%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM924^2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:16 AM UTC 2026
% Result : Theorem 25.50s 6.63s
% Output : Refutation 27.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 699
% Syntax : Number of formulae : 1400 (1002 unt; 0 typ; 0 def)
% Number of atoms : 2972 (1490 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 12333 ( 246 ~; 66 |; 124 &;11143 @)
% ( 0 <=>; 754 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 13 con; 0-3 aty)
% Number of variables : 2692 ( 0 ^;2684 !; 8 ?;2692 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(minus_minus_int_decl,type,
minus_minus_int: int > int > int ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(minus_minus_real_decl,type,
minus_minus_real: real > real > real ).
thf(one_one_int_decl,type,
one_one_int: int ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_real_decl,type,
one_one_real: real ).
thf(plus_plus_int_decl,type,
plus_plus_int: int > int > int ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_real_decl,type,
plus_plus_real: real > real > real ).
thf(times_times_int_decl,type,
times_times_int: int > int > int ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(times_times_real_decl,type,
times_times_real: real > real > real ).
thf(zero_zero_int_decl,type,
zero_zero_int: int ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(zcong_decl,type,
zcong: int > int > int > $o ).
thf(zprime_decl,type,
zprime: int > $o ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(min_decl,type,
min: int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_int_decl,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_decl,type,
number_number_of_nat: int > nat ).
thf(number267125858f_real_decl,type,
number267125858f_real: int > real ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_real_decl,type,
ord_less_real: real > real > $o ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(power_power_int_decl,type,
power_power_int: int > nat > int ).
thf(power_power_nat_decl,type,
power_power_nat: nat > nat > nat ).
thf(power_power_real_decl,type,
power_power_real: real > nat > real ).
thf(legendre_decl,type,
legendre: int > int > int ).
thf(quadRes_decl,type,
quadRes: int > int > $o ).
thf(dvd_dvd_int_decl,type,
dvd_dvd_int: int > int > $o ).
thf(dvd_dvd_nat_decl,type,
dvd_dvd_nat: nat > nat > $o ).
thf(dvd_dvd_real_decl,type,
dvd_dvd_real: real > real > $o ).
thf(twoSqu362149276sum2sq_decl,type,
twoSqu362149276sum2sq: int > $o ).
thf(m_decl,type,
m: int ).
thf(s1_decl,type,
s1: int ).
thf(s_decl,type,
s: int ).
thf(t_decl,type,
t: int ).
thf(66,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_zcong__zmult) ).
thf(892,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(331,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_power2__le__imp__le) ).
thf(1665,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(479,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_zle__diff1__eq) ).
thf(2094,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(19,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(760,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(471,axiom,
! [A: int] :
( min
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_rel__simps_I42_J) ).
thf(2072,plain,
! [A: int] :
( min
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(443,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_semiring__norm_I110_J) ).
thf(1995,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_arith__simps_I32_J) ).
thf(846,plain,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_power__dvd__imp__le) ).
thf(909,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(410,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( A != zero_zero_int )
=> ( dvd_dvd_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_zdvd__mult__cancel) ).
thf(1899,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
=> ( ( A != zero_zero_int )
=> ( dvd_dvd_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(387,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_zcong__zpower) ).
thf(1840,plain,
! [A: nat,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(391,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(1850,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(653,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_rel__simps_I27_J) ).
thf(2559,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ pls )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(168,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1179,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(25,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_real__two__squares__add__zero__iff) ).
thf(777,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(382,axiom,
! [A: int,B: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ A )
= ( times_times_int @ A @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_power__commutes) ).
thf(1818,plain,
! [A: int,B: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ A )
= ( times_times_int @ A @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(429,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_rel__simps_I39_J) ).
thf(1950,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(296,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_semiring__add__number__of) ).
thf(1554,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(305,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_semiring__numeral__1__eq__1) ).
thf(1586,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(276,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_Bit1__Min) ).
thf(1501,plain,
( ( bit1 @ min )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(671,axiom,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_p) ).
thf(2612,plain,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_divides__mul__r) ).
thf(1024,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(264,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__less__power2) ).
thf(1469,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(484,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_zcong__shift) ).
thf(2109,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(492,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_zadd__power2) ).
thf(2131,plain,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(135,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_number__of__mult) ).
thf(1083,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( times_times_int @ A @ B ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(440,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(1982,plain,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(648,axiom,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_power__eq__0__iff__number__of) ).
thf(2544,plain,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(82,axiom,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(941,plain,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(337,axiom,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_power__even__eq) ).
thf(1686,plain,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(536,axiom,
( ( t = zero_zero_int )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
thf(2250,plain,
( ( t = zero_zero_int )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(95,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_zcong__zdiff) ).
thf(977,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(106,axiom,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_realpow__minus__mult) ).
thf(1005,plain,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(487,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__special_I2_J) ).
thf(2117,plain,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(404,axiom,
! [A: int] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(1882,plain,
! [A: int] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(284,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ~ ( zcong @ B @ zero_zero_int @ C )
& ~ ( zcong @ A @ zero_zero_int @ C ) )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_zcong__zprime__prod__zero__contra) ).
thf(1522,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ~ ( zcong @ B @ zero_zero_int @ C )
& ~ ( zcong @ A @ zero_zero_int @ C ) )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(593,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2395,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(378,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_le__special_I3_J) ).
thf(1808,plain,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(131,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_zero__less__power) ).
thf(1073,plain,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(693,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_power__0__left__number__of) ).
thf(2671,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ A ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(353,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_semiring__mult__number__of) ).
thf(1728,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(307,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zero__power2) ).
thf(1591,plain,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(436,axiom,
! [A: nat,B: int] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_power__eq__0__iff__number__of) ).
thf(1971,plain,
! [A: nat,B: int] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(119,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_real__mult__le__cancel__iff1) ).
thf(1041,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(166,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_power__inject__exp) ).
thf(1173,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ( power_power_nat @ C @ A )
= ( power_power_nat @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(393,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_zmult__zless__mono2) ).
thf(1855,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(175,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_real__mult__order) ).
thf(1200,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(160,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_real__add__mult__distrib) ).
thf(1158,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(638,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( times_times_int @ B @ A ) )
= ( times_times_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2512,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( times_times_int @ B @ A ) )
= ( times_times_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(528,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_sum__squares__ge__zero) ).
thf(2231,plain,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(675,axiom,
ord_less_int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_rel__simps_I6_J) ).
thf(2622,plain,
ord_less_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(129,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_power__less__imp__less__exp) ).
thf(1068,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(101,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(994,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(641,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_power2__less__imp__less) ).
thf(2527,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(662,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_power2__sum) ).
thf(2590,plain,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(241,axiom,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ ( number267125858f_real @ B ) @ C ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_add__number__of__diff1) ).
thf(1401,plain,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ ( number267125858f_real @ B ) @ C ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(425,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
= ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_zmult__eq__1__iff) ).
thf(1939,plain,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
= ( ( ( A = one_one_int )
& ( B = one_one_int ) )
| ( ( A
= ( number_number_of_int @ min ) )
& ( B
= ( number_number_of_int @ min ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(535,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_semiring__norm_I110_J) ).
thf(2248,plain,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_power__eq__0__iff) ).
thf(873,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(177,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
thf(1205,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(486,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_right__distrib__number__of) ).
thf(2114,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(154,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_zle__refl) ).
thf(1142,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(196,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_power__mult) ).
thf(1269,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_nat @ ( power_power_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(61,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(878,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(587,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_power__less__imp__less__exp) ).
thf(2380,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(249,axiom,
! [A: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_eq__0__number__of) ).
thf(1426,plain,
! [A: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ A ) )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(328,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_int @ C @ ( times_times_int @ E @ A ) )
!= ( plus_plus_int @ D @ ( times_times_int @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_add__scale__eq__noteq) ).
thf(1655,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_int @ C @ ( times_times_int @ E @ A ) )
!= ( plus_plus_int @ D @ ( times_times_int @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(669,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_rel__simps_I2_J) ).
thf(2607,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(459,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__gt__zero__iff) ).
thf(2035,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(398,axiom,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_pos2) ).
thf(1867,plain,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(8,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(715,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(198,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1275,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(217,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_sum__squares__le__zero__iff) ).
thf(1327,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(222,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1342,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(323,axiom,
! [A: real,B: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_power2__eq__imp__eq) ).
thf(1640,plain,
! [A: real,B: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(430,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_int__0__neq__1) ).
thf(1954,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(80,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_zcong__scalar2) ).
thf(930,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(260,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1458,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(32,axiom,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_add__diff__add) ).
thf(797,plain,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) )
= ( plus_plus_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(562,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_even__less__0__iff) ).
thf(2316,plain,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(418,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_zpower__zadd__distrib) ).
thf(1919,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(617,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_one__power2) ).
thf(2459,plain,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(226,axiom,
ord_less_eq_int @ min @ min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_rel__simps_I24_J) ).
thf(1354,plain,
ord_less_eq_int @ min @ min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(497,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_nat__mult__2) ).
thf(2146,plain,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(358,axiom,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_mult__Pls) ).
thf(1746,plain,
! [A: int] :
( ( times_times_int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(385,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_divides__cases) ).
thf(1835,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( B = A )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(104,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ one_one_real @ A )
=> ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_power__strict__increasing) ).
thf(1001,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_real @ one_one_real @ A )
=> ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(462,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_power2__le__imp__le) ).
thf(2046,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(301,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_one__add__one__is__two) ).
thf(1576,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)],[301]) ).
thf(6,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(709,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(453,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_power2__eq__square) ).
thf(2020,plain,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(449,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_less__bin__lemma) ).
thf(2010,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ord_less_int @ ( minus_minus_int @ A @ B ) @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(474,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( power_power_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_zpower__zdvd__prop1) ).
thf(2082,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( dvd_dvd_int @ A @ B )
=> ( dvd_dvd_int @ A @ ( power_power_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(351,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_semiring__one__add__one__is__two) ).
thf(1724,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)],[351]) ).
thf(506,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_zprime__2) ).
thf(2173,plain,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(376,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C )
=> ( ( zcong @ B @ zero_zero_int @ C )
| ( zcong @ A @ zero_zero_int @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_zcong__zprime__prod__zero) ).
thf(1803,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C )
=> ( ( zcong @ B @ zero_zero_int @ C )
| ( zcong @ A @ zero_zero_int @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(43,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
= ( B
= ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_number__of__reorient) ).
thf(829,plain,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
= ( B
= ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ B )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_one__le__power) ).
thf(1095,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ B )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(606,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__special_I3_J) ).
thf(2432,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(416,axiom,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_power__even__eq) ).
thf(1914,plain,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(189,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_zmult__assoc) ).
thf(1243,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(149,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_zcong__def) ).
thf(1127,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(782,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(254,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_rel__simps_I40_J) ).
thf(1441,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(186,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1228,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(317,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(1623,plain,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(269,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_mult__2) ).
thf(1482,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(667,axiom,
quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(2603,plain,
quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(363,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_one__add__one__is__two) ).
thf(1760,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(691,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2667,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(28,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) )
!= ( plus_plus_real @ ( times_times_real @ C @ B ) @ ( times_times_real @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_crossproduct__noteq) ).
thf(785,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ D @ B ) )
!= ( plus_plus_real @ ( times_times_real @ C @ B ) @ ( times_times_real @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(400,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1871,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(633,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Bit0__Pls) ).
thf(2501,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(259,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ ( number_number_of_int @ B ) @ C ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_add__number__of__diff1) ).
thf(1455,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ ( number_number_of_int @ B ) @ C ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(654,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rel__simps_I21_J) ).
thf(2562,plain,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(218,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1330,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(611,axiom,
! [A: nat] :
( ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= one_one_int )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( number_number_of_int @ min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_neg__one__power) ).
thf(2444,plain,
! [A: nat] :
( ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= one_one_int )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( number_number_of_int @ min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(395,axiom,
! [A: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_add__special_I2_J) ).
thf(1860,plain,
! [A: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(194,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1264,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(523,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add__number__of__eq) ).
thf(2217,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(546,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_power2__le__imp__le) ).
thf(2274,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_power__less__power__Suc) ).
thf(917,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(3,axiom,
! [A: nat,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_dvd__power__same) ).
thf(702,plain,
! [A: nat,B: real,C: real] :
( ( dvd_dvd_real @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(384,axiom,
! [A: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_double__number__of__Bit0) ).
thf(1832,plain,
! [A: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(172,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_zdiff__zmult__distrib2) ).
thf(1191,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(657,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zero__less__power2) ).
thf(2571,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(577,axiom,
twoSqu362149276sum2sq @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_32_qf1pt) ).
thf(2356,plain,
twoSqu362149276sum2sq @ ( 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)],[577]) ).
thf(292,axiom,
ord_less_int @ t @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(1545,plain,
ord_less_int @ t @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(375,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_Int2_Ozcong__zero) ).
thf(1800,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(268,axiom,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_diff__bin__simps_I1_J) ).
thf(1479,plain,
! [A: int] :
( ( minus_minus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(109,axiom,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_zcong__refl) ).
thf(1013,plain,
! [A: int,B: int] : ( zcong @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(422,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_less__number__of__int__code) ).
thf(1931,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(501,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_rel__simps_I50_J) ).
thf(2158,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(368,axiom,
! [A: int] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_eq__number__of__0) ).
thf(1773,plain,
! [A: int] :
( ( ( number_number_of_nat @ A )
= zero_zero_nat )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(557,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_mult__numeral__1) ).
thf(2301,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(433,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_less__int__code_I15_J) ).
thf(1963,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(142,axiom,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
thf(1100,plain,
! [A: int] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(390,axiom,
! [A: int] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1847,plain,
! [A: int] :
( ( plus_plus_int @ A @ A )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(419,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_less__special_I4_J) ).
thf(1922,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(699,axiom,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(2691,plain,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(344,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__special_I4_J) ).
thf(1704,plain,
! [A: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(58,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( times_times_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(870,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( times_times_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(92,axiom,
! [A: nat,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_zero__le__power) ).
thf(969,plain,
! [A: nat,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(584,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_sum__power2__le__zero__iff) ).
thf(2373,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(356,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_diff__bin__simps_I7_J) ).
thf(1741,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(240,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_sum__squares__gt__zero__iff) ).
thf(1398,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) )
= ( ( A != zero_zero_real )
| ( B != zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(62,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(881,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(448,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_diff__bin__simps_I4_J) ).
thf(2007,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit1 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(78,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_order__le__neq__implies__less) ).
thf(924,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(673,axiom,
! [A: int,B: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add__number__of__eq) ).
thf(2616,plain,
! [A: int,B: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(456,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_left__distrib__number__of) ).
thf(2027,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(233,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_zdvd__zdiffD) ).
thf(1373,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) )
=> ( ( dvd_dvd_int @ A @ C )
=> ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(415,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_less__eq__int__code_I13_J) ).
thf(1911,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_divides__rev) ).
thf(1109,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( B != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(530,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add1__zle__eq) ).
thf(2236,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(489,axiom,
! [A: int,B: int] :
( ( ord_less_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ pls @ B ) )
& ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_less__nat__number__of) ).
thf(2122,plain,
! [A: int,B: int] :
( ( ord_less_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ pls @ B ) )
& ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(538,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_self__quotient__aux2) ).
thf(2254,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(201,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1283,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(40,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(821,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(379,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_zcong__eq__zdvd__prop) ).
thf(1811,plain,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(257,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ B @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_Euler_Oaux1) ).
thf(1450,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( B
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ B @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1136,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_nat__mult__dvd__cancel__disj_H) ).
thf(834,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( dvd_dvd_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(432,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_less__special_I3_J) ).
thf(1960,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(35,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_real @ C @ ( times_times_real @ E @ A ) )
!= ( plus_plus_real @ D @ ( times_times_real @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_add__scale__eq__noteq) ).
thf(806,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_real @ C @ ( times_times_real @ E @ A ) )
!= ( plus_plus_real @ D @ ( times_times_real @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(569,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_nat__numeral__1__eq__1) ).
thf(2335,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(91,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_eq__number__of) ).
thf(966,plain,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(766,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_power__Suc__less) ).
thf(1169,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ B @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(549,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_int )
=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_even__power__le__0__imp__0) ).
thf(2281,plain,
! [A: int,B: nat] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_int )
=> ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ D @ C )
=> ~ ( dvd_dvd_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_divides__div__not) ).
thf(1215,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) )
=> ( ( ord_less_nat @ zero_zero_nat @ D )
=> ( ( ord_less_nat @ D @ C )
=> ~ ( dvd_dvd_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(409,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_rel__simps_I12_J) ).
thf(1896,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(774,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(494,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_less__special_I3_J) ).
thf(2137,plain,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(225,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1351,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(482,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_sum__power2__le__zero__iff) ).
thf(2103,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(592,axiom,
! [A: nat,B: nat,C: int] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ C ) ) @ ( times_times_nat @ B @ ( number_number_of_nat @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_left__distrib__number__of) ).
thf(2392,plain,
! [A: nat,B: nat,C: int] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ C ) ) @ ( times_times_nat @ B @ ( number_number_of_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(582,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_le__number__of__eq__not__less) ).
thf(2367,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(421,axiom,
! [A: nat] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_power__m1__even) ).
thf(1928,plain,
! [A: nat] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(256,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_less__special_I1_J) ).
thf(1447,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(626,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_zmult__1__right) ).
thf(2483,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(223,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1345,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_number__of__diff) ).
thf(988,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(682,axiom,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I22_J) ).
thf(2639,plain,
! [A: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(341,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Numeral1__eq1__nat) ).
thf(1697,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_power__strict__mono) ).
thf(849,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(396,axiom,
( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(1863,plain,
( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(339,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sum__power2__gt__zero__iff) ).
thf(1691,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(209,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1306,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(503,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_zless__linear) ).
thf(2164,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(36,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_power__0) ).
thf(810,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(658,axiom,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_zmult__1) ).
thf(2574,plain,
! [A: int] :
( ( times_times_int @ one_one_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(253,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_rel__simps_I11_J) ).
thf(1438,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(211,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_sum__squares__eq__zero__iff) ).
thf(1311,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(555,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_semiring__add__number__of) ).
thf(2296,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(559,axiom,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__numeral__0) ).
thf(2307,plain,
! [A: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(366,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_semiring__numeral__0__eq__0) ).
thf(1768,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(399,axiom,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_IntPrimes_Ozcong__zero) ).
thf(1868,plain,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(588,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_zle__add1__eq__le) ).
thf(2382,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(121,axiom,
! [A: int,B: int,C: int] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_zcong__zmult__self) ).
thf(1047,plain,
! [A: int,B: int,C: int] : ( zcong @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1057,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(162,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1163,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(609,axiom,
~ ( ord_less_int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_rel__simps_I3_J) ).
thf(2441,plain,
~ ( ord_less_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(238,axiom,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_realpow__pos__nth__unique) ).
thf(1387,plain,
! [A: real,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ B )
= A )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(112,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_nat__zero__less__power__iff) ).
thf(1021,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(647,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_rel__simps_I48_J) ).
thf(2541,plain,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(55,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(862,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(271,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_eq__number__of__Pls__Min) ).
thf(1487,plain,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(458,axiom,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2032,plain,
! [A: nat,B: nat] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(600,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less__number__of) ).
thf(2414,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(451,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__Bit1__Bit0) ).
thf(2015,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(298,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_power__strict__decreasing) ).
thf(1560,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(88,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(957,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(184,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_real__le__trans) ).
thf(1223,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(67,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_real__le__eq__diff) ).
thf(894,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(14,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(746,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(138,axiom,
! [A: nat,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_power__mono) ).
thf(1091,plain,
! [A: nat,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(283,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_add__0__iff) ).
thf(1519,plain,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(664,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_q__neg__lemma) ).
thf(2596,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(227,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1355,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(303,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_less__int__code_I16_J) ).
thf(1580,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(29,axiom,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_right__diff__distrib__number__of) ).
thf(788,plain,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(232,axiom,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_real__squared__diff__one__factored) ).
thf(1370,plain,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(248,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_zpower__zpower) ).
thf(1423,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(619,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_sum__squares__gt__zero__iff) ).
thf(2464,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(624,axiom,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_zero__power2) ).
thf(2477,plain,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(568,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_add__Bit0__Bit1) ).
thf(2332,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(406,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__zmult__distrib2) ).
thf(1888,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(318,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_odd__less__0) ).
thf(1624,plain,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(65,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(889,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(371,axiom,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_pos__zmult__eq__1__iff__lemma) ).
thf(1787,plain,
! [A: int,B: int] :
( ( ( times_times_int @ A @ B )
= one_one_int )
=> ( ( A = one_one_int )
| ( A
= ( number_number_of_int @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(179,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1210,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(566,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_one__not__neg__one__mod__m) ).
thf(2327,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(204,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1291,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(974,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_power__strict__increasing__iff) ).
thf(1106,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_power__mult__distrib) ).
thf(1032,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(311,axiom,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_real__sum__squared__expand) ).
thf(1602,plain,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(435,axiom,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(1968,plain,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(655,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(2565,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(516,axiom,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(2200,plain,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(670,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( ? [D: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_zcong__iff__lin) ).
thf(2609,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( ? [D: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(18,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__eq__number__of__int__code) ).
thf(757,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(573,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_semiring__one__add__one__is__two) ).
thf(2345,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(521,axiom,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_less__special_I2_J) ).
thf(2211,plain,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(243,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1407,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(649,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_semiring__mult__2__right) ).
thf(2547,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(561,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_number__of__add) ).
thf(2313,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(629,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) )
=> ( ( dvd_dvd_int @ B @ C )
| ( dvd_dvd_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_zprime__zdvd__zmult) ).
thf(2492,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( zprime @ B )
=> ( ( dvd_dvd_int @ B @ ( times_times_int @ C @ A ) )
=> ( ( dvd_dvd_int @ B @ C )
| ( dvd_dvd_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(321,axiom,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_less__special_I1_J) ).
thf(1634,plain,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(527,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__special_I3_J) ).
thf(2228,plain,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(424,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_zdiff__power3) ).
thf(1936,plain,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(137,axiom,
! [A: nat,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_power__strict__mono) ).
thf(1089,plain,
! [A: nat,B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(441,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_mult__2__right) ).
thf(1983,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(659,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_power__0__left__number__of) ).
thf(2577,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(275,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_rel__simps_I25_J) ).
thf(1498,plain,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(700,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_zero__less__power) ).
thf(2694,plain,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(636,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_power__Suc__less) ).
thf(2509,plain,
! [A: nat,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(679,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_mult__2) ).
thf(2631,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(361,axiom,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_le__special_I1_J) ).
thf(1755,plain,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(544,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_nat__mult__2__right) ).
thf(2268,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(364,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_double__eq__0__iff) ).
thf(1762,plain,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(639,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_sum__power2__eq__zero__iff) ).
thf(2515,plain,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(481,axiom,
! [A: int] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_quartic__square__square) ).
thf(2100,plain,
! [A: int] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(586,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ C @ A @ B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_zcong__zless__imp__eq) ).
thf(2377,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ C @ A @ B )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_nat__power__eq__0__iff) ).
thf(948,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(289,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ B @ one_one_int ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_zcong__square__zless) ).
thf(1534,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ B @ one_one_int ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(373,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_order__le__neq__implies__less) ).
thf(1794,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(147,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1121,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(579,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_diff__bin__simps_I6_J) ).
thf(2359,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(234,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1375,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(349,axiom,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( zcong @ A @ one_one_int @ B )
| ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_zcong__square) ).
thf(1719,plain,
! [A: int,B: int] :
( ( zprime @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ B )
=> ( ( zcong @ A @ one_one_int @ B )
| ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(645,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(2537,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(273,axiom,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_semiring__mult__2) ).
thf(1493,plain,
! [A: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(63,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_power__inject__exp) ).
thf(884,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ( power_power_real @ C @ A )
= ( power_power_real @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(454,axiom,
~ ( ord_less_eq_int @ one_one_int @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
thf(2023,plain,
~ ( ord_less_eq_int @ one_one_int @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(229,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1361,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(169,axiom,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ A @ ( times_times_real @ B @ ( times_times_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1182,plain,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ A @ ( times_times_real @ B @ ( times_times_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(261,axiom,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1461,plain,
! [A: int] :
( ( times_times_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(615,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_semiring__norm_I112_J) ).
thf(2455,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(388,axiom,
! [A: int] :
( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
= one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_Legendre__1mod4) ).
thf(1842,plain,
! [A: int] :
( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) @ one_one_int ) )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(672,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_less__int__code_I13_J) ).
thf(2613,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(372,axiom,
! [A: int,B: int] :
( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int @ B )
= ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_inv__not__p__minus__1__aux) ).
thf(1791,plain,
! [A: int,B: int] :
( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ B @ one_one_int ) ) @ one_one_int @ B )
= ( zcong @ A @ ( minus_minus_int @ B @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(460,axiom,
( ( ord_less_eq_int @ zero_zero_int @ s )
& ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_s0p) ).
thf(2038,plain,
( ( ord_less_eq_int @ zero_zero_int @ s )
& ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(426,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_le__special_I1_J) ).
thf(1942,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(329,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
thf(1659,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(602,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_rel__simps_I46_J) ).
thf(2419,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_zero__le__power) ).
thf(1075,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(315,axiom,
! [A: int,B: nat,C: int] :
( ( ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_nat__number__of__mult__left) ).
thf(1612,plain,
! [A: int,B: nat,C: int] :
( ( ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ C @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ C ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(622,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_mult__numeral__1) ).
thf(2472,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1155,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(357,axiom,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_zero__le__power2) ).
thf(1744,plain,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(46,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(837,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1,conjecture,
ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(701,plain,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(191,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_power__0__left) ).
thf(1249,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(558,axiom,
( ~ ( quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
!= one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(2304,plain,
( ~ ( quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) )
=> ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
!= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(665,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2598,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(437,axiom,
! [A: nat,B: nat] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_power2__sum) ).
thf(1974,plain,
! [A: nat,B: nat] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(533,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_rel__simps_I5_J) ).
thf(2243,plain,
! [A: int] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
= ( ord_less_eq_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(126,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_real__add__left__mono) ).
thf(1060,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(73,axiom,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_even__less__0__iff) ).
thf(911,plain,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(631,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_power2__diff) ).
thf(2497,plain,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(428,axiom,
! [A: real,B: int] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_power__eq__0__iff__number__of) ).
thf(1947,plain,
! [A: real,B: int] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ B ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(392,axiom,
! [A: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zero__eq__power2) ).
thf(1852,plain,
! [A: real] :
( ( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(401,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_rel__simps_I37_J) ).
thf(1874,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(250,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ C @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_zprime__power__zdvd__cancel__left) ).
thf(1429,plain,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ C @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(439,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ B )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1979,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ B )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(495,axiom,
! [A: int,B: nat,C: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2140,plain,
! [A: int,B: nat,C: nat] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(216,axiom,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_left__distrib__number__of) ).
thf(1324,plain,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(550,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( dvd_dvd_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_zdvd__not__zless) ).
thf(2285,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( dvd_dvd_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(369,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zless__le) ).
thf(1776,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
= ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(102,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_power__strict__increasing) ).
thf(997,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ one_one_nat @ A )
=> ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(613,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_power__inject__exp) ).
thf(2450,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ( power_power_int @ C @ A )
= ( power_power_int @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(490,axiom,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_add__Pls) ).
thf(2125,plain,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(306,axiom,
! [A: int] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_number__of__Bit1) ).
thf(1588,plain,
! [A: int] :
( ( number_number_of_int @ ( bit1 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(98,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ C @ B ) @ E )
= ( zcong @ A @ ( times_times_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_zcong__zmult__prop1) ).
thf(985,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ C @ B ) @ E )
= ( zcong @ A @ ( times_times_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(206,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_power__add) ).
thf(1297,plain,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(695,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(2681,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(590,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_semiring__numeral__0__eq__0) ).
thf(2387,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(187,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_power__0__left) ).
thf(1231,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(310,axiom,
! [A: int] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_cube__square) ).
thf(1599,plain,
! [A: int] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(190,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_real__mult__le__cancel__iff2) ).
thf(1246,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
= ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(319,axiom,
~ ! [A: int] :
~ ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(1627,plain,
~ ! [A: int] :
~ ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(583,axiom,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) )
= ( dvd_dvd_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_zdvd__reduce) ).
thf(2370,plain,
! [A: int,B: int,C: int] :
( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ A @ C ) ) )
= ( dvd_dvd_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(286,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1525,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(219,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_double__eq__0__iff) ).
thf(1333,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(214,axiom,
! [A: real] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1318,plain,
! [A: real] :
( ( plus_plus_real @ A @ A )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(370,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_power__0__left__number__of) ).
thf(1779,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(461,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_sum__power2__eq__zero__iff) ).
thf(2043,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(77,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_zdiff__zmult__distrib) ).
thf(921,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(472,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2076,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(477,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_rel__simps_I33_J) ).
thf(2089,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(114,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1026,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(170,axiom,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
= ( B
= ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_number__of__reorient) ).
thf(1185,plain,
! [A: int,B: real] :
( ( ( number267125858f_real @ A )
= B )
= ( B
= ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(31,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_real__le__antisym) ).
thf(794,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(680,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_crossproduct__noteq) ).
thf(2634,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(394,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_rel__simps_I31_J) ).
thf(1857,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(176,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_add__0__iff) ).
thf(1202,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(518,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_rel__simps_I9_J) ).
thf(2203,plain,
! [A: int] :
( ( ord_less_int @ min @ ( bit1 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(380,axiom,
! [A: nat,B: nat,C: int,D: int] :
( ( dvd_dvd_int @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_dvd__power__le) ).
thf(1814,plain,
! [A: nat,B: nat,C: int,D: int] :
( ( dvd_dvd_int @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(136,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_number__of__diff) ).
thf(1086,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(466,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ B @ C ) ) @ D ) @ ( times_times_int @ ( minus_minus_int @ E @ ( times_times_int @ B @ F ) ) @ G ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ E @ G ) ) @ ( times_times_int @ B @ ( plus_plus_int @ ( times_times_int @ C @ D ) @ ( times_times_int @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_xzgcda__linear__aux1) ).
thf(2057,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ B @ C ) ) @ D ) @ ( times_times_int @ ( minus_minus_int @ E @ ( times_times_int @ B @ F ) ) @ G ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ E @ G ) ) @ ( times_times_int @ B @ ( plus_plus_int @ ( times_times_int @ C @ D ) @ ( times_times_int @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(124,axiom,
! [A: int,B: int] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_arith__simps_I32_J) ).
thf(1054,plain,
! [A: int,B: int] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( number267125858f_real @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(202,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_real__mult__1) ).
thf(1286,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(117,axiom,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ C @ ( times_times_real @ ( times_times_real @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1035,plain,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ C @ ( times_times_real @ ( times_times_real @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(684,axiom,
! [A: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_power__m1__even) ).
thf(2645,plain,
! [A: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(512,axiom,
! [A: nat] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2189,plain,
! [A: nat] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= ( plus_plus_nat @ A @ ( times_times_nat @ ( minus_minus_nat @ B @ one_one_nat ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_mult__eq__if) ).
thf(718,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ B @ A )
= ( plus_plus_nat @ A @ ( times_times_nat @ ( minus_minus_nat @ B @ one_one_nat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(603,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_zdiff__power2) ).
thf(2423,plain,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(642,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2529,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(71,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_real__zero__not__eq__one) ).
thf(906,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(199,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_divides__mul__l) ).
thf(1278,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(446,axiom,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_rel__simps_I8_J) ).
thf(2001,plain,
! [A: int] :
( ( ord_less_int @ min @ ( bit0 @ A ) )
= ( ord_less_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(280,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_rel__simps_I15_J) ).
thf(1510,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(660,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_power__gt1__lemma) ).
thf(2585,plain,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(53,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( times_times_real @ B @ A ) )
= ( times_times_real @ ( plus_plus_real @ B @ one_one_real ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(856,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( times_times_real @ B @ A ) )
= ( times_times_real @ ( plus_plus_real @ B @ one_one_real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(585,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(2376,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(320,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ one_one_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_self__quotient__aux1) ).
thf(1631,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( C
= ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ one_one_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(540,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(2260,plain,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_order__le__neq__implies__less) ).
thf(1146,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(553,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_power2__less__imp__less) ).
thf(2292,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(652,axiom,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_power__one) ).
thf(2556,plain,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_exp__eq__1) ).
thf(1103,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(537,axiom,
zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_s1) ).
thf(2253,plain,
zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(498,axiom,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(2149,plain,
! [A: int] :
( ( times_times_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(182,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_le__imp__power__dvd) ).
thf(1219,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(41,axiom,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_mult__diff__mult) ).
thf(824,plain,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(39,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_power__le__dvd) ).
thf(819,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(463,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_int__one__le__iff__zero__less) ).
thf(2048,plain,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(843,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(23,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_nat__power__less__imp__less) ).
thf(772,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(360,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_less__eq__int__code_I16_J) ).
thf(1752,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(327,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_zadd__power3) ).
thf(1652,plain,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(656,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_power__0) ).
thf(2568,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(13,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(743,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(594,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_sum__squares__eq__zero__iff) ).
thf(2398,plain,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(148,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ B )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1124,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ B )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(493,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(2134,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(316,axiom,
! [A: int] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_number__of__Bit0) ).
thf(1620,plain,
! [A: int] :
( ( number_number_of_int @ ( bit0 @ A ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ A ) ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(628,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( dvd_dvd_int @ D @ E )
=> ( ( dvd_dvd_int @ D @ ( plus_plus_int @ B @ C ) )
= ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_zdvd__period) ).
thf(2489,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( dvd_dvd_int @ D @ E )
=> ( ( dvd_dvd_int @ D @ ( plus_plus_int @ B @ C ) )
= ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ B @ ( times_times_int @ A @ E ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(524,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A = zero_zero_int )
| ( A = one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_int__pos__lt__two__imp__zero__or__one) ).
thf(2220,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A = zero_zero_int )
| ( A = one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(345,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_bin__less__0__simps_I3_J) ).
thf(1707,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(397,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_numeral__1__eq__1) ).
thf(1865,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(444,axiom,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_s) ).
thf(1997,plain,
zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(365,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_mult__numeral__1__right) ).
thf(1765,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(262,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( minus_minus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_diff__square) ).
thf(1464,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( minus_minus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(563,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_mult__Bit1) ).
thf(2319,plain,
! [A: int,B: int] :
( ( times_times_int @ ( bit1 @ A ) @ B )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(333,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_le__special_I4_J) ).
thf(1675,plain,
! [A: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(153,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1139,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(277,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_zadd__left__commute) ).
thf(1503,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(616,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_bin__less__0__simps_I1_J) ).
thf(2457,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_divides__exp) ).
thf(919,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(192,axiom,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1258,plain,
! [A: real,B: real,C: real,D: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( times_times_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(4,axiom,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_right__distrib__number__of) ).
thf(704,plain,
! [A: int,B: real,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ A ) @ B ) @ ( times_times_real @ ( number267125858f_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(96,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_real__mult__less__iff1) ).
thf(979,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
= ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(173,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1194,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(473,axiom,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_diff__bin__simps_I5_J) ).
thf(2079,plain,
! [A: int] :
( ( minus_minus_int @ min @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus_int @ min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(646,axiom,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_power3__eq__cube) ).
thf(2538,plain,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(683,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_less__int__code_I14_J) ).
thf(2642,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(681,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_zcong__zmult__prop3) ).
thf(2637,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ~ ( zcong @ A @ zero_zero_int @ C )
=> ~ ( zcong @ ( times_times_int @ B @ A ) @ zero_zero_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(285,axiom,
ord_less_int @ t @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(1524,plain,
ord_less_int @ t @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(11,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_zcong__eq__trans) ).
thf(736,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( D = B )
=> ( ( zcong @ B @ A @ E )
=> ( zcong @ C @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(480,axiom,
! [A: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add__special_I2_J) ).
thf(2097,plain,
! [A: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(539,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_power__one__right) ).
thf(2257,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(291,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_power2__eq__imp__eq) ).
thf(1542,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(515,axiom,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ ( number267125858f_real @ B ) @ C ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_add__number__of__left) ).
thf(2197,plain,
! [A: int,B: int,C: real] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ ( plus_plus_real @ ( number267125858f_real @ B ) @ C ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(69,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_crossproduct__eq) ).
thf(900,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(694,axiom,
! [A: int] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_power2__ge__self) ).
thf(2679,plain,
! [A: int] : ( ord_less_eq_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(475,axiom,
! [A: int,B: int] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_number__of__add) ).
thf(2084,plain,
! [A: int,B: int] :
( ( number267125858f_real @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(522,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_rel__simps_I28_J) ).
thf(2214,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(534,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_zprime__power__zdvd__cancel__right) ).
thf(2246,plain,
! [A: nat,B: int,C: int,D: int] :
( ( zprime @ D )
=> ( ~ ( dvd_dvd_int @ D @ C )
=> ( ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ ( times_times_int @ B @ C ) )
=> ( dvd_dvd_int @ ( power_power_int @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(556,axiom,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( dvd_dvd_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_zpower__zdvd__prop2) ).
thf(2299,plain,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( dvd_dvd_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(692,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_le__imp__power__dvd) ).
thf(2669,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(155,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ B @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_power__Suc__less) ).
thf(1144,plain,
! [A: nat,B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ( ( ord_less_real @ B @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(402,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ C @ B @ A )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ B @ A )
=> ( C = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_zcong__less__eq) ).
thf(1877,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ C @ B @ A )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ B @ A )
=> ( C = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(221,axiom,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_not__sum__squares__lt__zero) ).
thf(1339,plain,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(297,axiom,
! [A: int] :
( ( min
= ( bit1 @ A ) )
= ( min = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_rel__simps_I43_J) ).
thf(1557,plain,
! [A: int] :
( ( min
= ( bit1 @ A ) )
= ( min = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(572,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_q__pos__lemma) ).
thf(2343,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_divides__exp2) ).
thf(816,plain,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ A @ C ) @ B )
=> ( dvd_dvd_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(485,axiom,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__0__number__of) ).
thf(2111,plain,
! [A: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(414,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_nat__number__of__Pls) ).
thf(1909,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(157,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1149,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(690,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_semiring__mult__number__of) ).
thf(2664,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(236,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( times_times_int @ A @ B ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_number__of__mult) ).
thf(1381,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( times_times_int @ A @ B ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(618,axiom,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__less__0) ).
thf(2461,plain,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(146,axiom,
! [A: real,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= one_one_real ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= ( times_times_real @ A @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_realpow__num__eq__if) ).
thf(1112,plain,
! [A: real,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= one_one_real ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_real @ A @ B )
= ( times_times_real @ A @ ( power_power_real @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(332,axiom,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_mult__nat__number__of) ).
thf(1667,plain,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(509,axiom,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__special_I2_J) ).
thf(2180,plain,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_eq_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(455,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
| ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_zdvd__bounds) ).
thf(2025,plain,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
| ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(134,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1080,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(383,axiom,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_add__nat__number__of) ).
thf(1821,plain,
! [A: int,B: int] :
( ( ( ord_less_int @ B @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_int @ B @ pls )
=> ( ( ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ B ) ) )
& ( ~ ( ord_less_int @ A @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(354,axiom,
~ ! [A: int] :
~ ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283__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(1731,plain,
~ ! [A: int] :
~ ( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(598,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_int__0__less__1) ).
thf(2410,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(386,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_pos__zmult__pos) ).
thf(1838,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
=> ( ord_less_int @ zero_zero_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(663,axiom,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2593,plain,
! [A: real,B: nat] :
( ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(115,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_power__0) ).
thf(1029,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(22,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_less__eq__real__def) ).
thf(769,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
= ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(552,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Bit1__def) ).
thf(2289,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(548,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ A ) @ ( power_power_int @ ( number_number_of_int @ min ) @ B ) @ C )
=> ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( power_power_int @ ( number_number_of_int @ min ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_neg__one__power__eq__mod__m) ).
thf(2278,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ C )
=> ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ A ) @ ( power_power_int @ ( number_number_of_int @ min ) @ B ) @ C )
=> ( ( power_power_int @ ( number_number_of_int @ min ) @ A )
= ( power_power_int @ ( number_number_of_int @ min ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(651,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_rel__simps_I38_J) ).
thf(2553,plain,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(567,axiom,
! [A: int] :
( ( zprime @ A )
= ( ( ord_less_int @ one_one_int @ A )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_zprime__def) ).
thf(2329,plain,
! [A: int] :
( ( zprime @ A )
= ( ( ord_less_int @ one_one_int @ A )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( dvd_dvd_int @ B @ A ) )
=> ( ( B = one_one_int )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_power__eq__if) ).
thf(932,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(165,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_power__less__imp__less__base) ).
thf(1171,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(581,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zadd__zless__mono) ).
thf(2365,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(110,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_power__one__right) ).
thf(1015,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(167,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_le__number__of) ).
thf(1176,plain,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(252,axiom,
! [A: int] :
( ( minus_minus_int @ ( times_times_int @ A @ A ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ ( minus_minus_int @ A @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_real__squared__diff__one__factored) ).
thf(1435,plain,
! [A: int] :
( ( minus_minus_int @ ( times_times_int @ A @ A ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ A @ one_one_int ) @ ( minus_minus_int @ A @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(274,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_numeral__1__eq__1) ).
thf(1496,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_divides__ge) ).
thf(851,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(340,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_realpow__two__sum__zero__iff) ).
thf(1694,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(377,axiom,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( minus_minus_int @ B @ D ) ) @ ( times_times_int @ ( minus_minus_int @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_mult__diff__mult) ).
thf(1805,plain,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( minus_minus_int @ B @ D ) ) @ ( times_times_int @ ( minus_minus_int @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(470,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
= ( ord_less_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_rel__simps_I13_J) ).
thf(2069,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ min )
= ( ord_less_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(266,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_nat__1__add__1) ).
thf(1474,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)],[266]) ).
thf(575,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_number__of__Bit0) ).
thf(2350,plain,
! [A: int] :
( ( number267125858f_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(595,axiom,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_power__mult__distrib) ).
thf(2401,plain,
! [A: int,B: int,C: nat] :
( ( power_power_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(342,axiom,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_semiring__mult__2__right) ).
thf(1699,plain,
! [A: real] :
( ( times_times_real @ A @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(180,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_power__mono) ).
thf(1213,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(42,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_real__le__refl) ).
thf(827,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(464,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_zadd__0) ).
thf(2051,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(120,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_le__number__of__eq__not__less) ).
thf(1044,plain,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ~ ( ord_less_real @ ( number267125858f_real @ B ) @ ( number267125858f_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(650,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_power__mult) ).
thf(2550,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(287,axiom,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_add__Pls__right) ).
thf(1528,plain,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(57,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_real__mult__less__mono2) ).
thf(868,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(26,axiom,
! [A: nat,B: real] :
( ( ord_less_eq_real @ one_one_real @ B )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_one__le__power) ).
thf(780,plain,
! [A: nat,B: real] :
( ( ord_less_eq_real @ one_one_real @ B )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(324,axiom,
! [A: int,B: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_less__number__of) ).
thf(1643,plain,
! [A: int,B: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(352,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_power__strict__increasing) ).
thf(1726,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_int @ one_one_int @ A )
=> ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(230,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1364,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(635,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_add__numeral__0) ).
thf(2506,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(299,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_diff__bin__simps_I10_J) ).
thf(1562,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(465,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__Bit0__Bit0) ).
thf(2054,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(531,axiom,
! [A: int,B: int,C: int] :
( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_Euler_Oaux____1) ).
thf(2239,plain,
! [A: int,B: int,C: int] :
( ~ ( zcong @ B @ zero_zero_int @ C )
=> ( ( zcong @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ C )
=> ~ ( dvd_dvd_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(304,axiom,
! [A: int] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_number__of__Bit1) ).
thf(1583,plain,
! [A: int] :
( ( number267125858f_real @ ( bit1 @ A ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ A ) ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(330,axiom,
! [A: real] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_power2__less__0) ).
thf(1662,plain,
! [A: real] :
~ ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(178,axiom,
! [A: nat,B: real,C: nat,D: real] :
( ( dvd_dvd_real @ ( power_power_real @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_power__le__dvd) ).
thf(1208,plain,
! [A: nat,B: real,C: nat,D: real] :
( ( dvd_dvd_real @ ( power_power_real @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_real @ ( power_power_real @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(83,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_le__imp__power__dvd) ).
thf(944,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( dvd_dvd_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(263,axiom,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_two__realpow__ge__one) ).
thf(1467,plain,
! [A: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(545,axiom,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
= ( ord_less_eq_int @ min @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_rel__simps_I26_J) ).
thf(2271,plain,
! [A: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ A ) )
= ( ord_less_eq_int @ min @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(686,axiom,
! [A: int] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_power2__eq__square__number__of) ).
thf(2652,plain,
! [A: int] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(79,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(927,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(696,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_four__x__squared) ).
thf(2684,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(265,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zadd__left__mono) ).
thf(1472,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1018,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(122,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_right__diff__distrib__number__of) ).
thf(1049,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ A ) @ B ) @ ( times_times_int @ ( number_number_of_int @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(362,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_sum__power2__ge__zero) ).
thf(1758,plain,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(163,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_zle__antisym) ).
thf(1166,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(412,axiom,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
= ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_number__of__reorient) ).
thf(1905,plain,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
= ( B
= ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(246,axiom,
ord_less_eq_int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_rel__simps_I23_J) ).
thf(1420,plain,
ord_less_eq_int @ min @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(634,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_rel__simps_I10_J) ).
thf(2503,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(336,axiom,
! [A: real,B: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_zero__le__even__power_H) ).
thf(1684,plain,
! [A: real,B: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_add__0__iff) ).
thf(749,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(678,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ B @ zero_zero_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_zcong__not__zero) ).
thf(2629,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ B @ zero_zero_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(389,axiom,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_zcong__1) ).
thf(1845,plain,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(282,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_zadd__assoc) ).
thf(1516,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(130,axiom,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_power__one) ).
thf(1070,plain,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(689,axiom,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_power3__eq__cube) ).
thf(2661,plain,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ A )
= ( times_times_nat @ A @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_power__commutes) ).
thf(971,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ A )
= ( times_times_nat @ A @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(496,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_semiring__mult__2__right) ).
thf(2143,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(312,axiom,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_power__less__power__Suc) ).
thf(1605,plain,
! [A: nat,B: int] :
( ( ord_less_int @ one_one_int @ B )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( times_times_int @ B @ ( power_power_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(640,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_power__0__left) ).
thf(2518,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(288,axiom,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_power2__eq__imp__eq) ).
thf(1531,plain,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ B )
= ( times_times_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(712,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ B )
= ( times_times_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(105,axiom,
! [A: nat,B: nat,C: real,D: real] :
( ( dvd_dvd_real @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_dvd__power__le) ).
thf(1003,plain,
! [A: nat,B: nat,C: real,D: real] :
( ( dvd_dvd_real @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(367,axiom,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_less__special_I2_J) ).
thf(1770,plain,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(185,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1225,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(467,axiom,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_power2__sum) ).
thf(2060,plain,
! [A: real,B: real] :
( ( power_power_real @ ( plus_plus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(5,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_real__le__linear) ).
thf(707,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(513,axiom,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_zcong__id) ).
thf(2192,plain,
! [A: int] : ( zcong @ A @ zero_zero_int @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(64,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_zcong__scalar) ).
thf(887,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( zcong @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(597,axiom,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2407,plain,
! [A: int] :
( ( times_times_int @ A @ one_one_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(195,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_zle__trans) ).
thf(1267,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(478,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_le__imp__0__less) ).
thf(2092,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(348,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) @ zero_zero_int )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ F )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_zdiv__mono2__neg__lemma) ).
thf(1716,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) @ zero_zero_int )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ F )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(30,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(791,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(171,axiom,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_field__power__not__zero) ).
thf(1188,plain,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( power_power_real @ B @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_realpow__minus__mult) ).
thf(1038,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(47,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_real__mult__assoc) ).
thf(840,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(605,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_rel__simps_I17_J) ).
thf(2429,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(570,axiom,
! [A: real] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2337,plain,
! [A: real] :
( ( times_times_real @ A @ A )
= ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(564,axiom,
! [A: int] :
( ( power_power_real @ ( number267125858f_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_power2__eq__square__number__of) ).
thf(2322,plain,
! [A: int] :
( ( power_power_real @ ( number267125858f_real @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ A ) @ ( number267125858f_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(150,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( B = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_zero__less__power__nat__eq) ).
thf(1130,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( B = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(355,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1738,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(220,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_left__diff__distrib__number__of) ).
thf(1336,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_int @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ ( number_number_of_int @ C ) ) @ ( times_times_int @ B @ ( number_number_of_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(207,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_power__strict__increasing__iff) ).
thf(1300,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_real @ one_one_real @ C )
=> ( ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(322,axiom,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_add__numeral__0__right) ).
thf(1637,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( number267125858f_real @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(547,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ one_one_int @ B )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_one__le__power) ).
thf(2276,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ one_one_int @ B )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(491,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_mult__numeral__1__right) ).
thf(2128,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(627,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_zcong__zless__0) ).
thf(2486,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ( ( zcong @ B @ zero_zero_int @ A )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_nat @ C @ ( times_times_nat @ E @ A ) )
!= ( plus_plus_nat @ D @ ( times_times_nat @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_add__scale__eq__noteq) ).
thf(951,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( C = D )
& ( A != B ) )
=> ( ( plus_plus_nat @ C @ ( times_times_nat @ E @ A ) )
!= ( plus_plus_nat @ D @ ( times_times_nat @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(423,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_semiring__norm_I112_J) ).
thf(1934,plain,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(604,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_rel__simps_I14_J) ).
thf(2426,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(343,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_semiring__numeral__1__eq__1) ).
thf(1702,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(183,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_power__increasing) ).
thf(1221,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(578,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_semiring__norm_I113_J) ).
thf(2357,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(359,axiom,
! [A: int,B: int] :
( ( quadRes @ A @ B )
= ( ? [C: int] : ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_QuadRes__def) ).
thf(1749,plain,
! [A: int,B: int] :
( ( quadRes @ A @ B )
= ( ? [C: int] : ( zcong @ ( power_power_int @ C @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_realpow__num__eq__if) ).
thf(727,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= one_one_nat ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
= ( times_times_nat @ A @ ( power_power_nat @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(637,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(2511,plain,
ord_less_eq_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(374,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rel__simps_I32_J) ).
thf(1797,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_power__gt1__lemma) ).
thf(1008,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ B @ ( power_power_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(457,axiom,
~ ( ord_less_int @ min @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_rel__simps_I7_J) ).
thf(2030,plain,
~ ( ord_less_int @ min @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(197,axiom,
! [A: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_not__real__square__gt__zero) ).
thf(1272,plain,
! [A: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(54,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_power__one__right) ).
thf(859,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(242,axiom,
! [A: int] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_power2__eq__square__number__of) ).
thf(1404,plain,
! [A: int] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(228,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1358,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(599,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_zless__add1__eq) ).
thf(2411,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(632,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(2500,plain,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(270,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_number__of__Pls) ).
thf(1485,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(123,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_power__increasing) ).
thf(1052,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(278,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/sandbox2/benchmark/theBenchmark.p',fact_445__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(1506,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)],[278]) ).
thf(543,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_sum__power2__ge__zero) ).
thf(2266,plain,
! [A: int,B: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( twoSqu362149276sum2sq @ B )
=> ( ( twoSqu362149276sum2sq @ A )
=> ( twoSqu362149276sum2sq @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_is__mult__sum2sq) ).
thf(876,plain,
! [A: int,B: int] :
( ( twoSqu362149276sum2sq @ B )
=> ( ( twoSqu362149276sum2sq @ A )
=> ( twoSqu362149276sum2sq @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(188,axiom,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_power__one) ).
thf(1240,plain,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(100,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(991,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(607,axiom,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_zcong__zero__equiv__div) ).
thf(2435,plain,
! [A: int,B: int] :
( ( zcong @ A @ zero_zero_int @ B )
= ( dvd_dvd_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(625,axiom,
! [A: int] :
( ( bit0 @ A )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_rel__simps_I45_J) ).
thf(2479,plain,
! [A: int] :
( ( bit0 @ A )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(434,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of_int @ min ) @ B )
=> ~ ( zcong @ A @ one_one_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_zcong__neg__1__impl__ne__1) ).
thf(1966,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B )
=> ( ( zcong @ A @ ( number_number_of_int @ min ) @ B )
=> ~ ( zcong @ A @ one_one_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(295,axiom,
ord_less_int @ min @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_bin__less__0__simps_I2_J) ).
thf(1553,plain,
ord_less_int @ min @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(215,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(1321,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ A )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(514,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_semiring__add__number__of) ).
thf(2194,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( plus_plus_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(574,axiom,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_power2__eq__square) ).
thf(2347,plain,
! [A: real] :
( ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(565,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_zero__power2) ).
thf(2325,plain,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(520,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ E @ zero_zero_int )
=> ( ( ord_less_int @ A @ E )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_unique__quotient__lemma__neg) ).
thf(2209,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ E @ zero_zero_int )
=> ( ( ord_less_int @ A @ E )
=> ( ( ord_less_int @ A @ C )
=> ( ord_less_eq_int @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(108,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
= ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_real__less__def) ).
thf(1010,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
= ( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(688,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_diff__bin__simps_I9_J) ).
thf(2658,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( minus_minus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(445,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_rel__simps_I16_J) ).
thf(1998,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(247,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ E @ A )
=> ( ord_less_eq_int @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_unique__quotient__lemma) ).
thf(1421,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ B ) @ C ) @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ E ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ A )
=> ( ( ord_less_int @ E @ A )
=> ( ord_less_eq_int @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(450,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_zadd__strict__right__mono) ).
thf(2013,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(677,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_plus__numeral__code_I9_J) ).
thf(2626,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(213,axiom,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_zcong__trans) ).
thf(1316,plain,
! [A: int,B: int,C: int,D: int] :
( ( zcong @ B @ C @ D )
=> ( ( zcong @ C @ A @ D )
=> ( zcong @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(326,axiom,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_not__sum__squares__lt__zero) ).
thf(1649,plain,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(560,axiom,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_add__diff__add) ).
thf(2310,plain,
! [A: int,B: int,C: int,D: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(70,axiom,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_power__mult__distrib) ).
thf(903,plain,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(203,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_power__gt1__lemma) ).
thf(1289,plain,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(526,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
thf(2226,plain,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(258,axiom,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_zprime__zdvd__power) ).
thf(1453,plain,
! [A: int,B: nat,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( power_power_int @ A @ B ) )
=> ( dvd_dvd_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_dvd__power__le) ).
thf(946,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( dvd_dvd_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( dvd_dvd_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(447,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_zspecial__product) ).
thf(2004,plain,
! [A: int,B: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(325,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( dvd_dvd_int @ A @ B )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_zdvd__antisym__nonneg) ).
thf(1646,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( dvd_dvd_int @ B @ A )
=> ( ( dvd_dvd_int @ A @ B )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(610,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(2443,plain,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(37,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_power__mult) ).
thf(813,plain,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ A @ ( times_times_nat @ B @ C ) )
= ( power_power_real @ ( power_power_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(350,axiom,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1721,plain,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(90,axiom,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_zcong__sym) ).
thf(963,plain,
! [A: int,B: int,C: int] :
( ( zcong @ A @ B @ C )
= ( zcong @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(504,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_rel__simps_I4_J) ).
thf(2167,plain,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(507,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_sum__squares__le__zero__iff) ).
thf(2174,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ A ) @ ( times_times_int @ B @ B ) ) @ zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(591,axiom,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_semiring__mult__2) ).
thf(2389,plain,
! [A: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(267,axiom,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_power2__eq__square) ).
thf(1476,plain,
! [A: int] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(127,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_real__mult__right__cancel) ).
thf(1062,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(643,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_semiring__numeral__0__eq__0) ).
thf(2532,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(279,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_semiring__numeral__1__eq__1) ).
thf(1508,plain,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(499,axiom,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
thf(2152,plain,
! [A: real,B: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(541,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_rel__simps_I34_J) ).
thf(2262,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(612,axiom,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_semiring__mult__2) ).
thf(2447,plain,
! [A: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(338,axiom,
! [A: nat,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_power__strict__mono) ).
thf(1689,plain,
! [A: nat,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(623,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_power2__less__imp__less) ).
thf(2475,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(74,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_real__mult__left__cancel) ).
thf(914,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(685,axiom,
! [A: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_odd__nonzero) ).
thf(2648,plain,
! [A: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(205,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1294,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(469,axiom,
! [A: int] :
( ( ( bit1 @ A )
= min )
= ( A = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_rel__simps_I47_J) ).
thf(2066,plain,
! [A: int] :
( ( ( bit1 @ A )
= min )
= ( A = min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(510,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_rel__simps_I44_J) ).
thf(2183,plain,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(281,axiom,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_power__even__eq) ).
thf(1513,plain,
! [A: int,B: nat] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( power_power_int @ ( power_power_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(488,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Pls__def) ).
thf(2120,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(44,axiom,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_power__less__power__Suc) ).
thf(832,plain,
! [A: nat,B: real] :
( ( ord_less_real @ one_one_real @ B )
=> ( ord_less_real @ ( power_power_real @ B @ A ) @ ( times_times_real @ B @ ( power_power_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(676,axiom,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_le__number__of__eq__not__less) ).
thf(2623,plain,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(133,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1077,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(580,axiom,
! [A: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add__special_I3_J) ).
thf(2362,plain,
! [A: int] :
( ( plus_plus_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(502,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_one__is__num__one) ).
thf(2162,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(313,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mult__Bit0) ).
thf(1607,plain,
! [A: int,B: int] :
( ( times_times_int @ ( bit0 @ A ) @ B )
= ( bit0 @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(20,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( times_times_int @ ( number_number_of_int @ B ) @ C ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_mult__number__of__left) ).
thf(763,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( times_times_int @ ( number_number_of_int @ B ) @ C ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(210,axiom,
! [A: real,B: nat,C: real] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_power__less__imp__less__base) ).
thf(1309,plain,
! [A: real,B: nat,C: real] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(408,axiom,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add__numeral__0__right) ).
thf(1893,plain,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(554,axiom,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_zero__le__power2) ).
thf(2294,plain,
! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(630,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(2494,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(255,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zadd__zmult__distrib) ).
thf(1444,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(161,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_power__less__imp__less__exp) ).
thf(1161,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ C )
=> ( ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_le__number__of) ).
thf(800,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(413,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
thf(1908,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(151,axiom,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_left__diff__distrib__number__of) ).
thf(1133,plain,
! [A: real,B: real,C: int] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( number267125858f_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( number267125858f_real @ C ) ) @ ( times_times_real @ B @ ( number267125858f_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(224,axiom,
! [A: real,B: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ A )
= ( times_times_real @ A @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_power__commutes) ).
thf(1348,plain,
! [A: real,B: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ A )
= ( times_times_real @ A @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(16,axiom,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ ( power_power_real @ A @ B ) @ C )
= ( power_power_real @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(752,plain,
! [A: real,B: nat,C: nat] :
( ( power_power_real @ ( power_power_real @ A @ B ) @ C )
= ( power_power_real @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(200,axiom,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_eq__number__of) ).
thf(1280,plain,
! [A: int,B: int] :
( ( ( number267125858f_real @ A )
= ( number267125858f_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(529,axiom,
! [A: int] :
( ( zprime @ A )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_prime__g__5) ).
thf(2233,plain,
! [A: int] :
( ( zprime @ A )
=> ( ( A
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(293,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_rel__simps_I49_J) ).
thf(1546,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(239,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1395,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(56,axiom,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_power__eq__0__iff) ).
thf(865,plain,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(103,axiom,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( times_times_int @ A @ B ) )
=> ( ( dvd_dvd_int @ C @ A )
| ( dvd_dvd_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_zprime__zdvd__zmult__better) ).
thf(999,plain,
! [A: int,B: int,C: int] :
( ( zprime @ C )
=> ( ( dvd_dvd_int @ C @ ( times_times_int @ A @ B ) )
=> ( ( dvd_dvd_int @ C @ A )
| ( dvd_dvd_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(551,axiom,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_zdvd__imp__le) ).
thf(2287,plain,
! [A: int,B: int] :
( ( dvd_dvd_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(302,axiom,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_zero__le__power) ).
thf(1578,plain,
! [A: nat,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(431,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_semiring__mult__number__of) ).
thf(1957,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ pls @ B )
=> ( ( ord_less_eq_int @ pls @ A )
=> ( ( times_times_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
= ( number_number_of_nat @ ( times_times_int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(589,axiom,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(2385,plain,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(334,axiom,
! [A: int,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_realpow__minus__mult) ).
thf(1678,plain,
! [A: int,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) @ A )
= ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(500,axiom,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_diff__bin__simps_I3_J) ).
thf(2155,plain,
! [A: int] :
( ( minus_minus_int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus_int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(644,axiom,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_mult__2__right) ).
thf(2534,plain,
! [A: int] :
( ( times_times_int @ A @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(141,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ ( times_times_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1097,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ ( times_times_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(661,axiom,
! [A: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_double__number__of__Bit0) ).
thf(2587,plain,
! [A: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ A ) )
= ( number267125858f_real @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(308,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_Int2_Oaux1) ).
thf(1593,plain,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(668,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_rel__simps_I30_J) ).
thf(2604,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ min )
= ( ord_less_eq_int @ A @ min ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) )
=> ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_divides__add__revr) ).
thf(854,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ B @ ( plus_plus_nat @ C @ A ) )
=> ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(208,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1303,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(442,axiom,
! [A: int,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= one_one_int ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= ( times_times_int @ A @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_realpow__num__eq__if) ).
thf(1986,plain,
! [A: int,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= one_one_int ) )
& ( ( B != zero_zero_nat )
=> ( ( power_power_int @ A @ B )
= ( times_times_int @ A @ ( power_power_int @ A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(517,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_zcong__not) ).
thf(2201,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ C @ B )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ C )
=> ~ ( zcong @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(212,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(1314,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(381,axiom,
! [A: nat,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_power__mono) ).
thf(1816,plain,
! [A: nat,B: int,C: int] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(511,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_power3__eq__cube) ).
thf(2186,plain,
! [A: nat] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(596,axiom,
! [A: nat,B: int] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ B ) ) )
= ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_zero__less__power__nat__eq__number__of) ).
thf(2404,plain,
! [A: nat,B: int] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ B ) ) )
= ( ( ( number_number_of_nat @ B )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(407,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_zcong__zadd) ).
thf(1891,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ B @ E )
=> ( zcong @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(571,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( times_times_int @ B @ A )
= one_one_int )
= ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_pos__zmult__eq__1__iff) ).
thf(2340,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( times_times_int @ B @ A )
= one_one_int )
= ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(87,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_sum__squares__ge__zero) ).
thf(955,plain,
! [A: real,B: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(68,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_times__numeral__code_I5_J) ).
thf(897,plain,
! [A: int,B: int] :
( ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( times_times_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(244,axiom,
? [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) ).
thf(1410,plain,
? [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
& ( ord_less_int @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ A @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ! [B: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ B )
& ( ord_less_int @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
& ( zcong @ s1 @ B @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(601,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ C )
=> ( ( ord_less_eq_int @ B @ A )
| ( ord_less_eq_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_Euler_Oaux2) ).
thf(2417,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ( ord_less_int @ A @ C )
=> ( ( ord_less_eq_int @ B @ A )
| ( ord_less_eq_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(346,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
thf(1710,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(174,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1197,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(525,axiom,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_less__special_I4_J) ).
thf(2223,plain,
! [A: int] :
( ( ord_less_real @ ( number267125858f_real @ A ) @ one_one_real )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(89,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(960,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(674,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_rel__simps_I29_J) ).
thf(2619,plain,
! [A: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(128,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( times_times_nat @ B @ A ) )
= ( times_times_nat @ ( plus_plus_nat @ B @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1065,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( times_times_nat @ B @ A ) )
= ( times_times_nat @ ( plus_plus_nat @ B @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(468,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ F @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_zdiv__mono2__lemma) ).
thf(2063,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ D @ E ) @ F ) )
=> ( ( ord_less_int @ F @ D )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_int @ zero_zero_int @ D )
=> ( ( ord_less_eq_int @ D @ A )
=> ( ord_less_eq_int @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(314,axiom,
~ ( ord_less_eq_int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_rel__simps_I20_J) ).
thf(1610,plain,
~ ( ord_less_eq_int @ pls @ min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(12,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_crossproduct__eq) ).
thf(740,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(532,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( dvd_dvd_int @ ( power_power_int @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_power__le__dvd) ).
thf(2241,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( dvd_dvd_int @ ( power_power_int @ B @ C ) @ D )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(438,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_number__of__Pls) ).
thf(1977,plain,
( ( number267125858f_real @ pls )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(193,axiom,
! [A: real,B: nat,C: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1261,plain,
! [A: real,B: nat,C: nat] :
( ( times_times_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( power_power_real @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_power__add) ).
thf(1152,plain,
! [A: nat,B: nat,C: nat] :
( ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_nat__mult__eq__one) ).
thf(1378,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(542,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I19_J) ).
thf(2265,plain,
ord_less_eq_int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(620,axiom,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_power__eq__0__iff) ).
thf(2467,plain,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(294,axiom,
! [A: real,B: real] :
( ( power_power_real @ ( minus_minus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_power2__diff) ).
thf(1550,plain,
! [A: real,B: real] :
( ( power_power_real @ ( minus_minus_real @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(420,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_zadd__0__right) ).
thf(1925,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(347,axiom,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_le__nat__number__of) ).
thf(1713,plain,
! [A: int,B: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
= ( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(411,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_rel__simps_I51_J) ).
thf(1902,plain,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(405,axiom,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_field__power__not__zero) ).
thf(1885,plain,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( power_power_int @ B @ A )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(139,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_dvd__power__same) ).
thf(1093,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ ( power_power_nat @ B @ A ) @ ( power_power_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(576,axiom,
! [A: int,B: nat,C: nat] :
( ( times_times_nat @ ( number_number_of_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_right__distrib__number__of) ).
thf(2353,plain,
! [A: int,B: nat,C: nat] :
( ( times_times_nat @ ( number_number_of_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ A ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(666,axiom,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zero__eq__power2) ).
thf(2600,plain,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(237,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_crossproduct__noteq) ).
thf(1384,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(290,axiom,
~ ! [A: int] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(1537,plain,
~ ! [A: int] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(309,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_zless__imp__add1__zle) ).
thf(1597,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(697,axiom,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_power__add) ).
thf(2687,plain,
! [A: int,B: nat,C: nat] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(97,axiom,
! [A: int,B: int,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( times_times_real @ ( number267125858f_real @ B ) @ C ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_mult__number__of__left) ).
thf(982,plain,
! [A: int,B: int,C: real] :
( ( times_times_real @ ( number267125858f_real @ A ) @ ( times_times_real @ ( number267125858f_real @ B ) @ C ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(403,axiom,
! [A: nat,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_dvd__power__same) ).
thf(1880,plain,
! [A: nat,B: int,C: int] :
( ( dvd_dvd_int @ B @ C )
=> ( dvd_dvd_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(251,axiom,
! [A: real,B: nat] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_real )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_even__power__le__0__imp__0) ).
thf(1431,plain,
! [A: real,B: nat] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ zero_zero_real )
=> ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(34,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ B @ C ) @ E )
= ( zcong @ A @ ( times_times_int @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_zcong__zmult__prop2) ).
thf(803,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( zcong @ C @ D @ E )
=> ( ( zcong @ A @ ( times_times_int @ B @ C ) @ E )
= ( zcong @ A @ ( times_times_int @ B @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(231,axiom,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_real__mult__commute) ).
thf(1367,plain,
! [A: real,B: real] :
( ( times_times_real @ A @ B )
= ( times_times_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(427,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_semiring__one__add__one__is__two) ).
thf(1945,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)],[427]) ).
thf(519,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2206,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(335,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__eq__int__code_I14_J) ).
thf(1681,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(452,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_zero__is__num__zero) ).
thf(2018,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(614,axiom,
! [A: int,B: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_zero__le__even__power_H) ).
thf(2453,plain,
! [A: int,B: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(505,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_power__strict__increasing__iff) ).
thf(2170,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_int @ one_one_int @ C )
=> ( ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(621,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( zcong @ ( power_power_int @ B @ C ) @ one_one_int @ D )
=> ( zcong @ ( power_power_int @ B @ ( times_times_nat @ C @ A ) ) @ one_one_int @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_zcong__zpower__zmult) ).
thf(2470,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( zcong @ ( power_power_int @ B @ C ) @ one_one_int @ D )
=> ( zcong @ ( power_power_int @ B @ ( times_times_nat @ C @ A ) ) @ one_one_int @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(245,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_crossproduct__eq) ).
thf(1417,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(698,axiom,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_t__l__p) ).
thf(2690,plain,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(300,axiom,
! [A: int,B: int] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_Legendre__def) ).
thf(1565,plain,
! [A: int,B: int] :
( ( ( zcong @ A @ zero_zero_int @ B )
=> ( ( legendre @ A @ B )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ B )
=> ( ( ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= one_one_int ) )
& ( ~ ( quadRes @ B @ A )
=> ( ( legendre @ A @ B )
= ( number_number_of_int @ min ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(608,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__number__of__left) ).
thf(2438,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(272,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_less__eq__int__code_I15_J) ).
thf(1490,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(417,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_power__increasing) ).
thf(1917,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_zero__less__power) ).
thf(755,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(483,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2106,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(476,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_power__less__imp__less__base) ).
thf(2087,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(508,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_bin__less__0__simps_I4_J) ).
thf(2177,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(687,axiom,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_not__sum__power2__lt__zero) ).
thf(2655,plain,
! [A: int,B: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(2727,plain,
$false,
inference(e,[status(thm)],[892,1665,2094,760,2072,1995,846,909,1899,1840,1850,2559,1179,777,1818,1950,1554,1586,1501,2612,1024,1469,2109,2131,1083,1982,2544,941,1686,2250,977,1005,2117,1882,1522,2395,1808,1073,2671,1728,1591,1971,1041,1173,1855,1200,1158,2512,2231,2622,1068,994,2527,2590,1401,1939,2248,873,1205,2114,1142,1269,878,2380,1426,1655,2607,2035,1867,715,1275,1327,1342,1640,1954,930,1458,797,2316,1919,2459,1354,2146,1746,1835,1001,2046,1576,709,2020,2010,2082,1724,2173,1803,829,1095,2432,1914,1243,1127,782,1441,1228,1623,1482,2603,1760,2667,785,1871,2501,1455,2562,1330,2444,1860,1264,2217,2274,917,702,1832,1191,2571,2356,1545,1800,1479,1013,1931,2158,1773,2301,1963,1100,1847,1922,2691,1704,870,969,2373,1741,1398,881,2007,924,2616,2027,1373,1911,1109,2236,2122,2254,1283,821,1811,1450,1136,834,1960,806,2335,966,766,1169,2281,1215,1896,774,2137,1351,2103,2392,2367,1928,1447,2483,1345,988,2639,1697,849,1863,1691,1306,2164,810,2574,1438,1311,2296,2307,1768,1868,2382,1047,1057,1163,2441,1387,1021,2541,862,1487,2032,2414,2015,1560,957,1223,894,746,1091,1519,2596,1355,1580,788,1370,1423,2464,2477,2332,1888,1624,889,1787,1210,2327,1291,974,1106,1032,1602,1968,2565,2200,2609,757,2345,2211,1407,2547,2313,2492,1634,2228,1936,1089,1983,2577,1498,2694,2509,2631,1755,2268,1762,2515,2100,2377,948,1534,1794,1121,2359,1375,1719,2537,1493,884,2023,1361,1182,1461,2455,1842,2613,1791,2038,1942,1659,2419,1075,1612,2472,1155,1744,837,701,1249,2304,2598,1974,2243,1060,911,2497,1947,1852,1874,1429,1979,2140,1324,2285,1776,997,2450,2125,1588,985,1297,2681,2387,1231,1599,1246,1627,2370,1525,1333,1318,1779,2043,921,2076,2089,1026,1185,794,2634,1857,1202,2203,1814,1086,2057,1054,1286,1035,2645,2189,718,2423,2529,906,1278,2001,1510,2585,856,2376,1631,2260,1146,2292,2556,1103,2253,2149,1219,824,819,2048,843,772,1752,1652,2568,743,2398,1124,2134,1620,2489,2220,1707,1865,1997,1765,1464,2319,1675,1139,1503,2457,919,1258,704,979,1194,2079,2538,2642,2637,1524,736,2097,2257,1542,2197,900,2679,2084,2214,2246,2299,2669,1144,1877,1339,1557,2343,816,2111,1909,1149,2664,1381,2461,1112,1667,2180,2025,1080,1821,1731,2410,1838,2593,1029,769,2289,2278,2553,2329,932,1171,2365,1015,1176,1435,1496,851,1694,1805,2069,1474,2350,2401,1699,1213,827,2051,1044,2550,1528,868,780,1643,1726,1364,2506,1562,2054,2239,1583,1662,1208,944,1467,2271,2652,927,2684,1472,1018,1049,1758,1166,1905,1420,2503,1684,749,2629,1845,1516,1070,2661,971,2143,1605,2518,1531,712,1003,1770,1225,2060,707,2192,887,2407,1267,2092,1716,791,1188,1038,840,2429,2337,2322,1130,1738,1336,1300,1637,2276,2128,2486,951,1934,2426,1702,1221,2357,1749,727,2511,1797,1008,2030,1272,859,1404,1358,2411,2500,1485,1052,1506,2266,876,1240,991,2435,2479,1966,1553,1321,2194,2347,2325,2209,1010,2658,1998,1421,2013,2626,1316,1649,2310,903,1289,2226,1453,946,2004,1646,2443,813,1721,963,2167,2174,2389,1476,1062,2532,1508,2152,2262,2447,1689,2475,914,2648,1294,2066,2183,1513,2120,832,2623,1077,2362,2162,1607,763,1309,1893,2294,2494,1444,1161,800,1908,1133,1348,752,1280,2233,1546,1395,865,999,2287,1578,1957,2385,1678,2155,2534,1097,2587,1593,2604,854,1303,1986,2201,1314,1816,2186,2404,1891,2340,955,897,1410,2417,1710,1197,2223,960,2619,1065,2063,1610,740,2241,1977,1261,1152,1378,2265,2467,1550,1925,1713,1902,1885,1093,2353,2600,1384,1537,1597,2687,982,1880,1431,803,1367,1945,2206,1681,2018,2453,2170,2470,1417,2690,1565,2438,1490,1917,755,2106,2087,2177,2655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.23 % Computer : n014.cluster.edu
% 0.12/0.23 % Model : x86_64 x86_64
% 0.12/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.23 % Memory : 8046.5625MB
% 0.12/0.23 % OS : Linux 6.8.0-71-generic
% 0.12/0.23 % CPULimit : 300
% 0.12/0.23 % WCLimit : 300
% 0.12/0.23 % DateTime : Tue Sep 29 13:05:15 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.97/0.66 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.65/1.09 % [INFO] Parsing done (427ms).
% 2.65/1.10 % [INFO] Running in sequential loop mode.
% 4.47/1.56 % [INFO] eprover registered as external prover.
% 4.47/1.58 % [INFO] Scanning for conjecture ...
% 5.30/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 698 axioms. Running axiom selection ...
% 6.60/2.18 % [INFO] Axiom selection finished. Selected 698 axioms (removed 0 axioms).
% 8.44/2.75 % [INFO] Problem is higher-order (TPTP THF).
% 8.44/2.79 % [INFO] Type checking passed.
% 8.87/2.80 % [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 ...
% 25.50/6.61 % External prover 'e' found a proof!
% 25.50/6.61 % [INFO] Killing All external provers ...
% 25.50/6.61 % Time passed: 6240ms (effective reasoning time: 5505ms)
% 25.50/6.61 % 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)>
% 25.50/6.62 % Axioms used in derivation (698): fact_290_zprime__power__zdvd__cancel__right, fact_347_zero__less__power__nat__eq__number__of, fact_189_semiring__mult__2, fact_169_Bit0__Pls, fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_81_nat__number__of__Pls, fact_360_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_266_less__special_I2_J, fact_21_zero__power2, fact_590_realpow__minus__mult, fact_653_le__imp__power__dvd, fact_652_dvd__power__le, fact_353_power__even__eq, fact_670_power__strict__increasing, fact_25_add__special_I2_J, fact_108_zle__add1__eq__le, fact_193_mult__2, fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_681_power__increasing, fact_45_less__eq__int__code_I16_J, fact_434_zdiv__mono2__neg__lemma, fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_82_semiring__norm_I113_J, fact_407_add__scale__eq__noteq, fact_383_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_46_rel__simps_I34_J, fact_618_power__mult, fact_691_divides__add__revr, fact_91_zmult__1__right, fact_267_less__special_I2_J, fact_11_sum__power2__eq__zero__iff, fact_228_rel__simps_I4_J, fact_692_nat__mult__dvd__cancel__disj_H, fact_277_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_205_semiring__numeral__0__eq__0, fact_168_rel__simps_I38_J, fact_27_add__special_I3_J, fact_56_semiring__mult__number__of, fact_479_zcong__1, fact_661_power__less__power__Suc, fact_540_zdiff__power3, fact_449_rel__simps_I40_J, fact_281__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096, fact_405_add__scale__eq__noteq, fact_286_zprime__zdvd__power, fact_478_IntPrimes_Ozcong__zero, fact_100_less__int__code_I14_J, fact_236_zless__add1__eq, fact_663_power__less__power__Suc, fact_616_dvd__power__same, fact_294_zdvd__antisym__nonneg, fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_, fact_648_power__le__dvd, fact_474_order__le__neq__implies__less, fact_43_zle__antisym, fact_129_right__distrib__number__of, fact_408_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_32_qf1pt, fact_641_power__0, fact_584_real__mult__less__iff1, fact_257_less__special_I1_J, fact_599_real__le__refl, fact_482_zcong__scalar2, fact_627_zero__le__power, fact_552_zcong__zprime__prod__zero, fact_182_zadd__0, fact_215_less__number__of, fact_155_mult__numeral__1, fact_455_rel__simps_I13_J, fact_280_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_491_zcong__zless__imp__eq, fact_54_semiring__mult__number__of, fact_292_zpower__zpower, fact_484_zcong__zadd, fact_578_mult__diff__mult, fact_260_semiring__one__add__one__is__two, fact_602_real__le__antisym, fact_514_diff__bin__simps_I9_J, fact_41_zmult__assoc, fact_428_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_606_power__mult__distrib, fact_303_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_633_one__le__power, fact_580_real__mult__le__cancel__iff1, fact_432_zdiv__mono2__lemma, fact_208_number__of__Pls, fact_95_zadd__zmult__distrib2, fact_556_Legendre__def, fact_579_mult__diff__mult, fact_605_power__mult__distrib, fact_381_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_248_semiring__numeral__1__eq__1, fact_207_number__of__Pls, fact_77_rel__simps_I32_J, fact_194_semiring__mult__2__right, fact_672_power__strict__increasing, fact_643_power__0, fact_269_zadd__power3, fact_240_power2__sum, fact_89_mult__Bit0, fact_296_zdvd__reduce, fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_695_divides__div__not, fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_522_Euler_Oaux1, fact_508_number__of__diff, fact_210_semiring__norm_I112_J, fact_298_zprime__2, fact_90_less__number__of__int__code, fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_635_power__inject__exp, fact_548_zpower__zdvd__prop1, fact_173_rel__simps_I2_J, fact_596_power__strict__mono, fact_433_unique__quotient__lemma__neg, fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_75_rel__simps_I22_J, fact_49_rel__simps_I31_J, fact_625_power__mono, fact_48_less__eq__int__code_I13_J, fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_503_zdiff__zmult__distrib2, fact_687_divides__ge, fact_688_divides__exp, fact_223_rel__simps_I12_J, fact_382_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_679_power__increasing, fact_685_power__strict__decreasing, fact_504_zdiff__zmult__distrib, fact_176_int__0__neq__1, fact_516_diff__bin__simps_I3_J, fact_694_divides__exp2, fact_498__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, fact_658_power__less__imp__less__base, fact_502_zdvd__zdiffD, fact_567_real__mult__assoc, fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_16_zero__less__power2, fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_293_zdvd__not__zless, fact_630_zero__less__power, fact_588_real__squared__diff__one__factored, fact_573_real__mult__left__cancel, fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_200_power2__eq__square, fact_460_bin__less__0__simps_I2_J, fact_174_less__int__code_I13_J, fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_42_zle__trans, fact_621_power__one__right, fact_531_zspecial__product, fact_629_zero__less__power, fact_614_dvd__power__same, fact_83_le__special_I4_J, fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_175_rel__simps_I14_J, fact_544_zcong__zero__equiv__div, fact_299_zdvd__imp__le, fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_307_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_212_add__numeral__0, fact_403_zero__le__even__power_H, fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_386_crossproduct__eq, fact_427_power__0__left__number__of, fact_422_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_513_left__diff__distrib__number__of, fact_489_four__x__squared, fact_140_power2__le__imp__le, fact_34_number__of__is__id, fact_349_nat__mult__2, fact_0__096t_A_060_A0_096, fact_459_rel__simps_I8_J, fact_125_left__distrib__number__of, fact_306_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_231_add__Bit1__Bit0, fact_468_rel__simps_I25_J, fact_52_eq__number__of__0, fact_623_power__mono, fact_465_rel__simps_I28_J, fact_148_sum__power2__ge__zero, fact_4_calculation_I2_J, fact_133_zero__is__num__zero, fact_270_zadd__power2, fact_676_power__strict__increasing__iff, fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, 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fact_157_mult__numeral__1__right, fact_487_zcong__not, fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_430_q__neg__lemma, fact_271_int__pos__lt__two__imp__zero__or__one, fact_282__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1, fact_137_power2__eq__imp__eq, fact_225_rel__simps_I16_J, fact_35_zmult__commute, fact_3_t, fact_550_zcong__zmult__prop3, fact_185_double__number__of__Bit0, fact_31_p, fact_511_right__diff__distrib__number__of, fact_485_power__m1__even, fact_249_semiring__numeral__1__eq__1, fact_657_nat__zero__less__power__iff, fact_127_right__distrib__number__of, fact_475_order__le__neq__implies__less, fact_63_sum__squares__le__zero__iff, fact_235_odd__nonzero, fact_446_Bit1__Min, fact_99_rel__simps_I33_J, fact_554_Legendre__1mod4, fact_693_divides__rev, fact_542_zcong__not__zero, fact_39_le__number__of, fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_583_real__mult__order, fact_425_power__0__left__number__of, fact_451_rel__simps_I42_J, fact_359_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_490_zcong__zless__0, fact_88_mult__Pls, fact_183_zadd__strict__right__mono, fact_493_zprime__zdvd__zmult, fact_312_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_126_left__distrib__number__of, fact_139_power2__le__imp__le, fact_492_zcong__zpower__zmult, fact_697_divides__cases, fact_541_zcong__less__eq, fact_553_zpower__zdvd__prop2, fact_74_le__number__of__eq__not__less, fact_355_even__power__le__0__imp__0, fact_278_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_60_arith__simps_I32_J, fact_519_zcong__def, fact_603_field__power__not__zero, fact_284_s1, fact_163_rel__simps_I46_J, fact_172_rel__simps_I17_J, fact_190_semiring__mult__2, fact_258_less__special_I1_J, fact_453_rel__simps_I7_J, fact_5__096_126_A1_A_060_061_At_096, fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_488_zcong__iff__lin, fact_682_power__Suc__less, fact_180_Bit0__def, fact_448_rel__simps_I47_J, fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_164_rel__simps_I39_J, fact_420_pos__zmult__pos, fact_309_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_94_zadd__zmult__distrib, fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_615_dvd__power__same, fact_104_nat__numeral__1__eq__1, fact_222_number__of__add, fact_689_divides__mul__l, fact_507_Int2_Oaux1, fact_593_realpow__num__eq__if, fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_452_rel__simps_I45_J, fact_67_le__special_I3_J, fact_481_zcong__scalar, fact_171_less__int__code_I16_J, fact_276_self__quotient__aux2, fact_651_dvd__power__le, fact_466_eq__number__of__Pls__Min, fact_385_crossproduct__eq, fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_517_less__bin__lemma, fact_289_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_7_not__sum__power2__lt__zero, fact_103_int__one__le__iff__zero__less, fact_628_zero__le__power, fact_364_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_429_q__pos__lemma, fact_497_zcong__neg__1__impl__ne__1, fact_98_less__eq__int__code_I15_J, fact_58_mult__number__of__left, fact_595_realpow__num__eq__if, fact_247_semiring__numeral__1__eq__1, fact_92_zmult__1, fact_186_power3__eq__cube, fact_263_one__add__one__is__two, fact_647_power__le__dvd, fact_442_prime__g__5, fact_505_diff__bin__simps_I7_J, fact_61_number__of__mult, fact_220_add__number__of__eq, fact_76_less__eq__int__code_I14_J, fact_113_le__imp__0__less, fact_167_rel__simps_I44_J, fact_179_add__Bit0__Bit0, fact_467_rel__simps_I11_J, fact_639_power__eq__0__iff, fact_192_mult__2, fact_545_zcong__eq__zdvd__prop, fact_463_rel__simps_I23_J, fact_304_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_656_nat__power__less__imp__less, fact_68_le__special_I3_J, fact_581_real__mult__le__cancel__iff2, fact_195_semiring__mult__2__right, fact_184_double__number__of__Bit0, fact_211_add__numeral__0, fact_597_power__strict__mono, fact_78_rel__simps_I27_J, fact_574_real__mult__right__cancel, fact_107_add1__zle__eq, fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_262_one__add__one__is__two, fact_272_s0p, fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_64_sum__squares__le__zero__iff, fact_198_mult__2__right, fact_424_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_532_zcong__id, fact_9_sum__power2__gt__zero__iff, fact_145_power2__less__imp__less, fact_555_one__not__neg__one__mod__m, fact_216_less__number__of, fact_251_numeral__1__eq__1, fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096, fact_122_sum__squares__eq__zero__iff, fact_239_power2__eq__square__number__of, fact_102_less__nat__number__of, fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_354_power__even__eq, fact_6_p0, fact_472_zcong__refl, fact_375_crossproduct__noteq, fact_178_add__Pls, fact_123_sum__squares__eq__zero__iff, fact_55_semiring__mult__number__of, fact_10_sum__power2__gt__zero__iff, fact_38_less__eq__number__of__int__code, fact_352_power__even__eq, fact_480_zcong__zmult__self, fact_130_zadd__assoc, fact_23_zero__eq__power2, fact_536_zcong__zpower, fact_118_number__of__reorient, fact_197_mult__2__right, fact_443_pos2, fact_348_nat__mult__2__right, fact_638_power__eq__0__iff, fact_156_mult__numeral__1__right, fact_464_rel__simps_I20_J, fact_158_one__is__num__one, fact_219_add__number__of__eq, fact_246_number__of__Bit1, fact_275_self__quotient__aux1, fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_668_power__0__left, fact_310_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_561_diff__square, fact_534_zcong__zmult__prop1, fact_243_number__of__Bit0, fact_512_left__diff__distrib__number__of, fact_518_xzgcda__linear__aux1, fact_226_bin__less__0__simps_I4_J, fact_690_divides__mul__r, fact_610_power__commutes, fact_565_real__less__def, fact_165_rel__simps_I50_J, fact_611_power__one, fact_608_power__commutes, fact_440_Euler_Oaux____1, fact_667_power__0__left, fact_665_power__gt1__lemma, fact_285_zero__less__power__nat__eq, fact_592_two__realpow__ge__one, fact_520_add__number__of__diff1, fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_686_realpow__pos__nth__unique, fact_87_nat__1__add__1, fact_8_not__sum__power2__lt__zero, fact_450_rel__simps_I37_J, fact_109_semiring__add__number__of, fact_626_zero__le__power, fact_650_dvd__power__le, fact_17_one__power2, fact_217_add__number__of__left, fact_15_zero__less__power2, fact_370_add__0__iff, fact_589_realpow__minus__mult, fact_71_less__0__number__of, fact_29_t__l__p, fact_161_double__eq__0__iff, fact_351_nat__number__of__mult__left, fact_371_add__0__iff, fact_563_real__zero__not__eq__one, fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_666_power__gt1__lemma, fact_411_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_147_sum__power2__le__zero__iff, fact_640_power__eq__0__iff, fact_12_sum__power2__eq__zero__iff, fact_150_sum__squares__gt__zero__iff, fact_586_exp__eq__1, fact_283__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_, fact_154_mult__numeral__1, fact_65_sum__squares__ge__zero, fact_152_not__sum__squares__lt__zero, fact_96_rel__simps_I29_J, fact_253_semiring__norm_I110_J, fact_151_sum__squares__gt__zero__iff, fact_564_real__le__eq__diff, fact_406_add__scale__eq__noteq, fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_97_rel__simps_I5_J, fact_53_eq__0__number__of, fact_259_semiring__one__add__one__is__two, fact_369_add__0__iff, fact_188_power3__eq__cube, fact_654_le__imp__power__dvd, fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_295_zdvd__mult__cancel, fact_642_power__0, fact_591_realpow__minus__mult, fact_218_add__number__of__left, fact_110_semiring__add__number__of, fact_291_zprime__power__zdvd__cancel__left, fact_499__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_634_one__le__power, fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_559_mult__eq__if, fact_560_power__eq__if, fact_232_add__Bit0__Bit1, fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_620_power__one__right, fact_191_semiring__mult__2, fact_409_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_22_zero__power2, fact_120_rel__simps_I48_J, fact_1_calculation_I1_J, fact_637_power__inject__exp, fact_568_real__mult__commute, fact_84_le__special_I4_J, fact_435_quartic__square__square, fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_582_real__mult__less__mono2, fact_234_Bit1__def, fact_85_le__special_I2_J, fact_601_real__le__trans, fact_622_power__one__right, fact_456_rel__simps_I9_J, fact_535_zcong__shift, fact_221_number__of__add, fact_617_power__mult, fact_305_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_18_one__power2, fact_201_power2__eq__square, fact_358_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_607_power__mult__distrib, fact_213_add__numeral__0__right, fact_669_power__0__left, fact_37_times__numeral__code_I5_J, fact_153_not__sum__squares__lt__zero, fact_162_double__eq__0__iff, fact_136_power2__eq__imp__eq, fact_40_le__number__of, fact_117_number__of__reorient, fact_233_int__0__less__1, fact_587_real__squared__diff__one__factored, fact_143_power2__less__imp__less, fact_662_power__less__power__Suc, fact_26_add__special_I2_J, fact_204_semiring__numeral__0__eq__0, fact_486_power__m1__even, fact_265_less__special_I4_J, fact_469_zmult__eq__1__iff, fact_619_power__mult, fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_529_zcong__square__zless, fact_570_real__add__left__mono, fact_199_power2__eq__square, fact_356_even__power__le__0__imp__0, fact_571_add__diff__add, fact_461_rel__simps_I26_J, fact_250_numeral__1__eq__1, fact_447_rel__simps_I43_J, fact_86_le__special_I2_J, fact_203_even__less__0__iff, fact_116_number__of__reorient, fact_106_zless__imp__add1__zle, fact_44_zpower__zadd__distrib, fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_419_power__eq__0__iff__number__of, fact_138_power2__le__imp__le, fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_495__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_543_zdvd__bounds, fact_677_power__strict__increasing__iff, fact_245_number__of__Bit1, fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_454_rel__simps_I24_J, fact_674_power__less__imp__less__exp, fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_530_zcong__square, fact_576_real__add__mult__distrib, fact_566_less__eq__real__def, fact_413_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_313_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_572_add__diff__add, fact_57_mult__number__of__left, fact_28_add__special_I3_J, fact_181_zadd__0__right, fact_279_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_636_power__inject__exp, fact_196_semiring__mult__2__right, fact_577_nat__power__eq__0__iff, fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_389_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_645_power__add, fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_146_sum__power2__le__zero__iff, fact_170_Pls__def, fact_524_diff__bin__simps_I4_J, fact_72_le__number__of__eq__not__less, fact_412_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_539_zdiff__power2, fact_410_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_70_le__special_I1_J, fact_546_zprime__zdvd__zmult__better, fact_462_rel__simps_I30_J, fact_402_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_255_less__special_I3_J, fact_124_left__distrib__number__of, fact_609_power__commutes, fact_93_plus__numeral__code_I9_J, fact_538_power2__diff, fact_557_QuadRes__def, fact_421_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_112_add__nat__number__of, fact_166_rel__simps_I49_J, fact_683_power__Suc__less, fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_659_power__less__imp__less__base, fact_230_bin__less__0__simps_I3_J, fact_227_rel__simps_I10_J, fact_496_neg__one__power__eq__mod__m, fact_380_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_604_field__power__not__zero, fact_594_realpow__num__eq__if, fact_675_power__less__imp__less__exp, fact_575_nat__mult__eq__one, fact_244_number__of__Bit0, fact_111_semiring__add__number__of, fact_417_power__eq__0__iff__number__of, fact_598_power__strict__mono, fact_562_realpow__two__sum__zero__iff, fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_483_zcong__zmult, fact_36_zle__linear, fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_547_Int2_Ozcong__zero, fact_301_le__nat__number__of, fact_644_power__add, fact_457_rel__simps_I3_J, fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_47_rel__simps_I19_J, fact_551_zcong__zprime__prod__zero__contra, fact_274_power2__ge__self, fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_229_bin__less__0__simps_I1_J, fact_115_eq__number__of, fact_390_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_134_zmult__zless__mono2, fact_311_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_132_zadd__commute, fact_404_zero__le__even__power_H, fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_80_zadd__zless__mono, fact_238_power2__eq__square__number__of, fact_209_semiring__norm_I112_J, fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_649_power__le__dvd, fact_149_sum__power2__ge__zero, fact_187_power3__eq__cube, fact_268__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096, fact_521_add__number__of__diff1, fact_500_not__real__square__gt__zero, fact_141_zero__le__power2, fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_69_le__special_I1_J, fact_131_zadd__left__commute, fact_473_zcong__trans, fact_431_unique__quotient__lemma, fact_384_crossproduct__eq, fact_224_less__int__code_I15_J, fact_558_real__sum__squared__expand, fact_533_zcong__zmult__prop2, fact_254_odd__less__0, fact_202_even__less__0__iff, fact_525_diff__bin__simps_I6_J, fact_24_zero__eq__power2, fact_79_rel__simps_I21_J, fact_241_power2__sum, fact_377_crossproduct__noteq, fact_441_zprime__def, fact_664_power__gt1__lemma
% 25.50/6.62 % No. of inferences in proof: 1400
% 25.50/6.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6240 ms resp. 5505 ms w/o parsing
% 26.71/7.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.36/7.07 % [INFO] Killing All external provers ...
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