ min ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_less__nat__number__of) ).
thf(1835,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(272,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_less__irrefl__nat) ).
thf(2216,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1218,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_power__one__right) ).
thf(5740,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( is_int @ E )
=> ( ( ( 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(3502,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( is_int @ E )
=> ( ( ( ( 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 ) )
& ( ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C )
= E )
=> ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_trans__less__add2) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4679,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(117,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( plus_plus_real @ A @ one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_less__add__one) ).
thf(1613,plain,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( plus_plus_real @ A @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1080,axiom,
( ( succ @ min )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_succ__Min) ).
thf(5301,plain,
( ( succ @ min )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_dvd_Ole__less) ).
thf(2516,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_power__decreasing) ).
thf(4322,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(79,axiom,
! [A: $i] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_diff__0__right) ).
thf(1482,plain,
! [A: $i] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( times_times_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_zmult__int) ).
thf(5024,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( times_times_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1147,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(5533,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)],[1147]) ).
thf(766,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_zero__less__one) ).
thf(4142,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1064,axiom,
( ( hAPP_nat_real @ ( 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(5252,plain,
( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( plus_plus_int @ B @ A )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3766,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( plus_plus_int @ B @ A )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[667]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2432,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ B @ A ) ) @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(727,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_rel__simps_I25_J) ).
thf(3994,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_power__strict__increasing) ).
thf(3915,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(164,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_of__nat__0__less__iff) ).
thf(1782,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(826,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4371,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ C @ A ) ) @ ( plus_plus_real @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(799,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_power__strict__decreasing) ).
thf(4266,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_zdvd__antisym__nonneg) ).
thf(2010,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1213,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5723,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1213]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ( 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(5056,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(440,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2886,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ B @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(962,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_less__or__eq__imp__le) ).
thf(4916,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(764,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_le__add1) ).
thf(4137,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_power__less__imp__less__exp) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( 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(3809,plain,
! [A: $i,B: $i] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: $i] :
( ( is_int @ D )
=> ( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( minus_minus_int @ D @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( minus_minus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_decr__mult__lemma) ).
thf(2173,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: $i] :
( ( is_int @ D )
=> ( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( minus_minus_int @ D @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( minus_minus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1366,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ B @ A ) ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(972,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(4948,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)],[972]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2405,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( B = zero_zero_nat ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( B = zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_mult__less__imp__less__left) ).
thf(3688,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(4775,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
=> ( ( A = C )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = C )
| ( B = zero_zero_nat ) )
=> ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(531,axiom,
! [A: $i] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_add__0__right) ).
thf(3263,plain,
! [A: $i] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1709,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ B @ A ) ) @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_nat__add__left__cancel__less) ).
thf(2698,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_zdiff__int) ).
thf(4070,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
=> ( ( nat @ A )
= ( nat @ ( if_int @ C @ A @ B ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( ( nat @ B )
= ( nat @ ( if_int @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_nat__if__cong) ).
thf(3495,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
=> ( ( nat @ A )
= ( nat @ ( if_int @ C @ A @ B ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( ( nat @ B )
= ( nat @ ( if_int @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_transfer__nat__int__relations_I4_J) ).
thf(2708,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ B ) ) @ ( nat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(327,axiom,
! [A: $i] :
( ( 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(2444,plain,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(627,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( times_times_nat @ ( nat @ B ) @ ( nat @ A ) )
= ( nat @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
thf(3612,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( times_times_nat @ ( nat @ B ) @ ( nat @ A ) )
= ( nat @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( minus_minus_nat @ B @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_dvd__diffD1) ).
thf(1511,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( minus_minus_nat @ B @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( 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(3125,plain,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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 ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3744,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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 ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[661]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( 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(2126,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(693,axiom,
! [A: $i] :
( ( one_one_real = A )
<=> ( A = one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_one__reorient) ).
thf(3855,plain,
! [A: $i] :
( ( ( one_one_real = A )
=> ( A = one_one_real ) )
& ( ( A = one_one_real )
=> ( one_one_real = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(684,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_linorder__neqE__linordered__idom) ).
thf(3820,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_zcong__sym) ).
thf(4637,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_real__mult__commute) ).
thf(2654,plain,
! [A: $i,B: $i] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_real @ ( 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(3976,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) )
=> ( ( hAPP_nat_real @ ( power_power_real @ A ) @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( nat @ ( abs_abs_int @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_int__dvd__iff) ).
thf(4524,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( nat @ ( abs_abs_int @ B ) ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( nat @ ( abs_abs_int @ B ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_dvd_Oord__le__eq__trans) ).
thf(3938,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(821,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_rel__simps_I7_J) ).
thf(4348,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1082,axiom,
is_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
thf(5306,plain,
is_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(167,axiom,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( 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(1792,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_self__quotient__aux1) ).
thf(2814,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4422,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(579,axiom,
( ( hAPP_nat_real @ semiri132038758t_real @ zero_zero_nat )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_of__nat__0) ).
thf(3410,plain,
( ( hAPP_nat_real @ semiri132038758t_real @ zero_zero_nat )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1035,axiom,
! [A: $i] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_rel__simps_I42_J) ).
thf(5160,plain,
! [A: $i] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1042,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(5182,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3845,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_dvd_Oeq__iff) ).
thf(4023,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_of__nat__less__imp__less) ).
thf(1992,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1077,axiom,
! [A: $i] :
( ( times_times_int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_mult__Pls) ).
thf(5289,plain,
! [A: $i] :
( ( times_times_int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(984,axiom,
( ( hAPP_nat_int @ ( 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(4984,plain,
( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(794,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ B @ one_one_int ) ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zless__add1__eq) ).
thf(4243,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ B @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2703,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1058,axiom,
! [A: $i] :
( ( succ @ ( bit1 @ A ) )
= ( bit0 @ ( succ @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_succ__Bit1) ).
thf(5231,plain,
! [A: $i] :
( ( succ @ ( bit1 @ A ) )
= ( bit0 @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_dvd_Oless__le) ).
thf(3099,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( A != B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ B @ C ) ) @ E ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ B @ D ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_zcong__zmult__prop2) ).
thf(2713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ B @ C ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ B @ D ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ B @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ B @ C ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1704,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( times_times_int @ B @ A ) ) @ B ) )
=> ( ( abs_abs_int @ A )
= one_one_int ) )
& ( ( ( abs_abs_int @ A )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( times_times_int @ B @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ B ) ) @ C ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= ( hAPP_nat_int @ ( 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(5480,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ B ) ) @ C ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_rel__simps_I32_J) ).
thf(3657,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1220,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
thf(5746,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_pos__add__strict) ).
thf(4632,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4390,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[832]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( hAPP_nat_int @ B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( hAPP_nat_int @ B @ D ) ) ) ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ B @ zero_zero_nat ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ B @ C ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
& ( ( hAPP_nat_int @ B @ D )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_nat0__intermed__int__val) ).
thf(2852,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( hAPP_nat_int @ B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( hAPP_nat_int @ B @ D ) ) ) ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ B @ zero_zero_nat ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ B @ C ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
& ( ( hAPP_nat_int @ B @ D )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4353,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ( ( times_times_int @ B @ A )
= one_one_int )
=> ( ( B = one_one_int )
& ( A = one_one_int ) ) )
& ( ( ( B = one_one_int )
& ( A = one_one_int ) )
=> ( ( times_times_int @ B @ A )
= one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(949,axiom,
! [A: $i] :
( ( 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(4862,plain,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4617,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[889]) ).
thf(1049,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_number__of__Pls) ).
thf(5199,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_le__trans) ).
thf(4179,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(5604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[1171]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4664,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(891,axiom,
! [A: $i,B: $i] :
( ( ( B = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= ( times_times_nat @ A @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_power__eq__if) ).
thf(4622,plain,
! [A: $i,B: $i] :
( ( ( B = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= ( times_times_nat @ A @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1087,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OBit1) ).
thf(5323,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(710,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3919,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[710]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1347,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( times_times_real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( 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(1572,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( minus_minus_real @ A @ B )
= zero_zero_real ) )
& ( ( ( minus_minus_real @ A @ B )
= zero_zero_real )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_add__less__imp__less__right) ).
thf(1398,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(489,axiom,
! [A: $i] :
( ( 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(3084,plain,
! [A: $i] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_diff__add__cancel) ).
thf(2635,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3470,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(658,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_zcong__zero__equiv__div) ).
thf(3734,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4368,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[825]) ).
thf(974,axiom,
! [A: $i] :
( ( succ @ ( bit0 @ A ) )
= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_succ__Bit0) ).
thf(4952,plain,
! [A: $i] :
( ( succ @ ( bit0 @ A ) )
= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_power__strict__increasing) ).
thf(4383,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(173,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_n0) ).
thf(1815,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ C @ A ) ) @ ( plus_plus_int @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(934,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_of__nat__le__iff) ).
thf(4793,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(190,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1875,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1232,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) ) @ E ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4253,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4967,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[979]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_zmult__commute) ).
thf(2829,plain,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_998_zdvd__reduce) ).
thf(3788,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_mult__right__le__imp__le) ).
thf(4595,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4432,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_add__le__imp__le__right) ).
thf(4205,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(364,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2616,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_add__le__cancel__right) ).
thf(2324,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_zle__antisym) ).
thf(3075,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ( 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(5027,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ ( succ @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(123,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_le__special_I3_J) ).
thf(1632,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(917,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_real @ semiri132038758t_real @ A )
= ( hAPP_nat_real @ semiri132038758t_real @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_of__nat__eq__iff) ).
thf(4724,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_real @ semiri132038758t_real @ A )
= ( hAPP_nat_real @ semiri132038758t_real @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_real @ semiri132038758t_real @ A )
= ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( hAPP_nat_int @ B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( hAPP_nat_int @ B @ D ) ) ) ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ B @ zero_zero_nat ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ B @ C ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
& ( ( hAPP_nat_int @ B @ D )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_int__val__lemma) ).
thf(2925,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( hAPP_nat_int @ B @ ( plus_plus_nat @ D @ one_one_nat ) ) @ ( hAPP_nat_int @ B @ D ) ) ) ) @ one_one_int ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ B @ zero_zero_nat ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ B @ C ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
& ( ( hAPP_nat_int @ B @ D )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1000,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( A
= ( plus_plus_int @ A @ B ) )
<=> ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_add__0__iff) ).
thf(5032,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( A
= ( plus_plus_int @ A @ B ) )
=> ( B = zero_zero_int ) )
& ( ( B = zero_zero_int )
=> ( A
= ( plus_plus_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_q__pos__lemma) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1100,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_add__0__left) ).
thf(5360,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(938,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4810,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[938]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(839,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_zero__neq__one) ).
thf(4411,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_of__nat__power) ).
thf(5264,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(549,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_less__eq__nat_Osimps_I1_J) ).
thf(3322,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3524,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[609]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ? [C: $i] :
( ( is_int @ C )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3431,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ? [C: $i] :
( ( is_int @ C )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[585]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1664,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(416,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( min
= ( bit1 @ A ) )
<=> ( min = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_rel__simps_I43_J) ).
thf(2794,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( min
= ( bit1 @ A ) )
=> ( min = A ) )
& ( ( min = A )
=> ( min
= ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ C )
=> ( ( C != zero_zero_int )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4857,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ C )
=> ( ( C != zero_zero_int )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1373,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( times_times_real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(34,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_even__less__0__iff) ).
thf(1334,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( ( 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(3527,plain,
! [A: $i,B: $i] :
( ( ( 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)],[610]) ).
thf(184,axiom,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_mult_Ocomm__neutral) ).
thf(1858,plain,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(2122,plain,
! [A: $i,B: $i,C: $i] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4134,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[763]) ).
thf(561,axiom,
is_int @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_y____) ).
thf(3357,plain,
is_int @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_add__diff__cancel) ).
thf(2254,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(350,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit0 @ A ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2555,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit0 @ A ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3290,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1028,axiom,
! [A: $i] :
( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_number__of__int) ).
thf(5135,plain,
! [A: $i] :
( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_add__less__imp__less__left) ).
thf(4798,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(875,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_dvd_Oantisym__conv) ).
thf(4556,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5259,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1068]) ).
thf(1217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_zcong__zpower) ).
thf(5738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(310,axiom,
! [A: $i] :
( ( hAPP_nat_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(2367,plain,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2639,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3226,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[520]) ).
thf(460,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ( ( minus_minus_nat @ ( nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( nat @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_Int2_Oaux__1) ).
thf(2965,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ( ( minus_minus_nat @ ( nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( nat @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(912,axiom,
! [A: $i] :
~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_dvd_Oless__irrefl) ).
thf(4707,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_add1__zle__eq) ).
thf(2392,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1089,axiom,
( ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( hAPP_nat_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(5328,plain,
( ( minus_minus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_dvd_Oless__asym_H) ).
thf(2718,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ ( nat @ B ) ) @ A )
= ( nat @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
thf(1696,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ ( nat @ B ) ) @ A )
= ( nat @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(572,axiom,
! [A: $i] :
( ( 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(3389,plain,
! [A: $i] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(340,axiom,
! [A: $i] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_add__numeral__0) ).
thf(2508,plain,
! [A: $i] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( hAPP_nat_int @ ( 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(5059,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ B )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( plus_plus_nat @ A @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add__gr__0) ).
thf(1843,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( plus_plus_nat @ A @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( plus_plus_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3986,plain,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_real )
=> ( ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(485,axiom,
! [A: $i] :
( ( A != zero_zero_nat )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_neq0__conv) ).
thf(3068,plain,
! [A: $i] :
( ( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1377,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( minus_minus_real @ A @ B ) ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( minus_minus_real @ A @ B ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_diff__is__0__eq) ).
thf(2618,plain,
! [A: $i,B: $i] :
( ( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1112,axiom,
! [A: $i,B: $i] :
( ( 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(5401,plain,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3189,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ B @ A ) ) @ ( times_times_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3739,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[659]) ).
thf(1104,axiom,
! [A: $i] :
( ( ( hAPP_nat_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(5375,plain,
! [A: $i] :
( ( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(1106,axiom,
! [A: $i] :
( ( ( hAPP_nat_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(5384,plain,
! [A: $i] :
( ( ( hAPP_nat_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)],[1106]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( 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(3712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( 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)],[652]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_of__nat__less__iff) ).
thf(1622,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_zdvd__imp__le) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1093,axiom,
( zero_zero_int
= ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_transfer__int__nat__numerals_I1_J) ).
thf(5343,plain,
( zero_zero_int
= ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_mult__le__cancel1) ).
thf(2137,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(964,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_one__less__power) ).
thf(4924,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1038,axiom,
! [A: $i] :
( ( 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(5169,plain,
! [A: $i] :
( ( 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)],[1038]) ).
thf(564,axiom,
! [A: $i] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_one__reorient) ).
thf(3361,plain,
! [A: $i] :
( ( ( one_one_nat = A )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( one_one_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(869,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__special_I4_J) ).
thf(4536,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_zle__trans) ).
thf(1975,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(742,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_mult__left__less__imp__less) ).
thf(4065,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_transfer__nat__int__relations_I3_J) ).
thf(1863,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( nat @ B ) ) @ ( nat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(492,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_semiring__norm_I112_J) ).
thf(3097,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(521,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rel__simps_I12_J) ).
thf(3229,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(886,axiom,
! [A: $i] :
( ! [B: $i] : ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
<=> ! [B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_all__nat) ).
thf(4604,plain,
! [A: $i] :
( ( ! [B: $i] : ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ! [B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) ) ) ) )
& ( ! [B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1034,axiom,
! [A: $i] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_mult__zero__left) ).
thf(5157,plain,
! [A: $i] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4199,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ B @ A ) ) @ ( times_times_int @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(784,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_not__one__less__zero) ).
thf(4216,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1146,axiom,
! [A: $i] :
( ( 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(5530,plain,
! [A: $i] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(837,axiom,
! [A: $i] :
( ( 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(4407,plain,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1691,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ B @ A ) ) @ ( times_times_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3186,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[510]) ).
thf(547,axiom,
! [A: $i] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_add_Ocomm__neutral) ).
thf(3318,plain,
! [A: $i] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(2641,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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(3550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( 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 ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1023,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zadd__int) ).
thf(5122,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_Legendre__def) ).
thf(1730,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ B ) @ A ) )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1604,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(704,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( nat @ A ) )
= A ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( nat @ A ) )
= zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_int__nat__eq) ).
thf(3899,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( nat @ A ) )
= A ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( nat @ A ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(452,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_real__zero__not__eq__one) ).
thf(2922,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( ( plus_plus_real @ B @ A )
= one_one_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( ( plus_plus_real @ B @ A )
= one_one_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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)],[63]) ).
thf(655,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( number_number_of_int @ B ) )
<=> ( ( A
= ( nat @ ( number_number_of_int @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3720,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( number_number_of_int @ B ) )
=> ( ( A
= ( nat @ ( number_number_of_int @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ B ) ) ) ) )
& ( ( ( A
= ( nat @ ( number_number_of_int @ B ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ B ) ) ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1116,axiom,
( ~ ( hBOOL @ ( hAPP_int_bool @ ( 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(5411,plain,
( ~ ( hBOOL @ ( hAPP_int_bool @ ( 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)],[1116]) ).
thf(28,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( abs_abs_real @ A ) ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_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(1306,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( abs_abs_real @ A ) ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(996,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_of__nat__eq__iff) ).
thf(5017,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1150,axiom,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_rel__simps_I39_J) ).
thf(5540,plain,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(2083,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_dvd__imp__le) ).
thf(4100,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1005,axiom,
~ ! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ~ ( ( B
= ( minus_minus_int @ x @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_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(5049,plain,
~ ! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ~ ( ( B
= ( minus_minus_int @ x @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(347,axiom,
! [A: $i] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_mult_Ocomm__neutral) ).
thf(2541,plain,
! [A: $i] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1212,axiom,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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(5719,plain,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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)],[1212]) ).
thf(1102,axiom,
is_int @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OPls) ).
thf(5366,plain,
is_int @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4785,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ B ) )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(859,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_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(4493,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(805,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_less__0__number__of) ).
thf(4284,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(606,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751_le__special_I2_J) ).
thf(3514,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_is__mult__sum2sq) ).
thf(3778,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1560,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(389,axiom,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_add_Ocomm__neutral) ).
thf(2705,plain,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(284,axiom,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_mult__1__left) ).
thf(2264,plain,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_add__le__imp__le__right) ).
thf(1387,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_power__strict__decreasing) ).
thf(1900,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ one_one_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(5630,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[1180]) ).
thf(399,axiom,
! [A: $i] :
( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_gr0I) ).
thf(2733,plain,
! [A: $i] :
( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3867,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( ( ( minus_minus_nat @ C @ B )
= A )
=> ( C
= ( plus_plus_nat @ A @ B ) ) )
& ( ( C
= ( plus_plus_nat @ A @ B ) )
=> ( ( minus_minus_nat @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_zcong__zmult) ).
thf(4397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( 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(1580,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( 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 ) )
& ( ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C )
= E )
=> ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(287,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_rel__simps_I30_J) ).
thf(2277,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_mult__le__cancel__left__neg) ).
thf(1255,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ zero_zero_real ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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(4434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( 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 ) ) ) )
& ( ( ( 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 ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4878,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1164,axiom,
~ ! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ~ ( ( B
= ( minus_minus_int @ y @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_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(5579,plain,
~ ! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ~ ( ( B
= ( minus_minus_int @ y @ ( times_times_int @ A @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ B ) ) ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(986,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_semiring__numeral__0__eq__0) ).
thf(4989,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1003,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_add__0__right) ).
thf(5044,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_int__int__eq) ).
thf(5455,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(155,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_int__0__less__1) ).
thf(1751,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(660,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3742,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ one_one_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(819,axiom,
is_int @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_m) ).
thf(4344,plain,
is_int @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4091,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(781,axiom,
is_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_t____) ).
thf(4204,plain,
is_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1130,axiom,
! [A: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= one_one_int )
| ( ( hAPP_nat_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(5470,plain,
! [A: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= one_one_int )
| ( ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ min ) ) @ A )
= ( number_number_of_int @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1139,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) @ ( minus_minus_int @ ( hAPP_nat_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(5507,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) @ ( minus_minus_int @ ( hAPP_nat_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)],[1139]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3814,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2132,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( minus_minus_int @ A @ B ) ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( minus_minus_int @ A @ B ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2414,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[320]) ).
thf(526,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_zmult__1) ).
thf(3250,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_mult__less__cancel__right__disj) ).
thf(4160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(902,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_transfer__nat__int__relations_I2_J) ).
thf(4661,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ ( nat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_real @ ( power_power_real @ ( times_times_real @ A @ B ) ) @ C )
= ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_power__mult__distrib) ).
thf(4295,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_real @ ( power_power_real @ ( times_times_real @ A @ B ) ) @ C )
= ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3191,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ B @ A ) ) @ ( times_times_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1189,axiom,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_nat @ ( 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(5655,plain,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_nat @ ( 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)],[1189]) ).
thf(778,axiom,
! [A: $i] :
( ( ( nat @ A )
= zero_zero_nat )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_nat__0__iff) ).
thf(4192,plain,
! [A: $i] :
( ( ( ( nat @ A )
= zero_zero_nat )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( ( nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( nat @ A )
= B )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1920,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( ( nat @ A )
= B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_nat ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_nat ) ) )
=> ( ( nat @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(881,axiom,
! [A: $i,B: $i] :
( ( ( 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(4585,plain,
! [A: $i,B: $i] :
( ( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) )
=> ( ( times_times_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(830,axiom,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4385,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ B @ A ) ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1001,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_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(5038,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1159,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__numeral__0__right) ).
thf(5566,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(349,axiom,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_power__0__left) ).
thf(2547,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(639,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_Nat_Odiff__le__self) ).
thf(3667,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(151,axiom,
! [A: $i] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_diff__0__eq__0) ).
thf(1740,plain,
! [A: $i] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1090,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( 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(5330,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( minus_minus_int @ A @ B )
= zero_zero_int )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_right__minus__eq) ).
thf(4316,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( minus_minus_int @ A @ B )
= zero_zero_int )
=> ( A = B ) )
& ( ( A = B )
=> ( ( minus_minus_int @ A @ B )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(536,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_rel__simps_I34_J) ).
thf(3282,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(458,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_rel__simps_I21_J) ).
thf(2958,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(533,axiom,
! [A: $i,B: $i] :
( ( ( 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(3269,plain,
! [A: $i,B: $i] :
( ( ( 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)],[533]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_power__increasing) ).
thf(1602,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_mult__left__less__imp__less) ).
thf(1968,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_Euler_Oaux2) ).
thf(3198,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(379,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_zle__refl) ).
thf(2663,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(1555,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[100]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4994,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[988]) ).
thf(927,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( plus_plus_nat @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_dvd__reduce) ).
thf(4757,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( plus_plus_nat @ B @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( plus_plus_nat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(484,axiom,
! [A: $i] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_add__0__left) ).
thf(3065,plain,
! [A: $i] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1201,axiom,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_real @ ( 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(5690,plain,
! [A: $i] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_real @ ( 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)],[1201]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( times_times_int @ C @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_zprime__zdvd__zmult) ).
thf(3578,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ ( times_times_int @ C @ A ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(24,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1296,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ A ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4553,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[874]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_add__le__cancel__right) ).
thf(4187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1092,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_zero__less__power) ).
thf(5341,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( 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(3535,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( 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 ) ) ) ) )
& ( ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) )
=> ( ( times_times_int @ A @ B )
= one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1139_zcong__zless__0) ).
thf(1787,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(982,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_int__1) ).
thf(4979,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1050,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_int__less__0__conv) ).
thf(5201,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_add__less__cancel__left) ).
thf(4417,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1190,axiom,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rel__simps_I50_J) ).
thf(5658,plain,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(1281,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[20]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(2741,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) )
& ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_self__quotient__aux2) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1291,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( minus_minus_real @ A @ B ) ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( minus_minus_real @ A @ B ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(747,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4080,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[747]) ).
thf(1210,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_int__0) ).
thf(5714,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1054,axiom,
is_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).
thf(5221,plain,
is_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(1072,axiom,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ 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(5270,plain,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1121,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_int__if__cong) ).
thf(5423,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( if_nat @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1094,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( minus_minus_int @ A @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( hAPP_nat_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 ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_zdiff__power2) ).
thf(5345,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( minus_minus_int @ A @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( hAPP_nat_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 ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1173,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ m1 ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_mn) ).
thf(5615,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ m1 ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(208,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rel__simps_I4_J) ).
thf(1970,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(945,axiom,
! [A: $i] :
( ( 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(4845,plain,
! [A: $i] :
( ( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( zero_zero_real
= ( plus_plus_real @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3386,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( ( abs_abs_int @ A )
= ( abs_abs_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3119,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( abs_abs_int @ A ) ) @ ( abs_abs_int @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_realpow__minus__mult) ).
thf(3078,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(3650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1200,axiom,
! [A: $i] :
( ( 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(5687,plain,
! [A: $i] :
( ( 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)],[1200]) ).
thf(1132,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_odd__less__0) ).
thf(5475,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_power__less__imp__less__exp) ).
thf(1402,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(657,axiom,
! [A: $i] :
( ( 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(3731,plain,
! [A: $i] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(721,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ A )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_power__one) ).
thf(3968,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1084,axiom,
( ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) )
= ( nat @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_transfer__nat__int__numerals_I3_J) ).
thf(5313,plain,
( ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) )
= ( nat @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1045,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(5189,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)],[1045]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[594]) ).
thf(1178,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_zero__zle__int) ).
thf(5626,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3909,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[706]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_of__nat__less__iff) ).
thf(3615,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(253,axiom,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_mult__1__left) ).
thf(2157,plain,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(243,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_zcong__1) ).
thf(2115,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_of__nat__less__imp__less) ).
thf(1270,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1772,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ B @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3122,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[497]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( nat @ B )
= ( nat @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_eq__nat__nat__iff) ).
thf(2946,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( ( nat @ B )
= ( nat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( nat @ B )
= ( nat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(465,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ A @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2990,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ A @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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(4512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( 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 ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(992,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_of__nat__1) ).
thf(5006,plain,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(308,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_mult_Ocomm__neutral) ).
thf(2359,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1375,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( ( number267125858f_real @ A )
= B )
<=> ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_number__of__reorient) ).
thf(3218,plain,
! [A: $i,B: $i] :
( ( ( ( number267125858f_real @ A )
= B )
=> ( B
= ( number267125858f_real @ A ) ) )
& ( ( B
= ( number267125858f_real @ A ) )
=> ( ( number267125858f_real @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_power__increasing__iff) ).
thf(4544,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(845,axiom,
! [A: $i] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_mult__zero__right) ).
thf(4429,plain,
! [A: $i] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_zero__less__power) ).
thf(1498,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(108,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1587,plain,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( times_times_real @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(132,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_zmult__1__right) ).
thf(1672,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_eq__number__of) ).
thf(3704,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_add__le__imp__le__left) ).
thf(1540,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_zdvd__bounds) ).
thf(3963,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( is_int @ C )
=> ( ( ( 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(3087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( is_int @ C )
=> ( ( ( ( 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 ) ) )
& ( ( C
= ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) )
=> ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( 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(3018,plain,
! [A: $i,B: $i] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(905,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_one__neq__zero) ).
thf(4676,plain,
one_one_real != zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(333,axiom,
! [A: $i] :
( ( zero_zero_nat = A )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_zero__reorient) ).
thf(2460,plain,
! [A: $i] :
( ( ( zero_zero_nat = A )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( zero_zero_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1041,axiom,
hBOOL @ ( hAPP_int_bool @ zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_zprime__2) ).
thf(5181,plain,
hBOOL @ ( hAPP_int_bool @ zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1011,axiom,
! [A: $i] :
( ( succ @ A )
= ( plus_plus_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_succ__def) ).
thf(5080,plain,
! [A: $i] :
( ( succ @ A )
= ( plus_plus_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1219,axiom,
! [A: $i] :
( ( abs_abs_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( 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(5743,plain,
! [A: $i] :
( ( abs_abs_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ ( abs_abs_int @ A ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(968,axiom,
! [A: $i] :
( ( 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(4938,plain,
! [A: $i] :
( ( 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)],[968]) ).
thf(57,axiom,
! [A: $i] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_diff__self) ).
thf(1414,plain,
! [A: $i] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(848,axiom,
! [A: $i,B: $i] :
( ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) @ A )
= ( times_times_real @ A @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_power__commutes) ).
thf(4444,plain,
! [A: $i,B: $i] :
( ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) @ A )
= ( times_times_real @ A @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2649,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[374]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_add__le__imp__le__left) ).
thf(3573,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_zcong__zprime__prod__zero) ).
thf(4333,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
| ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( 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(3954,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( ( 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 ) ) ) )
& ( ( ( 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 ) ) )
=> ( ( C != D )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(738,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_of__nat__0__less__iff) ).
thf(4049,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_power__decreasing) ).
thf(1329,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( times_times_nat @ A @ B ) )
= ( times_times_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_of__nat__mult) ).
thf(3775,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( times_times_nat @ A @ B ) )
= ( times_times_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ ( minus_minus_nat @ B @ C ) ) ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_zdiff__int__split) ).
thf(3141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ ( minus_minus_nat @ B @ C ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ zero_zero_int ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ zero_zero_int ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ ( minus_minus_nat @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(544,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ ( abs_abs_int @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_zero__le__zpower__abs) ).
thf(3311,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ ( abs_abs_int @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ D ) )
& ( ( hAPP_nat_real @ ( power_power_real @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_realpow__pos__nth__unique) ).
thf(4301,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ D ) )
& ( ( hAPP_nat_real @ ( power_power_real @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(223,axiom,
! [A: $i] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_eq__0__number__of) ).
thf(2023,plain,
! [A: $i] :
( ( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( zero_zero_nat
= ( number_number_of_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(551,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_zero__less__nat__eq) ).
thf(3326,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1037,axiom,
! [A: $i] :
( ( times_times_int @ A @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_cube__square) ).
thf(5166,plain,
! [A: $i] :
( ( times_times_int @ A @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_realpow__pos__nth) ).
thf(1964,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
& ( ( hAPP_nat_real @ ( power_power_real @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( 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(4276,plain,
! [A: $i,B: $i] :
( ( B != zero_zero_real )
=> ( ( A != zero_zero_real )
=> ( ( times_times_real @ B @ A )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(712,axiom,
! [A: $i] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_mult__0__right) ).
thf(3922,plain,
! [A: $i] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3407,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1207,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( times_times_int @ A @ B ) ) @ C )
= ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(5705,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( times_times_int @ A @ B ) ) @ C )
= ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(352,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_rel__simps_I23_J) ).
thf(2561,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3094,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[491]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(4721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[916]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1461,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ B @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(2868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[434]) ).
thf(1176,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(5620,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[1176]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_zless__int) ).
thf(2312,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(472,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3010,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[472]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( plus_plus_nat @ C @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_divides__add__revr) ).
thf(2455,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( plus_plus_nat @ C @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_zle__int) ).
thf(4750,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1153,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ 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(5547,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( times_times_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4744,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[923]) ).
thf(257,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( minus_minus_nat @ ( nat @ 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(2172,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( minus_minus_nat @ ( nat @ t ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(899,axiom,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_add__0__left) ).
thf(4648,plain,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(739,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_le__refl) ).
thf(4054,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ A ) ) @ ( nat @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_nat__mono__iff) ).
thf(3428,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ A ) ) @ ( nat @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ A ) ) @ ( nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ( 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(5662,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(306,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_of__nat__0__less__iff) ).
thf(2349,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_less__imp__le__nat) ).
thf(2038,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(67,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_of__nat__less__0__iff) ).
thf(1446,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2317,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) ) @ ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1107,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(5387,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_power__le__imp__le__exp) ).
thf(2781,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(867,axiom,
! [A: $i] :
( ( 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(4530,plain,
! [A: $i] :
( ( 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)],[867]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_le__number__of) ).
thf(1263,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(980,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( 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(4970,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( zero_zero_int
= ( plus_plus_int @ A @ A ) )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( zero_zero_int
= ( plus_plus_int @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rel__simps_I48_J) ).
thf(5234,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( bit0 @ A )
= ( bit0 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit0 @ A )
= ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_divides__ge) ).
thf(1552,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1136,axiom,
! [A: $i,B: $i] :
( ( 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(5498,plain,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_zprime__zdvd__power) ).
thf(2006,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(1799,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[168]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_of__nat__le__iff) ).
thf(4231,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(483,axiom,
is_int @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_x____) ).
thf(3064,plain,
is_int @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3005,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[470]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3920,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3162,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[505]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
<=> ? [D: $i] :
( ( is_int @ D )
& ( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_zcong__iff__lin) ).
thf(1825,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ? [D: $i] :
( ( is_int @ D )
& ( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) )
& ( ? [D: $i] :
( ( is_int @ D )
& ( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) )
<=> ( ! [C: $i] :
( ( B
= ( hAPP_nat_int @ semiri1621563631at_int @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_split__nat) ).
thf(2968,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) )
=> ( ! [C: $i] :
( ( B
= ( hAPP_nat_int @ semiri1621563631at_int @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) ) ) )
& ( ( ! [C: $i] :
( ( B
= ( hAPP_nat_int @ semiri1621563631at_int @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(2504,plain,
! [A: $i,B: $i,C: $i] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5576,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1163]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_of__nat__power) ).
thf(2450,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_real @ ( power_power_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(636,axiom,
! [A: $i] :
( ( nat @ ( number_number_of_int @ A ) )
= ( number_number_of_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_nat__number__of) ).
thf(3654,plain,
! [A: $i] :
( ( nat @ ( number_number_of_int @ A ) )
= ( number_number_of_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_mult__left__le__imp__le) ).
thf(1478,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1214,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( zero_zero_int = A )
<=> ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_zero__reorient) ).
thf(5726,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( zero_zero_int = A )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( zero_zero_int = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_add__less__cancel__right) ).
thf(1451,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1031,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).
thf(5149,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1456,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( minus_minus_real @ A @ B ) ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( minus_minus_real @ A @ B ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(47,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1382,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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)],[47]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_less__imp__diff__less) ).
thf(2487,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(430,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I2_J) ).
thf(2845,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( A
= ( nat @ B ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( B
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2598,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( A
= ( nat @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( B
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( A = zero_zero_nat ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( B
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( A = zero_zero_nat ) ) )
=> ( A
= ( nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( C = B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1062_zcong__less__eq) ).
thf(3354,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( C = B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint) ).
thf(2387,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1429,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(525,axiom,
! [A: $i] :
( ( 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(3247,plain,
! [A: $i] :
( ( 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)],[525]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ ( abs_abs_int @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_dvd__int__iff) ).
thf(2766,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ ( abs_abs_int @ A ) ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ ( abs_abs_int @ A ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( plus_plus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_trans__le__add1) ).
thf(3692,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_real__mult__le__cancel__iff2) ).
thf(1599,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_add__pos__pos) ).
thf(1246,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_803_less__eq__int__code_I15_J) ).
thf(4086,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( 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(2756,plain,
! [A: $i,B: $i] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_add__le__cancel__right) ).
thf(1627,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ ( 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(2370,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( times_times_nat @ A @ B ) ) @ C )
= ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( times_times_nat @ A @ B ) ) @ C )
= ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(824,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4361,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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(1525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ( A = B )
=> ( C = D ) )
& ( ( C = D )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
( ( 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(5245,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( 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(3755,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ( A = B )
=> ( C = D ) )
& ( ( C = D )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4644,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) )
=> ( hBOOL @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_dvd_Oless__imp__triv) ).
thf(2208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) )
=> ( hBOOL @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( minus_minus_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_zcong__def) ).
thf(4476,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( minus_minus_int @ A @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( minus_minus_int @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(104,axiom,
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_not__one__less__zero) ).
thf(1563,plain,
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1119,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_int__0__neq__1) ).
thf(5419,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(1118,axiom,
( ( hAPP_nat_nat @ ( 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(5417,plain,
( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( times_times_nat @ A @ B ) )
= ( times_times_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_of__nat__mult) ).
thf(3508,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( times_times_nat @ A @ B ) )
= ( times_times_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(879,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_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(4572,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(768,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(4148,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1019,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_add__0) ).
thf(5112,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(1156,axiom,
! [A: $i] :
( ( nat @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_nat__int) ).
thf(5557,plain,
! [A: $i] :
( ( nat @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2788,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[414]) ).
thf(1151,axiom,
( one_one_int
= ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_transfer__int__nat__numerals_I2_J) ).
thf(5544,plain,
( one_one_int
= ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_less__eq__real__def) ).
thf(1318,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1209,axiom,
! [A: $i,B: $i] :
( ( 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(5711,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( plus_plus_int @ B @ A )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( plus_plus_int @ B @ A )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[615]) ).
thf(405,axiom,
! [A: $i] :
( ( hAPP_nat_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(2761,plain,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) )
=> ( C = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_zcong__zless__imp__eq) ).
thf(3279,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) )
=> ( C = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(956,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_rel__simps_I9_J) ).
thf(4889,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1161,axiom,
! [A: $i] :
( ( hAPP_nat_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(5571,plain,
! [A: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_mult__le__cancel2) ).
thf(3592,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(728,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_not__add__less1) ).
thf(3999,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(459,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2963,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_diff__eq__diff__less) ).
thf(1286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(548,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ tn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_tn0) ).
thf(3321,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ tn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1127,axiom,
! [A: $i,B: $i] :
( ( ( 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(5447,plain,
! [A: $i,B: $i] :
( ( ( ( number_number_of_nat @ A )
= B )
=> ( B
= ( number_number_of_nat @ A ) ) )
& ( ( B
= ( number_number_of_nat @ A ) )
=> ( ( number_number_of_nat @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( hAPP_nat_real @ ( power_power_real @ C ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_power__inject__exp) ).
thf(1466,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( ( hAPP_nat_real @ ( power_power_real @ C ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_real @ ( power_power_real @ C ) @ A )
= ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( 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(2402,plain,
! [A: $i,B: $i] :
( ( 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)],[318]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) ) @ ( minus_minus_nat @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_le__diff__iff) ).
thf(2189,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) ) @ ( minus_minus_nat @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) ) @ ( minus_minus_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_zcong__zmult__prop3) ).
thf(3422,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1142,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( hAPP_nat_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(5513,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( ( hAPP_nat_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 ) ) )
& ( ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_power__increasing) ).
thf(2995,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1079,axiom,
~ ! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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 @ ( hAPP_nat_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(5295,plain,
~ ! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_dvd_Oless__le__not__le) ).
thf(2617,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(730,axiom,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ A ) @ one_one_nat )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4004,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ A ) @ one_one_nat )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[730]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_add__less__imp__less__right) ).
thf(2338,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ B @ A ) ) @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_add__neg__neg) ).
thf(3675,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ B @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(810,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( 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(4308,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(448,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_power__0) ).
thf(2909,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_nat__dvd__not__less) ).
thf(3807,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) ) @ C ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_le__diff__conv) ).
thf(2144,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( plus_plus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( ( 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(4921,plain,
! [A: $i,B: $i] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(217,axiom,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_add__0) ).
thf(2001,plain,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4131,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[762]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4872,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[952]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( B != zero_zero_real )
=> ( ( hAPP_nat_real @ ( power_power_real @ B ) @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_field__power__not__zero) ).
thf(2585,plain,
! [A: $i,B: $i] :
( ( B != zero_zero_real )
=> ( ( hAPP_nat_real @ ( power_power_real @ B ) @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( nat @ B ) )
= ( times_times_int @ A @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( minus_minus_nat @ ( nat @ B ) @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_Euler_Oaux__1) ).
thf(2570,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( nat @ B ) )
= ( times_times_int @ A @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( minus_minus_nat @ ( nat @ B ) @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(876,axiom,
! [A: $i] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_mult__1__right) ).
thf(4562,plain,
! [A: $i] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(860,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_number__of__Pls) ).
thf(4503,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(645,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ B ) ) @ ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_zmult__zless__mono2__lemma) ).
thf(3686,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ B ) ) @ ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_zpower__zdvd__prop1) ).
thf(4599,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_dvd_Ole__imp__less__or__eq) ).
thf(3396,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(556,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( nat @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_Int2_Oaux__2) ).
thf(3343,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( nat @ ( minus_minus_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1251,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1134,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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(5483,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
=> ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) )
& ( ( ( A != zero_zero_int )
| ( B != zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ ( minus_minus_nat @ B @ C ) ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
& ! [D: $i] :
( ( B
= ( plus_plus_nat @ C @ D ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_nat__diff__split) ).
thf(2677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( minus_minus_nat @ B @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
& ! [D: $i] :
( ( B
= ( plus_plus_nat @ C @ D ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
& ! [D: $i] :
( ( B
= ( plus_plus_nat @ C @ D ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( minus_minus_nat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4708,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[913]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( legendre @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Residues_OLegendre) ).
thf(4685,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( legendre @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(157,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_zprime__def) ).
thf(1754,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ A ) )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_dvd_Oless__asym) ).
thf(2292,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3358,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_of__nat__less__imp__less) ).
thf(4613,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1029,axiom,
~ ! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( hAPP_nat_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(5138,plain,
~ ! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( hAPP_nat_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)],[1029]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( times_times_nat @ A @ B ) ) @ C )
= ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_power__mult__distrib) ).
thf(2149,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ ( times_times_nat @ A @ B ) ) @ C )
= ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[701]) ).
thf(1074,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zero__is__num__zero) ).
thf(5278,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1140,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_numeral__1__eq__1) ).
thf(5508,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(26,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_real__le__refl) ).
thf(1301,plain,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_add__lessD1) ).
thf(3888,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1144,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_of__nat__mult) ).
thf(5525,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3111,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[494]) ).
thf(970,axiom,
! [A: $i] :
( ( 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(4943,plain,
! [A: $i] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_unique__quotient__lemma__neg) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_real @ ( 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(1884,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) )
& ( ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) )
=> ( ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3519,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ C @ A ) ) @ ( plus_plus_int @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( ( 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(2981,plain,
! [A: $i,B: $i] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_q__neg__lemma) ).
thf(1752,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ C @ A ) ) @ ( plus_plus_nat @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(854,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_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(4465,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( A != zero_zero_real ) )
& ( ( A != zero_zero_real )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( 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(5097,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(971,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(4946,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(386,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( 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(2695,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( B != zero_zero_int )
=> ( ( A != zero_zero_int )
=> ( ( times_times_int @ B @ A )
!= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(1148,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ ( 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(5535,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1204,axiom,
! [A: $i,B: $i] : ( is_int @ ( hAPP_nat_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
thf(5698,plain,
! [A: $i,B: $i] : ( is_int @ ( hAPP_nat_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(566,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_dvd_Oneq__le__trans) ).
thf(3372,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4341,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[818]) ).
thf(800,axiom,
! [A: $i] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_minus__nat_Odiff__0) ).
thf(4268,plain,
! [A: $i] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_gr__implies__not0) ).
thf(2727,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(522,axiom,
! [A: $i] :
( ! [B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) )
<=> ! [B: $i] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_transfer__int__nat__quantifiers_I1_J) ).
thf(3234,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ! [B: $i] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ! [B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ? [C: $i] :
( B
= ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_le__iff__add) ).
thf(2048,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ? [C: $i] :
( B
= ( plus_plus_nat @ A @ C ) ) )
& ( ? [C: $i] :
( B
= ( plus_plus_nat @ A @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3925,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[713]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(2938,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( times_times_real @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_real__mult__order) ).
thf(1615,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( times_times_real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1110,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ 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(5395,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ 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)],[1110]) ).
thf(415,axiom,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_mult__1) ).
thf(2791,plain,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(626,axiom,
! [A: $i] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_mult__zero__right) ).
thf(3609,plain,
! [A: $i] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(377,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2657,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_mult__left__less__imp__less) ).
thf(1620,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(596,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_less__nat__zero__code) ).
thf(3472,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ A ) ) @ B ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2489,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ A ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_nat ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_nat ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( nat @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(488,axiom,
! [A: $i] :
( ( 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(3081,plain,
! [A: $i] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( 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(3945,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( times_times_int @ A @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) )
& ( ( ( A = zero_zero_int )
| ( B = zero_zero_int ) )
=> ( ( times_times_int @ A @ B )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( 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(4926,plain,
! [A: $i,B: $i] :
( ( 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)],[965]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3266,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[532]) ).
thf(383,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_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(2674,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_less__number__of) ).
thf(1535,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_dvd_Oless__imp__not__eq) ).
thf(2806,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(142,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_less__zeroE) ).
thf(1701,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_mult__less__imp__less__left) ).
thf(3590,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2716,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[393]) ).
thf(625,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_rel__simps_I28_J) ).
thf(3604,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_diff__eq__diff__less__eq) ).
thf(1520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3404,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_less__not__refl2) ).
thf(2817,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4769,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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 ) ) )
& ( ( B
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) )
=> ( ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B )
= ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_add__less__cancel__left) ).
thf(4505,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(624,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( nat @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_zless__nat__eq__int__zless) ).
thf(3599,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( nat @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1152,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(5546,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[1152]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_mult__less__imp__less__right) ).
thf(3751,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_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(4112,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) )
& ( ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(929,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ B @ one_one_int ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_zle__add1__eq__le) ).
thf(4764,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ B @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1258,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1123,axiom,
! [A: $i] :
( ( 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(5432,plain,
! [A: $i] :
( ( 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)],[1123]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ A @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_diff__less) ).
thf(1675,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ A @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3023,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[477]) ).
thf(131,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_mult__1__right) ).
thf(1669,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1021,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_pos2) ).
thf(5118,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1101,axiom,
! [A: $i] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ A )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_power__one) ).
thf(5363,plain,
! [A: $i] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_dvd_Ole__neq__trans) ).
thf(2891,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(994,axiom,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_IH) ).
thf(5011,plain,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_mult__less__imp__less__left) ).
thf(1371,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_dvd_Oord__eq__less__trans) ).
thf(3208,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_add__less__cancel__right) ).
thf(4236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(785,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_realpow__minus__mult) ).
thf(4218,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_nat__mult__less__cancel1) ).
thf(3002,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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 ) )
& ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B )
= C )
=> ( ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B )
= ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(1013,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(5086,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(7,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_less__special_I1_J) ).
thf(1239,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_add__le__imp__le__right) ).
thf(2442,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( nat @ ( abs_abs_int @ ( times_times_int @ A @ B ) ) )
= ( times_times_nat @ ( nat @ ( abs_abs_int @ A ) ) @ ( nat @ ( abs_abs_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_nat__abs__mult__distrib) ).
thf(3783,plain,
! [A: $i,B: $i] :
( ( nat @ ( abs_abs_int @ ( times_times_int @ A @ B ) ) )
= ( times_times_nat @ ( nat @ ( abs_abs_int @ A ) ) @ ( nat @ ( abs_abs_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(3487,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( minus_minus_int @ A @ B ) ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_less__bin__lemma) ).
thf(2055,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( minus_minus_int @ A @ B ) ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( minus_minus_int @ A @ B ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(687,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= B )
<=> ( ( A
= ( nat @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_int__eq__iff) ).
thf(3832,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= B )
=> ( ( A
= ( nat @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) ) )
& ( ( ( A
= ( nat @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1765,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(2457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[332]) ).
thf(947,axiom,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_mult__1) ).
thf(4854,plain,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_nat__add__commute) ).
thf(1897,plain,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[542]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_less__eq__int__code_I16_J) ).
thf(3568,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_pos__add__strict) ).
thf(2573,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_mult__right__less__imp__less) ).
thf(2319,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( times_times_real @ A @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_zero__le__mult__iff) ).
thf(1356,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( times_times_real @ A @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( times_times_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1030,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( hAPP_nat_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(5143,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(966,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_less__imp__of__nat__less) ).
thf(4929,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1194,axiom,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
thf(5671,plain,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(276,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_bin__less__0__simps_I1_J) ).
thf(2229,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_int_bool @ ( 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(2214,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(666,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ A @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_less__add__one) ).
thf(3764,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ A @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(1088,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ ( power_power_real @ ( plus_plus_real @ A @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( 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(5325,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ ( power_power_real @ ( plus_plus_real @ A @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( 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)],[1088]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4620,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ B @ A ) ) @ ( plus_plus_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1589,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_power__less__imp__less__exp) ).
thf(4073,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(443,axiom,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_add__0__right) ).
thf(2896,plain,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(789,axiom,
is_int @ s1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s1____) ).
thf(4228,plain,
is_int @ s1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(631,axiom,
! [A: $i] :
( ? [B: $i] :
( ( is_int @ B )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
<=> ? [B: $i] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_transfer__int__nat__quantifiers_I2_J) ).
thf(3631,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( is_int @ B )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ? [B: $i] : ( hBOOL @ ( hAPP_int_bool @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ? [B: $i] :
( ( is_int @ B )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_add__less__imp__less__right) ).
thf(1853,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(537,axiom,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_plus__nat_Oadd__0) ).
thf(3287,plain,
! [A: $i] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(942,axiom,
! [A: $i] :
( ( hAPP_nat_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(4828,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ C @ B ) ) @ ( minus_minus_nat @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_less__diff__iff) ).
thf(2906,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ C @ B ) ) @ ( minus_minus_nat @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ C @ B ) ) @ ( minus_minus_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_of__nat__add) ).
thf(3419,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(38,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ A @ A ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1349,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ A @ A ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( 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(5303,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(1135,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( one_one_int = A )
<=> ( A = one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_one__reorient) ).
thf(5491,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( one_one_int = A )
=> ( A = one_one_int ) )
& ( ( A = one_one_int )
=> ( one_one_int = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_of__nat__power) ).
thf(4601,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( minus_minus_nat @ B @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_dvd__diffD) ).
thf(1542,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ ( minus_minus_nat @ B @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(937,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_rel__simps_I27_J) ).
thf(4805,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(1055,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add__numeral__0) ).
thf(5222,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(765,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_757_realpow__minus__mult) ).
thf(4139,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_zcong__trans) ).
thf(3710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ( 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(4958,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1114,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pls__def) ).
thf(5407,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(904,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( 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(4667,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( abs_abs_int @ A )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) )
& ( ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) )
=> ( ( abs_abs_int @ A )
= one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(772,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_not__less0) ).
thf(4176,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_nat__mult__commute) ).
thf(3138,plain,
! [A: $i,B: $i] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1174,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Numeral1__eq1__nat) ).
thf(5616,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(435,axiom,
! [A: $i] :
( ( 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(2871,plain,
! [A: $i] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_of__nat__add) ).
thf(4107,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_real @ semiri132038758t_real @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1071,axiom,
! [A: $i] :
( ( 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(5267,plain,
! [A: $i] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4388,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) ) @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(2180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[260]) ).
thf(1103,axiom,
( ( t = one_one_int )
=> ? [A: $i,B: $i] :
( ( is_int @ A )
& ( is_int @ B )
& ( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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(5367,plain,
( ( t = one_one_int )
=> ? [A: $i,B: $i] :
( ( is_int @ A )
& ( is_int @ B )
& ( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1103]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( 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(4401,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( 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)],[835]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_zless__linear) ).
thf(2632,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
| ( A = B )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_le__antisym) ).
thf(4541,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_of__nat__le__iff) ).
thf(1339,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(367,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2625,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(878,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( number_number_of_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_number__of__is__id) ).
thf(4569,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( number_number_of_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5392,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1109]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2785,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[413]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_add__less__imp__less__left) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(290,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_not__add__less2) ).
thf(2289,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_dvd_Oless__imp__neq) ).
thf(3893,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1158,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
thf(5563,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_less__int__code_I16_J) ).
thf(2824,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(500,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint) ).
thf(3133,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
<=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_nat__mult__dvd__cancel__disj_H) ).
thf(3055,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4462,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[853]) ).
thf(961,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rel__simps_I10_J) ).
thf(4911,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(285,axiom,
! [A: $i] :
( ( 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(2267,plain,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( D = B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_zcong__eq__trans) ).
thf(4731,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( D = B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ A ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_add__le__imp__le__left) ).
thf(1821,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(678,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_less__special_I2_J) ).
thf(3800,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(798,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4264,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ B @ A ) ) @ ( times_times_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1169,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nat__number__of__Pls) ).
thf(5599,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1076,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_one__neq__zero) ).
thf(5286,plain,
one_one_int != zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3165,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[506]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_dvd_Oless__imp__not__less) ).
thf(4181,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(722,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3971,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ zprime @ A ) )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1344,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_zcong__zdiff) ).
thf(2329,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(429,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_mult__1) ).
thf(2842,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1396,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1065,axiom,
hBOOL @ ( hAPP_int_bool @ ( 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(5254,plain,
hBOOL @ ( hAPP_int_bool @ ( 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)],[1065]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_power__le__imp__le__exp) ).
thf(1474,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2835,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) ) @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ( 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(5646,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ A )
& ( is_int @ C ) )
=> ( ( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_zcong__not__zero) ).
thf(3917,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1063,axiom,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rel__simps_I49_J) ).
thf(5248,plain,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(641,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_zero__less__one) ).
thf(3674,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(523,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ A @ pls )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_diff__bin__simps_I1_J) ).
thf(3241,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( minus_minus_int @ A @ pls )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(163,axiom,
? [A: $i] :
( ( is_int @ A )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ A ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( 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(1775,plain,
? [A: $i] :
( ( is_int @ A )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ s1 @ A ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ! [B: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( 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)],[163]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_mult__right__le__imp__le) ).
thf(1726,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(293,axiom,
! [A: $i] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_eq__number__of__0) ).
thf(2303,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( ( number_number_of_nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ C @ A ) ) @ ( plus_plus_nat @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(743,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_le__neq__implies__less) ).
thf(4067,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2725,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ B @ A ) ) @ ( plus_plus_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(111,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__special_I3_J) ).
thf(1594,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( number267125858f_real @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( times_times_int @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_zprime__power__zdvd__cancel__right) ).
thf(1699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( times_times_int @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( number_number_of_int @ min ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_zcong__neg__1__impl__ne__1) ).
thf(2212,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( number_number_of_int @ min ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ one_one_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(256,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_bin__less__0__simps_I2_J) ).
thf(2171,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1048,axiom,
( ( hAPP_nat_real @ ( 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(5197,plain,
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1015,axiom,
! [A: $i] :
( ( 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(5094,plain,
! [A: $i] :
( ( 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)],[1015]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ( 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(5218,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_int @ B )
& ( is_int @ C ) )
=> ( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(66,axiom,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_zero__less__one) ).
thf(1445,plain,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1185,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_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 @ ( hAPP_nat_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 ) ) ) @ ( hAPP_nat_int @ ( 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 ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_zdiff__power3) ).
thf(5641,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_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 @ ( hAPP_nat_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 ) ) ) @ ( hAPP_nat_int @ ( 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 ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2999,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[468]) ).
thf(1202,axiom,
! [A: $i] :
( ( 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(5693,plain,
! [A: $i] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(558,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_nat__less__eq__zless) ).
thf(3348,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ ( nat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(3876,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
=> ( ( A = zero_zero_nat )
| ( B = C ) ) )
& ( ( ( A = zero_zero_nat )
| ( B = C ) )
=> ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2693,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ A @ C ) ) @ ( minus_minus_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ A ) ) @ ( nat @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_zless__nat__conj) ).
thf(2984,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ A ) ) @ ( nat @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ A ) ) @ ( nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(4481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[857]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( plus_plus_int @ B @ C ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4473,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( plus_plus_int @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ ( plus_plus_int @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_one__less__power) ).
thf(3380,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(103,axiom,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1562,plain,
hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1124,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_semiring__numeral__1__eq__1) ).
thf(5435,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(783,axiom,
! [A: $i,B: $i] :
( ( ( 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(4207,plain,
! [A: $i,B: $i] :
( ( ( ( times_times_nat @ A @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( ( times_times_nat @ A @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4741,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[922]) ).
thf(238,axiom,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_nat__mult__1) ).
thf(2096,plain,
! [A: $i] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_diff__eq__diff__less__eq) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(958,axiom,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ s ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ s ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( 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(4901,plain,
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ s ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ s ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( 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)],[958]) ).
thf(1145,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_semiring__numeral__0__eq__0) ).
thf(5528,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_nat__mult__dvd__cancel1) ).
thf(2665,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(939,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
<=> ? [C: $i] :
( B
= ( plus_plus_int @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_zle__iff__zadd) ).
thf(4813,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ? [C: $i] :
( B
= ( plus_plus_int @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) ) )
& ( ? [C: $i] :
( B
= ( plus_plus_int @ A @ ( hAPP_nat_int @ semiri1621563631at_int @ C ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4735,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( minus_minus_nat @ B @ A ) ) @ ( minus_minus_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(866,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_rel__simps_I19_J) ).
thf(4529,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ C @ A ) ) @ ( plus_plus_real @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2629,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[369]) ).
thf(1197,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_zero__neq__one) ).
thf(5678,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2564,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[354]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_790_zpower__zadd__distrib) ).
thf(5652,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(444,axiom,
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_not__one__less__zero) ).
thf(2899,plain,
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(991,axiom,
! [A: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( 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(5003,plain,
! [A: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4986,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[985]) ).
thf(1117,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__0__right) ).
thf(5414,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(836,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_dvd_Oorder__refl) ).
thf(4405,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_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(3031,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = one_one_nat )
| ( B = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( 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(1809,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( times_times_int @ A @ B )
= zero_zero_int )
=> ( ( A = zero_zero_int )
| ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(457,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( bit1 @ A )
= min )
<=> ( A = min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_rel__simps_I47_J) ).
thf(2952,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( bit1 @ A )
= min )
=> ( A = min ) )
& ( ( A = min )
=> ( ( bit1 @ A )
= min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2652,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(539,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( ( nat @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_nat__le__0) ).
thf(3293,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
=> ( ( nat @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_add__eq__self__zero) ).
thf(2878,plain,
! [A: $i,B: $i] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_zless__le) ).
thf(1684,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) ) @ ( plus_plus_nat @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_less__imp__of__nat__less) ).
thf(1472,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ semiri132038758t_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1099,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_numeral__1__eq__1) ).
thf(5358,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1027,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_Bit1__Min) ).
thf(5133,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(632,axiom,
( ( hAPP_nat_real @ semiri132038758t_real @ one_one_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_of__nat__1) ).
thf(3640,plain,
( ( hAPP_nat_real @ semiri132038758t_real @ one_one_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1172,axiom,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_power__0__left) ).
thf(5607,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_rel__simps_I31_J) ).
thf(2397,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3842,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[688]) ).
thf(1024,axiom,
! [A: $i] :
( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_number__of__int) ).
thf(5125,plain,
! [A: $i] :
( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(116,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1611,plain,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(264,axiom,
! [A: $i] :
( ( number_number_of_nat @ A )
= ( nat @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_nat__number__of__def) ).
thf(2192,plain,
! [A: $i] :
( ( number_number_of_nat @ A )
= ( nat @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(705,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_rel__simps_I15_J) ).
thf(3904,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1221,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_rel__simps_I51_J) ).
thf(5748,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( bit1 @ A )
= ( bit1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit1 @ A )
= ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ ( minus_minus_nat @ B @ C ) ) )
<=> ~ ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
| ? [D: $i] :
( ( B
= ( plus_plus_nat @ C @ D ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_nat__diff__split__asm) ).
thf(1941,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( minus_minus_nat @ B @ C ) ) )
=> ~ ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
| ? [D: $i] :
( ( B
= ( plus_plus_nat @ C @ D ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) ) )
& ( ~ ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) )
| ? [D: $i] :
( ( B
= ( plus_plus_nat @ C @ D ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ ( minus_minus_nat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1167,axiom,
! [A: $i] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_rel__simps_I45_J) ).
thf(5592,plain,
! [A: $i] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2821,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[423]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_add__less__cancel__right) ).
thf(2720,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(441,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_power__one__right) ).
thf(2888,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( 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(4255,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_int @ A )
& ( is_int @ B )
& ( is_int @ C )
& ( is_int @ D ) )
=> ( ( ( ( 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 ) ) )
& ( ( ( A = C )
| ( B = D ) )
=> ( ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2513,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[342]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( 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(2567,plain,
! [A: $i,B: $i] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1547,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1004,axiom,
( ( hAPP_nat_int @ ( 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(5047,plain,
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_diff__add__inverse) ).
thf(1748,plain,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1211,axiom,
! [A: $i,B: $i] :
( ( 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(5716,plain,
! [A: $i,B: $i] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) ) @ E ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_less__number__of__int__code) ).
thf(2060,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( 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(1743,plain,
! [A: $i,B: $i] :
( ( 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)],[152]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(973,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OBit0) ).
thf(4950,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3260,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[530]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129_zcong__scalar) ).
thf(2588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ E ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_unique__quotient__lemma) ).
thf(3786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ E ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(957,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
<=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_le__nat__number__of) ).
thf(4894,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ) )
& ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( number_number_of_nat @ A ) ) @ ( number_number_of_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(4961,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[977]) ).
thf(1010,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(5079,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ one_one_int @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(814,axiom,
! [A: $i,B: $i] :
( ( ( 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(4324,plain,
! [A: $i,B: $i] :
( ( ( ( times_times_nat @ A @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( ( times_times_nat @ A @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4630,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) ) @ ( minus_minus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1230,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ B @ A ) ) @ ( plus_plus_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_power__increasing) ).
thf(2160,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_mult__less__cancel2) ).
thf(3642,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4905,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[959]) ).
thf(166,axiom,
( tn
= ( minus_minus_nat @ ( nat @ t ) @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_tn) ).
thf(1790,plain,
( tn
= ( minus_minus_nat @ ( nat @ t ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( nat @ B )
= ( nat @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_transfer__nat__int__relations_I1_J) ).
thf(3305,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( ( ( nat @ B )
= ( nat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( nat @ B )
= ( nat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_mult__less__cancel1) ).
thf(1658,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(920,axiom,
is_int @ m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_m1____) ).
thf(4737,plain,
is_int @ m1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1184,axiom,
! [A: $i] :
( ( 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(5638,plain,
! [A: $i] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(334,axiom,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2468,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[334]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1199,axiom,
! [A: $i] :
( ( number267125858f_real @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_real @ semiri132038758t_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_number__of__int) ).
thf(5684,plain,
! [A: $i] :
( ( number267125858f_real @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) )
= ( hAPP_nat_real @ semiri132038758t_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_mult__less__imp__less__right) ).
thf(4522,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1069,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_semiring__norm_I113_J) ).
thf(5262,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1637,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ B @ A ) ) @ ( times_times_real @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(495,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_le__special_I3_J) ).
thf(3114,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ C @ B ) ) @ E ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ D @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_zcong__zmult__prop1) ).
thf(3334,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ C @ B ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ D @ B ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ D @ B ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ ( times_times_int @ C @ B ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_less__add__eq__less) ).
thf(4222,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_power__increasing__iff) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3475,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ B @ A ) ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_add__le__cancel__left) ).
thf(3026,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_power__strict__increasing__iff) ).
thf(2429,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ A )
= ( hAPP_nat_nat @ semiri984289939at_nat @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_of__nat__eq__iff) ).
thf(3823,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ A )
= ( hAPP_nat_nat @ semiri984289939at_nat @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ semiri984289939at_nat @ A )
= ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1157,axiom,
! [A: $i] :
( ( 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(5560,plain,
! [A: $i] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(999,axiom,
( ( plus_plus_int @ ( hAPP_nat_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(5030,plain,
( ( plus_plus_int @ ( hAPP_nat_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)],[999]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( 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(2219,plain,
! [A: $i,B: $i] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5154,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1033]) ).
thf(793,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_zcong__refl) ).
thf(4241,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3847,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[690]) ).
thf(446,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_one__neq__zero) ).
thf(2903,plain,
one_one_nat != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(936,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_rel__simps_I22_J) ).
thf(4800,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(135,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_zcong__id) ).
thf(1679,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( 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(3412,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( ( ( number_number_of_int @ A )
= B )
=> ( B
= ( number_number_of_int @ A ) ) )
& ( ( B
= ( number_number_of_int @ A ) )
=> ( ( number_number_of_int @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ B ) @ A )
!= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
thf(5106,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( B != zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ B ) @ A )
!= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(3041,plain,
! [A: $i,B: $i,C: $i] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_zcong__not) ).
thf(3853,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( plus_plus_nat @ ( nat @ B ) @ ( nat @ A ) )
= ( nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
thf(3769,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( plus_plus_nat @ ( nat @ B ) @ ( nat @ A ) )
= ( nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( 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(4875,plain,
! [A: $i,B: $i] :
( ( 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)],[953]) ).
thf(653,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_le0) ).
thf(3715,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(307,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_rel__simps_I11_J) ).
thf(2354,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(169,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_rel__simps_I26_J) ).
thf(1802,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_le__number__of) ).
thf(2379,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(981,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_mult__Bit0) ).
thf(4976,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1060,axiom,
( ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) )
= ( nat @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_transfer__nat__int__numerals_I4_J) ).
thf(5240,plain,
( ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) )
= ( nat @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( plus_plus_real @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_pos__add__strict) ).
thf(1284,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ ( plus_plus_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5633,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1181]) ).
thf(767,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_less__special_I2_J) ).
thf(4143,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(433,axiom,
! [A: $i] :
( ( zero_zero_real = A )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_zero__reorient) ).
thf(2860,plain,
! [A: $i] :
( ( ( zero_zero_real = A )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( zero_zero_real = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_real__less__def) ).
thf(1272,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_int__mult) ).
thf(5596,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( times_times_nat @ A @ B ) )
= ( times_times_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(840,axiom,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Nat_Oadd__0__right) ).
thf(4414,plain,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(940,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_zero__neq__one) ).
thf(4819,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_add__diff__cancel) ).
thf(1617,plain,
! [A: $i,B: $i] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ zero_zero_real ) )
<=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_mult__le__0__iff) ).
thf(1404,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ zero_zero_real ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( 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(2247,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( 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)],[280]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( nat @ ( plus_plus_int @ B @ A ) )
= ( plus_plus_nat @ ( nat @ B ) @ ( nat @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_nat__add__distrib) ).
thf(2558,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( nat @ ( plus_plus_int @ B @ A ) )
= ( plus_plus_nat @ ( nat @ B ) @ ( nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1179,axiom,
( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ 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(5628,plain,
( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1216,axiom,
( ( hAPP_nat_nat @ ( 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(5736,plain,
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(322,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_less__not__refl) ).
thf(2426,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1981,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C ) ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) ) @ ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(862,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_two__realpow__ge__one) ).
thf(4510,plain,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) @ C ) )
= ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zadd__int__left) ).
thf(5504,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) @ C ) )
= ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_add__less__cancel__left) ).
thf(1485,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(987,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_add_Ocomm__neutral) ).
thf(4991,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( nat @ ( minus_minus_int @ B @ one_one_int ) ) ) @ one_one_int ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_Little__Fermat) ).
thf(2511,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( nat @ ( minus_minus_int @ B @ one_one_int ) ) ) @ one_one_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4634,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[894]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2030,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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 ) ) )
& ( ( ( A = zero_zero_int )
& ( B = zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ) @ zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(788,axiom,
! [A: $i,B: $i] :
( ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) @ A )
= ( times_times_nat @ A @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_power__commutes) ).
thf(4225,plain,
! [A: $i,B: $i] :
( ( times_times_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) @ A )
= ( times_times_nat @ A @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_dvd_Oorder__trans) ).
thf(3256,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1012,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hAPP_nat_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(5083,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ one_one_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2013,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ pls ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[222]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3401,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[576]) ).
thf(227,axiom,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_real__mult__1) ).
thf(2045,plain,
! [A: $i] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ A @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_zero__le__mult__iff) ).
thf(3171,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ A @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3447,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( minus_minus_int @ B @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_norR__mem__unique__aux) ).
thf(2347,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( minus_minus_int @ B @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(1998,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[216]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( ( nat @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_nat @ ( nat @ A ) @ ( nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_nat__diff__distrib) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( ( nat @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_nat @ ( nat @ A ) @ ( nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(202,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_tpos) ).
thf(1940,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(873,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( minus_minus_nat @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_zero__less__diff) ).
thf(4548,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( minus_minus_nat @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( minus_minus_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ zero_zero_int ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_IntPrimes_Ozcong__zero) ).
thf(4289,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ zero_zero_int ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(900,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ A ) ) @ zero_zero_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_even__less__0__iff) ).
thf(4651,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ A ) ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ zero_zero_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ A @ A ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(629,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ min ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_rel__simps_I13_J) ).
thf(3620,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ min ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ min ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4424,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[843]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( C = A )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_dvd_Oord__less__eq__trans) ).
thf(3457,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( C = A )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_divides__div__not) ).
thf(1649,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2078,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[234]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_dvd_Oless__imp__not__eq2) ).
thf(1913,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(901,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_less__special_I1_J) ).
thf(4656,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(294,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_of__nat__less__two__power) ).
thf(2310,plain,
! [A: $i] : ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ semiri132038758t_real @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3874,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4997,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[989]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( times_times_int @ A @ B ) ) @ C )
= ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_power__mult__distrib) ).
thf(5510,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( times_times_int @ A @ B ) ) @ C )
= ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(921,axiom,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_nat__mult__1__right) ).
thf(4738,plain,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5115,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1020]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ B )
<=> ( hBOOL @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ B ) )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_imp__le__cong) ).
thf(3928,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) ) )
=> ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ A ) ) )
& ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(776,axiom,
( one_one_nat
= ( nat @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_transfer__nat__int__numerals_I2_J) ).
thf(4185,plain,
( one_one_nat
= ( nat @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( times_times_nat @ A @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_nat__0__less__mult__iff) ).
thf(3625,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( times_times_nat @ A @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( times_times_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_power__strict__decreasing) ).
thf(4646,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_dvd_Oless__imp__le) ).
thf(2997,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4102,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[753]) ).
thf(451,axiom,
! [A: $i] :
( ( 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(2919,plain,
! [A: $i] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(771,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4170,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( abs_abs_int @ A ) ) @ one_one_int ) )
=> ( A = zero_zero_int ) )
& ( ( A = zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( abs_abs_int @ A ) ) @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1108,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( 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(5389,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_dvd_Oless__le__trans) ).
thf(1866,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( minus_minus_int @ B @ one_one_int ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_zle__diff1__eq) ).
thf(2658,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( minus_minus_int @ B @ one_one_int ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( minus_minus_int @ B @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(1807,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[170]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( A != zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_zdvd__mult__cancel) ).
thf(4061,plain,
! [A: $i,B: $i,C: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( A != zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1043,axiom,
! [A: $i] :
( ( 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(5184,plain,
! [A: $i] :
( ( 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)],[1043]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_zcong__shift) ).
thf(3729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1253,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_Euler_Oaux1) ).
thf(3484,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( ( minus_minus_real @ A @ B )
= zero_zero_real )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_right__minus__eq) ).
thf(1639,plain,
! [A: $i,B: $i] :
( ( ( ( minus_minus_real @ A @ B )
= zero_zero_real )
=> ( A = B ) )
& ( ( A = B )
=> ( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(993,axiom,
! [A: $i] :
( ( 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(5008,plain,
! [A: $i] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1105,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).
thf(5382,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_Int2_Ozcong__zero) ).
thf(3383,plain,
! [A: $i,B: $i] :
( ( is_int @ B )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ A ) )
=> ( B = zero_zero_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4250,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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)],[795]) ).
thf(1096,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(5351,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ B )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( 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(5228,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4338,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[817]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_real @ ( power_power_real @ ( times_times_real @ A @ B ) ) @ C )
= ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3331,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_real @ ( power_power_real @ ( times_times_real @ A @ B ) ) @ C )
= ( times_times_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_diff__add__cancel) ).
thf(1646,plain,
! [A: $i,B: $i] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1085,axiom,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( 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(5315,plain,
! [A: $i] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( nat @ ( times_times_int @ B @ A ) )
= ( times_times_nat @ ( nat @ B ) @ ( nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_nat__mult__distrib) ).
thf(2389,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( nat @ ( times_times_int @ B @ A ) )
= ( times_times_nat @ ( nat @ B ) @ ( nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_add__less__imp__less__left) ).
thf(1476,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ A ) @ B ) )
<=> ? [C: $i] :
( ( is_int @ C )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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(5272,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ A ) @ B ) )
=> ? [C: $i] :
( ( is_int @ C )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ C ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ A ) ) ) )
& ( ? [C: $i] :
( ( is_int @ C )
& ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ C ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( quadRes @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4615,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2251,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(907,axiom,
is_int @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s____) ).
thf(4681,plain,
is_int @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_zpower__zpower) ).
thf(5191,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) @ C )
= ( hAPP_nat_int @ ( power_power_int @ A ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(565,axiom,
! [A: $i] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_mult__zero__left) ).
thf(3369,plain,
! [A: $i] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(760,axiom,
! [A: $i] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_mult__zero__left) ).
thf(4126,plain,
! [A: $i] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(736,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_le__special_I1_J) ).
thf(4042,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(933,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( abs_abs_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oabs__class_Oabs_000tc__Int__Oint) ).
thf(4791,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( abs_abs_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_power__decreasing) ).
thf(2004,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ C ) ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
| ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_real__le__linear) ).
thf(1244,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
| ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( plus_plus_nat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_add__pos__pos) ).
thf(2764,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( plus_plus_nat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__int__code_I13_J) ).
thf(3662,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3780,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[672]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2152,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[251]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2447,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[328]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_dvd_Oless__not__sym) ).
thf(1861,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2081,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3324,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1036,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_one__is__num__one) ).
thf(5164,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(769,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4153,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ one_one_int ) )
=> ( ( abs_abs_int @ A )
= one_one_int ) )
& ( ( ( abs_abs_int @ A )
= one_one_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1018,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ pls @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__Pls) ).
thf(5109,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ pls @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1025,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) @ A )
= ( times_times_int @ A @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_power__commutes) ).
thf(5128,plain,
! [A: $i,B: $i] :
( ( times_times_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) @ A )
= ( times_times_int @ A @ ( hAPP_nat_int @ ( power_power_int @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_trans__le__add2) ).
thf(2779,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(509,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ pls ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_rel__simps_I29_J) ).
thf(3181,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ pls ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ A ) ) @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(313,axiom,
! [A: $i] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__numeral__0__right) ).
thf(2384,plain,
! [A: $i] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
<=> ( ( A = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_nat__mult__dvd__cancel__disj) ).
thf(2475,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( A = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) ) )
& ( ( ( A = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(649,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_nat__neq__iff) ).
thf(3694,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(978,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( 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(4964,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ zero_zero_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_zcong__eq__zdvd__prop) ).
thf(2912,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ zero_zero_int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_mult__less__cancel__right__disj) ).
thf(1308,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ C ) ) )
| ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ zero_zero_real ) )
& ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1115,axiom,
( ( succ @ pls )
= ( bit1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_succ__Pls) ).
thf(5409,plain,
( ( succ @ pls )
= ( bit1 @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2198,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[266]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(309,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit0 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_rel__simps_I8_J) ).
thf(2362,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit0 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) ) ) )
<=> ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_zero__less__power__nat__eq__number__of) ).
thf(2162,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) ) ) )
=> ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) )
& ( ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ ( number_number_of_nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( minus_minus_nat @ B @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_less__diff__conv) ).
thf(3793,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( minus_minus_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ C ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( plus_plus_nat @ A @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( minus_minus_nat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( 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(2183,plain,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_add__leE) ).
thf(3351,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(89,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1513,plain,
! [A: $i] :
( ( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( times_times_real @ A @ A ) ) )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( times_times_real @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1022,axiom,
! [A: $i] :
( ( abs_abs_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( 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(5119,plain,
! [A: $i] :
( ( abs_abs_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ ( abs_abs_int @ A ) ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1052,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( 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(5211,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( abs_abs_int @ A )
= ( abs_abs_int @ B ) ) )
& ( ( ( abs_abs_int @ A )
= ( abs_abs_int @ B ) )
=> ( ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( ( 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(1893,plain,
! [A: $i,B: $i] :
( ( ( 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)],[195]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( ( 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(2294,plain,
! [A: $i,B: $i] :
( ( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
=> ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(951,axiom,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_power__one) ).
thf(4869,plain,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ one_one_real ) @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_zcong__scalar2) ).
thf(2917,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: $i] :
( ( is_int @ D )
=> ( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( plus_plus_int @ D @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( plus_plus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_incr__mult__lemma) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ C ) )
=> ( ! [D: $i] :
( ( is_int @ D )
=> ( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( plus_plus_int @ D @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ B @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ B @ ( plus_plus_int @ D @ ( times_times_int @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( 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(5194,plain,
! [A: $i,B: $i] :
( ( 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)],[1047]) ).
thf(726,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_less__imp__of__nat__less) ).
thf(3992,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ A ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
<=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_zero__less__power__nat__eq) ).
thf(4880,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) )
=> ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1196,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(5677,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(162,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_rel__simps_I6_J) ).
thf(1774,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ min ) @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(605,axiom,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_mult__1__right) ).
thf(3511,plain,
! [A: $i] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3865,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1155,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zadd__0) ).
thf(5554,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ zero_zero_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1149,axiom,
! [A: $i] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_diff__self) ).
thf(5537,plain,
! [A: $i] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1122,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_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(5430,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(593,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_mult__1__left) ).
thf(3464,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_real__mult__less__iff1) ).
thf(1248,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1170,axiom,
! [A: $i] :
( ( 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(5601,plain,
! [A: $i] :
( ( 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)],[1170]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_divides__exp) ).
thf(4597,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1111,axiom,
! [A: $i] :
( ( 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(5398,plain,
! [A: $i] :
( ( 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)],[1111]) ).
thf(1002,axiom,
! [A: $i] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_mult__zero__right) ).
thf(5041,plain,
! [A: $i] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1044,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(5187,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)],[1044]) ).
thf(283,axiom,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( 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(2258,plain,
~ ! [A: $i] :
( ( is_int @ A )
=> ~ ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
& ( hBOOL @ ( hAPP_int_bool @ ( 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)],[283]) ).
thf(289,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_rel__simps_I20_J) ).
thf(2287,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1098,axiom,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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(5357,plain,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( 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)],[1098]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_878_nat__less__le) ).
thf(4014,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(204,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_rel__simps_I5_J) ).
thf(1957,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit1 @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( minus_minus_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_dvd__diff__nat) ).
thf(4399,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ ( minus_minus_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_divides__antisym) ).
thf(4687,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_zero__less__power) ).
thf(2155,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( power_power_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(828,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rel__simps_I17_J) ).
thf(4378,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit1 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ ( plus_plus_int @ B @ one_one_int ) ) )
=> ( ! [D: $i] :
( ( is_int @ D )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( plus_plus_int @ D @ one_one_int ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_int__gr__induct) ).
thf(2534,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ ( plus_plus_int @ B @ one_one_int ) ) )
=> ( ! [D: $i] :
( ( is_int @ D )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ ( plus_plus_int @ D @ one_one_int ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3521,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[608]) ).
thf(191,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(1876,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_of__nat__less__iff) ).
thf(2736,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_diff__add__inverse2) ).
thf(1986,plain,
! [A: $i,B: $i] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_zle__linear) ).
thf(2008,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(1303,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[27]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(5522,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[1143]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(3337,plain,
! [A: $i,B: $i,C: $i] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4579,plain,
! [A: $i,B: $i,C: $i] :
( ( C != zero_zero_real )
=> ( ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(995,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( plus_plus_int @ A @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( hAPP_nat_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 ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_zadd__power2) ).
thf(5014,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( plus_plus_int @ A @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( hAPP_nat_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 ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3690,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1480,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_less__int__code_I14_J) ).
thf(3203,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(851,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_less__eq__number__of__int__code) ).
thf(4455,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_power__strict__increasing) ).
thf(1436,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ B ) ) @ ( hAPP_nat_real @ ( power_power_real @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_mult__right__less__imp__less) ).
thf(4427,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_Euler_Oaux____1) ).
thf(5339,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( zcong @ B @ zero_zero_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(583,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_ex__least__nat__less) ).
thf(3424,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_nat__add__left__cancel__le) ).
thf(2040,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ ( plus_plus_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( ( 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(3045,plain,
! [A: $i,B: $i] :
( ( ( ( times_times_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) )
& ( ( ( A = zero_zero_real )
| ( B = zero_zero_real ) )
=> ( ( times_times_real @ A @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1086,axiom,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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(5322,plain,
hBOOL @ ( hAPP_int_bool @ ( zcong @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1086]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_add__leD2) ).
thf(2783,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_dvd_Oless__trans) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1205,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(5700,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ one_one_int @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_less__number__of) ).
thf(2751,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ E ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ E @ D ) @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ E @ A ) @ B ) ) @ ( plus_plus_nat @ ( times_times_nat @ D @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( times_times_int @ B @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_pos__zmult__pos) ).
thf(3897,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( times_times_int @ B @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(267,axiom,
! [A: $i] :
( ( ( 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(2201,plain,
! [A: $i] :
( ( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
=> ( A = zero_zero_real ) )
& ( ( A = zero_zero_real )
=> ( ( plus_plus_real @ A @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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(4565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(213,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( 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(1989,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ A @ one_one_int )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_power__strict__increasing__iff) ).
thf(4350,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ ( power_power_int @ C ) @ A ) ) @ ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_diff__eq__diff__less) ).
thf(1816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_mult__le__cancel__left__pos) ).
thf(1495,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(983,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ pls )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add__Pls__right) ).
thf(4981,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( plus_plus_int @ A @ pls )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3560,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[614]) ).
thf(926,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_add__leD1) ).
thf(4755,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1113,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_of__nat__add) ).
thf(5404,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2186,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[262]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( minus_minus_int @ B @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_zdvd__zdiffD) ).
thf(3277,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ ( minus_minus_int @ B @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_dvd__antisym) ).
thf(1693,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(748,axiom,
! [A: $i,B: $i] :
( ( 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(4083,plain,
! [A: $i,B: $i] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(2070,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
& ( ( plus_plus_nat @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1129,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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(5462,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( ( ( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
=> ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) )
& ( ( ( A = zero_zero_int )
& ( B = zero_zero_int ) )
=> ( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3850,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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)],[691]) ).
thf(599,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_le__special_I4_J) ).
thf(3479,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( number267125858f_real @ A ) ) @ one_one_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_le__eq__less__or__eq) ).
thf(2417,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_zdvd__int) ).
thf(2091,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1165,axiom,
! [A: $i] :
( ( 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(5586,plain,
! [A: $i] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(950,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_zero__less__imp__eq__int) ).
thf(4865,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( A
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4034,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[734]) ).
thf(304,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
<=> ? [B: $i] :
( ( is_int @ B )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_ex__nat) ).
thf(2340,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ? [B: $i] :
( ( is_int @ B )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) ) ) )
& ( ? [B: $i] :
( ( is_int @ B )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ A @ ( nat @ B ) ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2668,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[381]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_zcong__zadd) ).
thf(3805,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ C @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( zcong @ A @ B ) @ E ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1126,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(5440,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(3244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[524]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_power__inject__exp) ).
thf(2241,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ C ) )
=> ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( power_power_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(723,axiom,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint) ).
thf(3974,plain,
! [A: $i,B: $i] :
( ( ( is_int @ A )
& ( is_int @ B ) )
=> ( is_int @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( times_times_real @ C @ A ) ) @ ( times_times_real @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_real__mult__le__cancel__iff1) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_zdiv__mono2__neg__lemma) ).
thf(3772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ F ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(943,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_less__not__refl3) ).
thf(4831,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(915,axiom,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_power__0__left) ).
thf(4713,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( hAPP_nat_real @ ( power_power_real @ zero_zero_real ) @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_mult__left__le__imp__le) ).
thf(3886,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_add__le__cancel__left) ).
thf(1431,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(4345,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[820]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(3341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ D ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(420,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_eq__imp__le) ).
thf(2810,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(398,axiom,
( ( nat @ zero_zero_int )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_nat__0) ).
thf(2731,plain,
( ( nat @ zero_zero_int )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1051,axiom,
! [A: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= zero_zero_int )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_int__eq__0__conv) ).
thf(5204,plain,
! [A: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= zero_zero_int )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_less__eq__int__code_I13_J) ).
thf(3128,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(4129,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ B @ A ) ) @ ( plus_plus_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_dvd_Oord__eq__le__trans) ).
thf(1977,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1032,axiom,
! [A: $i,B: $i] :
( ( 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(5151,plain,
! [A: $i,B: $i] :
( ( 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)],[1032]) ).
thf(1192,axiom,
hBOOL @ ( hAPP_int_bool @ 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(5668,plain,
hBOOL @ ( hAPP_int_bool @ 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)],[1192]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_nat__less__iff) ).
thf(2803,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ B ) @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( nat @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_power__strict__increasing__iff) ).
thf(1532,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ one_one_real ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( hAPP_nat_real @ ( power_power_real @ C ) @ A ) ) @ ( hAPP_nat_real @ ( power_power_real @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_nat__le__eq__zle) ).
thf(2847,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( nat @ B ) ) @ ( nat @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( nat @ B ) ) @ ( nat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(563,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_rel__simps_I24_J) ).
thf(3360,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ min ) @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1183,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) @ ( plus_plus_int @ ( hAPP_nat_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(5637,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ s ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( 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(4484,plain,
! [A: $i,B: $i] :
( ( ( one_one_nat
= ( times_times_nat @ A @ B ) )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( one_one_nat
= ( times_times_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1075,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_rel__simps_I38_J) ).
thf(5280,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1500,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ C ) @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ zero_zero_int ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_mult__le__cancel__left__neg) ).
thf(3965,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ C ) @ zero_zero_int ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ C @ A ) ) @ ( times_times_int @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1198,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ 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(5681,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(838,axiom,
is_int @ min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OMin) ).
thf(4410,plain,
is_int @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_nat__le__linear) ).
thf(3392,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1177,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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(5623,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( plus_plus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_trans__less__add1) ).
thf(4229,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_power__dvd__imp__le) ).
thf(2539,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( power_power_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_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(1713,plain,
! [A: $i,B: $i] :
( ( is_int @ A )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ ( abs_abs_int @ A ) ) @ B ) ) )
=> ( ( A != zero_zero_int )
| ( B = zero_zero_nat ) ) )
& ( ( ( A != zero_zero_int )
| ( B = zero_zero_nat ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ ( abs_abs_int @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1097,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_of__nat__less__0__iff) ).
thf(5354,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(975,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_rel__simps_I37_J) ).
thf(4955,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_mult__right__le__imp__le) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ A @ B ) ) @ ( times_times_real @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( 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(1902,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
=> ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) )
& ( ( ( A != zero_zero_real )
| ( B != zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real ) @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(574,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( succ @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_Osucc) ).
thf(3394,plain,
! [A: $i] :
( ( is_int @ A )
=> ( is_int @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_linorder__neqE__nat) ).
thf(2484,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_add__pos__pos) ).
thf(3812,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ B ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1505,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ B ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ A ) @ one_one_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ B @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(801,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_le__special_I4_J) ).
thf(4271,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ one_one_int ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( bit1 @ pls ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( number_number_of_int @ A ) ) @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( A
= ( plus_plus_nat @ A @ B ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_add__0__iff) ).
thf(2270,plain,
! [A: $i,B: $i] :
( ( ( A
= ( plus_plus_nat @ A @ B ) )
=> ( B = zero_zero_nat ) )
& ( ( B = zero_zero_nat )
=> ( A
= ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(786,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_number__of2) ).
thf(4221,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1131,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(5473,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3437,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ ( times_times_nat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ zero_zero_int ) )
<=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_mult__le__0__iff) ).
thf(3580,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ zero_zero_int ) )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ zero_zero_int ) ) )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ zero_zero_int ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( hAPP_nat_int @ ( power_power_int @ C ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_power__inject__exp) ).
thf(5073,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ C ) )
=> ( ( ( ( hAPP_nat_int @ ( power_power_int @ C ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_int @ ( power_power_int @ C ) @ A )
= ( hAPP_nat_int @ ( power_power_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_mult__left__le__imp__le) ).
thf(1962,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( times_times_int @ A @ B ) ) @ ( times_times_int @ A @ C ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1189_nat__mult__le__cancel1) ).
thf(3299,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ C @ A ) ) @ ( times_times_nat @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1175,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_power2__ge__self) ).
thf(5618,plain,
! [A: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(426,axiom,
! [A: $i] :
( ( minus_minus_int @ A @ min )
= ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_diff__bin__simps_I2_J) ).
thf(2832,plain,
! [A: $i] :
( ( minus_minus_int @ A @ min )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(872,axiom,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
thf(4547,plain,
hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ one_one_int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1160,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_semiring__norm_I110_J) ).
thf(5569,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(546,axiom,
( zero_zero_nat
= ( nat @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_transfer__nat__int__numerals_I1_J) ).
thf(3316,plain,
( zero_zero_nat
= ( nat @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(3296,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[540]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(3753,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( times_times_nat @ A @ B ) ) @ ( times_times_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(868,axiom,
! [A: $i] :
( ( 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(4533,plain,
! [A: $i] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( 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(1331,plain,
! [A: $i,B: $i] :
( ( number267125858f_real @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(115,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_le__special_I1_J) ).
thf(1606,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ pls ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ ( number267125858f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4335,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1039,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_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(5172,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( A != zero_zero_int ) )
& ( ( A != zero_zero_int )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(128,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_le__special_I2_J) ).
thf(1653,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( number_number_of_int @ A ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( bit1 @ pls ) ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ ( number_number_of_int @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(298,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ 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(2321,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( times_times_int @ A @ A ) ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( times_times_int @ A @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_zprime__zdvd__zmult__better) ).
thf(4642,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ ( times_times_int @ A @ B ) ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ A ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1083,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_rel__simps_I44_J) ).
thf(5307,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_rel__simps_I14_J) ).
thf(2881,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ ( bit0 @ A ) ) @ ( bit0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_dvd_Oantisym) ).
thf(1681,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_dvd_Oeq__refl) ).
thf(2074,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_linorder__neqE__linordered__idom) ).
thf(1463,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( 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(1565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( 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 ) ) )
& ( ( C
= ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) )
=> ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(278,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( 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(2238,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ ( hAPP_nat_real @ ( power_power_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_real @ ( power_power_real @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(81,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ A ) ) @ zero_zero_real ) )
<=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1490,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ A ) ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) ) )
& ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ A ) @ zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_real @ ( plus_plus_real @ A @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(811,axiom,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_power__0) ).
thf(4313,plain,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1066,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_nQ1) ).
thf(5255,plain,
~ ( hBOOL @ ( hAPP_int_bool @ twoSqu1154269391sum2sq @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ 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(4908,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(1917,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[200]) ).
thf(330,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_rel__simps_I3_J) ).
thf(2453,plain,
~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ pls ) @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(740,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
<=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_806_int__one__le__iff__zero__less) ).
thf(4056,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int ) @ A ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(515,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( 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(3200,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( times_times_int @ one_one_int @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1449,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ B ) @ zero_zero_real ) )
=> ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real ) @ A ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( times_times_real @ B @ A ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(172,axiom,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( nat @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_nat__0__le) ).
thf(1812,plain,
! [A: $i] :
( ( is_int @ A )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int ) @ A ) )
=> ( ( hAPP_nat_int @ semiri1621563631at_int @ ( nat @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1162,axiom,
( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ x ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_xy) ).
thf(5574,plain,
( ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ x ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( 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 @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(619,axiom,
! [A: $i,B: $i] :
( ( 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(3575,plain,
! [A: $i,B: $i] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(2177,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[259]) ).
thf(808,axiom,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_power__one__right) ).
thf(4298,plain,
! [A: $i] :
( ( hAPP_nat_real @ ( power_power_real @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( times_times_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1032_zprime__power__zdvd__cancel__left) ).
thf(4002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_int_bool @ zprime @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ ( times_times_int @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ ( power_power_int @ D ) @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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(1417,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ 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 ) ) )
& ( ( ( A = zero_zero_real )
& ( B = zero_zero_real ) )
=> ( hBOOL @ ( hAPP_real_bool @ ( hAPP_r1134773055l_bool @ ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_Nat__Transfer_Otransfer__int__nat__relations_I4_J) ).
thf(3669,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ dvd_dvd_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ dvd_dvd_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
thf(2771,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(11757,plain,
$false,
inference(cvc4,[status(thm)],[4201,1767,3798,3434,4852,3449,2544,3566,3021,5437,4447,1879,5422,5088,1369,4835,1823,4450,3345,2336,3008,2109,2876,1237,4183,3477,3863,3830,2595,1850,2331,4682,5733,5131,1549,2210,2231,5292,5242,2590,4697,3912,1728,2837,5348,4747,3382,1855,3680,4931,4037,4376,2117,2104,5225,4075,1882,5696,3762,5069,5644,1443,5000,2776,3377,2527,3153,2671,1544,4711,3012,2099,2282,1591,5669,5501,4105,3439,5589,3648,4110,2933,1327,1354,4762,2575,2195,5550,1426,3530,3942,4011,3135,4097,5257,2434,1872,5701,4279,2627,1260,5674,3253,2901,3313,5178,5708,5636,1507,1222,3717,4941,4047,1746,1835,2216,5740,3502,2227,4679,1613,5301,2516,4322,1482,5024,5533,4142,5252,3766,2432,3994,3915,1782,4371,1441,4266,2010,4124,5723,5056,2886,4916,4137,1724,3809,2173,1366,4948,2405,3688,4775,3263,1709,2698,4070,3495,2708,2444,3612,1511,3125,3744,2126,3855,3820,4637,2654,3976,4524,3938,4348,5306,1792,2814,4422,3410,5160,5182,3845,2562,4023,1992,5289,4984,4243,2703,5231,3099,2713,1704,5480,3657,5746,4632,4390,2852,4353,4862,4617,5199,4179,5604,4664,4622,5323,3919,1347,1572,1398,3084,2635,3470,3734,4368,4952,4383,1815,4460,4793,1875,1232,4253,4967,3258,2829,3788,4595,4432,4205,2616,2324,3075,5027,1632,4724,2925,5032,1677,5360,4810,2222,4411,5264,3322,3524,3431,1664,2794,4857,1373,1334,3527,1858,2122,4134,3357,2254,2555,3290,5135,4798,4556,5259,5738,2367,1394,2639,3226,2965,4707,2392,5328,2718,1696,3389,2508,5059,1843,3986,3068,1377,2618,5401,3189,3739,5375,5384,3712,1622,2979,5343,2137,4924,5169,3361,4536,1975,4065,1863,3097,3229,4604,5157,4199,4216,5530,4407,1691,3186,3318,2641,3550,5122,1730,1604,3899,2922,1438,3720,5411,1306,5017,5540,2083,4100,5049,2541,5719,5366,4785,4493,4284,3514,3778,1560,2705,2264,1387,1900,5630,2733,3867,4397,1580,2277,1255,4434,4878,5579,4989,5044,5455,1751,3742,4344,4091,4204,5470,5507,3814,2132,2414,3250,4160,4661,4295,3191,5655,4192,1920,4585,4385,5038,5566,2547,3667,1740,5330,4316,3282,2958,3269,1602,1968,3198,2663,1555,4994,4757,3065,5690,3578,1296,4553,4187,5341,3535,1787,4979,5201,4417,5658,1281,2741,2112,1291,4080,5714,5221,5270,5423,5345,5615,1970,4845,3386,3119,3078,3650,5687,5475,1402,3731,3968,5313,5189,3467,5626,3909,3615,2157,2115,1270,1772,3122,2946,2990,4512,5006,2359,1375,3218,4544,4429,1498,1587,1672,3704,1540,3963,3087,3018,4676,2460,5181,5080,5743,4938,1414,4444,2649,3573,4333,3954,4049,1329,3775,3141,3311,4301,2023,3326,5166,1964,4276,3922,3407,5705,2561,3094,4721,1461,2868,5620,2312,3010,2455,4750,5547,4744,2172,4648,4054,3428,5662,2349,2038,1446,2317,5387,2781,4530,1263,4970,5234,1552,5498,2006,1799,4231,3064,3005,3920,3162,1825,2968,2504,5576,2450,3654,1478,5726,1451,5149,1456,1382,2487,2845,2598,3354,2387,1429,3247,2766,3692,1599,1246,4086,2756,1627,2370,3215,4361,1525,5245,3755,4644,2208,4476,1563,5419,5417,3508,4572,4148,5112,5557,2788,5544,1318,5711,3563,2761,3279,4889,5571,3592,3999,2963,1286,3321,5447,1466,2402,2189,3422,5513,2995,5295,2617,4004,2338,3675,4308,2909,3807,2144,4921,2001,4131,4872,2585,2570,4562,4503,3686,4599,3396,3343,1251,5483,2677,4708,4685,1754,2292,3358,4613,5138,2149,3890,5278,5508,1301,3888,5525,3111,4943,1833,1884,3519,2981,1752,4122,4465,5097,4946,2695,5535,5698,3372,4341,4268,2727,3234,2048,3925,2938,1615,1389,5395,2791,3609,2657,1620,3472,2489,3081,3945,4926,3266,2674,1535,2806,1701,3590,2716,3604,1520,3404,2817,4769,4505,3599,5546,3751,4112,4764,1258,5432,1675,3023,1669,5118,5363,2891,5011,1371,3208,4236,4218,3002,4822,5086,1239,2442,2759,3783,3487,2055,3832,1765,2457,4854,1897,3302,3568,2573,2319,1356,5143,4929,5671,2229,2214,3764,5325,4620,1589,4073,2896,4228,3631,1853,3287,4828,2906,3419,1349,5303,5491,4601,1542,4805,5222,4139,3710,4958,5407,4667,4176,3138,5616,2871,4107,5267,2065,4388,2180,5367,4401,2632,4541,1339,2625,4569,5392,2785,2874,2289,3893,5563,2824,3133,3055,4462,4911,2267,4731,1821,3800,4264,5599,5286,3165,4181,3971,1344,2329,2842,1396,5254,1474,2835,5646,3917,5248,3674,3241,1775,1726,2303,4282,4067,2725,1594,1699,2212,2171,5197,5094,5218,1445,5641,2999,5693,3348,3876,2693,2984,4481,4473,3380,1562,5435,4207,4741,2096,3193,4901,5528,2665,4813,4735,4529,1509,2629,5678,2564,5652,2899,5003,4986,5414,4405,3031,1809,2952,2652,3293,2878,1684,3455,1472,5358,5133,3640,5607,2397,3842,5125,1611,2192,3904,5748,1941,5592,2821,2720,2888,4255,2513,2567,1547,5047,1748,5716,1770,1225,2060,1743,1400,4950,3260,2588,3786,4894,4961,5079,4324,4630,1230,2160,3642,4905,1790,3305,1658,4737,5638,2468,1711,5684,4522,5262,1637,3114,3334,4222,1869,3475,3026,2429,3823,5560,5030,2219,5154,4241,3847,2903,4800,1679,3412,5106,3041,3853,3769,4875,3715,2354,1802,2379,4976,5240,1284,5633,4143,2860,1272,5596,4414,4819,1617,1404,2247,2558,5628,5736,2426,1981,4510,5504,1485,2711,4991,2511,4634,2030,4225,3256,5083,2013,3401,2045,3171,3447,2347,1998,3168,1940,4548,4289,4651,3620,4424,3457,1649,2078,1913,4656,2310,3874,4997,5510,4738,5115,3928,4185,3625,4646,2997,4102,2919,4170,5389,1866,2658,1807,4061,5184,3729,1253,3484,1639,5008,5382,3383,4250,5351,5228,4338,3331,1646,5315,2389,1476,5272,4615,2251,4681,5191,3369,4126,4042,4791,2004,1244,2764,3662,3780,1558,2152,2447,1861,2081,3324,5164,4153,5109,5128,2779,3181,2384,2475,3694,4964,2912,1308,5409,2198,3677,2362,2162,3793,2183,3351,1513,5119,5211,1893,2294,4869,2917,1994,5194,3992,4880,5677,1774,3511,3865,5554,5537,5430,3464,1248,5601,4597,5398,5041,5187,2258,2287,5357,4014,1957,4399,4687,2155,4378,2534,3521,1876,2736,1986,2008,1303,5522,3337,4579,5014,3690,1480,3203,4455,1436,4427,5339,3424,2040,3045,5322,2783,3015,5700,2751,2800,3897,2201,4565,1989,4350,1816,1495,4981,3560,4755,5404,2186,3277,1693,4083,2070,5462,3850,3479,2417,2091,5586,4865,4034,2340,2668,3805,5440,3244,2241,3974,1268,1384,3772,4831,4713,3886,1431,4345,3341,2810,2731,5204,3128,4129,1977,5151,5668,2803,1532,2847,3360,5637,4484,5280,1500,3965,5681,4410,3392,5623,4229,2539,1713,5354,4955,1299,1902,3394,2484,3812,1505,4271,2270,4221,5473,3437,3580,5073,1962,3299,5618,2832,4547,5569,3316,3296,3753,4533,1331,1606,4335,5172,1653,2321,4642,5307,2881,1681,2074,1463,1565,2238,1490,4313,5255,4908,1917,2453,4056,3200,1449,1812,5574,3575,2177,4298,4002,1417,3669,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 16:59:23 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.16 % [INFO] Parsing done (273ms).
% 1.64/1.16 % [INFO] Running in sequential loop mode.
% 2.49/1.36 % [INFO] eprover registered as external prover.
% 2.49/1.36 % [INFO] cvc4 registered as external prover.
% 2.49/1.37 % [INFO] Scanning for conjecture ...
% 3.16/1.52 % [INFO] Found a conjecture and 1232 axioms. Running axiom selection ...
% 3.90/1.74 % [INFO] Axiom selection finished. Selected 1219 axioms (removed 13 axioms).
% 5.16/2.07 % [INFO] Problem is first-order (TPTP FOF).
% 5.31/2.11 % [INFO] Type checking passed.
% 5.31/2.11 % [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 ...
% 41.48/10.00 % External prover 'cvc4' found a proof!
% 41.48/10.00 % [INFO] Killing All external provers ...
% 41.48/10.01 % Time passed: 9487ms (effective reasoning time: 8837ms)
% 41.48/10.01 % 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)>
% 41.48/10.02 % Axioms used in derivation (1219): fact_259_pos__add__strict, 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_664_mult__1, gsy_c_Int_OBit0, fact_726_transfer__nat__int__relations_I2_J, gsy_v_y____, 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_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_868_mult__cancel1, gsy_c_Residues_OLegendre, 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_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_1047_nat__mult__dvd__cancel__disj_H, gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint, 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, gsy_v_x____, 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, gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint, 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, gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint, 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, gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint, 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_147_semiring__numeral__1__eq__1, gsy_v_t____, 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_1014_rel__simps_I45_J, 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fact_779_pos__zmult__pos, fact_613_mult__eq__0__iff, fact_887_add__le__mono1, fact_604_add__diff__cancel, fact_873_real__mult__right__cancel, fact_1192_nat__eq__add__iff1, fact_699_power__mult__distrib, fact_907_diff__le__mono2, fact_294_of__nat__0, gsy_c_Int_OMin, fact_258_pos__add__strict, fact_706_Nat_Odiff__cancel, fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_1005_rel__simps_I26_J, fact_307_add__pos__pos, fact_672_add__le__imp__le__left, fact_709_mult__Bit0, fact_0_n1pos, fact_1058_zcong__id, fact_498_mult__right__mono, fact_240_less__imp__of__nat__less, fact_127_add__Bit0__Bit1, fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_205_Nat__Transfer_Otransfer__int__nat__relations_I2_J, fact_479_split__mult__neg__le, fact_85_less__special_I4_J, fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_333_add__left__cancel, fact_250_of__nat__1, fact_131_number__of__int, fact_560_mult__le__less__imp__less, fact_278_power__less__imp__less__exp, fact_364_add__0__right, fact_958_nat__mult__2, fact_366_add__0__right, fact_380_add__less__imp__less__left, gsy_v_m, fact_262_not__one__less__zero, fact_1124_zcong__refl, fact_634_combine__common__factor, fact_197_gr__implies__not0, fact_712_rel__simps_I19_J, fact_75_rel__simps_I16_J, fact_1036__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_, fact_16_one__add__one__is__two, fact_274_power__inject__exp, fact_778_rel__simps_I27_J, fact_209_linorder__neqE__linordered__idom, fact_164_power__strict__decreasing, fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_1039__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4, fact_84_less__special_I4_J, fact_212_add__is__0, fact_160_power__0__left, fact_1082__096_091s_____A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_, fact_402_nat__power__eq__0__iff, fact_782_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_484_mult__mono, fact_754_le__special_I4_J, fact_1080_divides__cases, fact_206_zero__less__power__nat__eq__number__of, fact_1120_QuadRes__def, fact_780_zmult__zless__mono2, fact_1169_abs__power2__distrib, fact_614_mult__eq__0__iff, fact_963_two__realpow__ge__one, fact_566_mult__strict__mono_H, fact_1143_zcong__square, fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_1126_IntPrimes_Ozcong__zero, fact_130_number__of__int, fact_1045_nat__dvd__not__less, fact_690_add__le__cancel__right, fact_1113_dvd_Oeq__iff, fact_536_less__add__iff1, fact_166_zero__less__two, fact_991_zprime__zdvd__zmult__better, fact_529_zero__le__mult__iff, fact_661_mult__1__right, fact_1183_nat__mult__eq__cancel__disj, fact_743_Nat__Transfer_Otransfer__nat__int__functions_I1_J, fact_198_nat__power__less__imp__less, fact_1168_dvd__int__iff, fact_395_add__less__cancel__left, fact_58_number__of__reorient, fact_781_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_1159_abs__int__eq, fact_1061_zcong__zpower, fact_26_semiring__norm_I110_J, gsy_v_s1____, fact_808_succ__Pls, fact_917_mult__less__mono2, fact_284_power__eq__0__iff, fact_996_zdvd__mult__cancel, fact_770_diff__less, fact_557_mult__right__less__imp__less, fact_1003_rel__simps_I3_J, fact_1121_Little__Fermat, fact_502_mult__nonpos__nonpos, fact_986_real__sum__squared__expand, fact_938_le__add__diff__inverse, fact_860_zdiff__int, fact_470_of__nat__mult, fact_192_add__less__mono, fact_234_power__one, fact_228_zero__neq__one, fact_1152_number__of1, fact_1018_rel__simps_I43_J, fact_47_rel__simps_I17_J, fact_697_power__mult__distrib, fact_732_power__decreasing, fact_1053_zdvd__int, fact_124_number__of__add
% 41.48/10.02 % No. of inferences in proof: 2442
% 41.48/10.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9487 ms resp. 8837 ms w/o parsing
% 42.67/10.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.67/10.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------