%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP095^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:06:44 AM UTC 2026
% Result : Theorem 19.66s 5.56s
% Output : Refutation 21.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 342
% Syntax : Number of formulae : 686 ( 354 unt; 0 typ; 0 def)
% Number of atoms : 1878 ( 804 equ; 2 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 5017 ( 132 ~; 44 |; 72 &;4185 @)
% ( 0 <=>; 584 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 65 usr; 27 con; 0-2 aty)
% Number of variables : 1232 ( 18 ^;1192 !; 22 ?;1232 :)
% Comments :
%------------------------------------------------------------------------------
thf(poly_poly_real_type,type,
poly_poly_real: $tType ).
thf(set_poly_real_type,type,
set_poly_real: $tType ).
thf(poly_real_type,type,
poly_real: $tType ).
thf(poly_nat_type,type,
poly_nat: $tType ).
thf(poly_int_type,type,
poly_int: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(abs_abs_int_decl,type,
abs_abs_int: int > int ).
thf(abs_abs_poly_real_decl,type,
abs_abs_poly_real: poly_real > poly_real ).
thf(abs_abs_real_decl,type,
abs_abs_real: real > real ).
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_poly_int_decl,type,
one_one_poly_int: poly_int ).
thf(one_one_poly_nat_decl,type,
one_one_poly_nat: poly_nat ).
thf(one_one_poly_real_decl,type,
one_one_poly_real: poly_real ).
thf(one_one_real_decl,type,
one_one_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_poly_int_decl,type,
zero_zero_poly_int: poly_int ).
thf(zero_zero_poly_nat_decl,type,
zero_zero_poly_nat: poly_nat ).
thf(zero_z1423781445y_real_decl,type,
zero_z1423781445y_real: poly_poly_real ).
thf(zero_zero_poly_real_decl,type,
zero_zero_poly_real: poly_real ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(ring_1_Ints_int_decl,type,
ring_1_Ints_int: set_int ).
thf(ring_1_Ints_real_decl,type,
ring_1_Ints_real: set_real ).
thf(ring_1_of_int_int_decl,type,
ring_1_of_int_int: int > int ).
thf(ring_12102921859ly_int_decl,type,
ring_12102921859ly_int: int > poly_int ).
thf(ring_11511526659y_real_decl,type,
ring_11511526659y_real: int > poly_real ).
thf(ring_1_of_int_real_decl,type,
ring_1_of_int_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_poly_real_decl,type,
ord_less_poly_real: poly_real > poly_real > $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_le1180086932y_real_decl,type,
ord_le1180086932y_real: poly_real > poly_real > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(algebraic_real_decl,type,
algebraic_real: real > $o ).
thf(degree_int_decl,type,
degree_int: poly_int > nat ).
thf(degree_nat_decl,type,
degree_nat: poly_nat > nat ).
thf(degree_poly_real_decl,type,
degree_poly_real: poly_poly_real > nat ).
thf(degree_real_decl,type,
degree_real: poly_real > nat ).
thf(poly_poly_real2_decl,type,
poly_poly_real2: poly_poly_real > poly_real > poly_real ).
thf(poly_real2_decl,type,
poly_real2: poly_real > real > real ).
thf(coeff_int_decl,type,
coeff_int: poly_int > nat > int ).
thf(coeff_nat_decl,type,
coeff_nat: poly_nat > nat > nat ).
thf(coeff_poly_real_decl,type,
coeff_poly_real: poly_poly_real > nat > poly_real ).
thf(coeff_real_decl,type,
coeff_real: poly_real > nat > real ).
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_poly_int_decl,type,
power_power_poly_int: poly_int > nat > poly_int ).
thf(power_power_poly_nat_decl,type,
power_power_poly_nat: poly_nat > nat > poly_nat ).
thf(power_2108872382y_real_decl,type,
power_2108872382y_real: poly_real > nat > poly_real ).
thf(power_power_real_decl,type,
power_power_real: real > nat > real ).
thf(field_1537545994s_real_decl,type,
field_1537545994s_real: set_real ).
thf(divide_divide_int_decl,type,
divide_divide_int: int > int > int ).
thf(divide_divide_nat_decl,type,
divide_divide_nat: nat > nat > nat ).
thf(divide1727078534y_real_decl,type,
divide1727078534y_real: poly_real > poly_real > poly_real ).
thf(divide_divide_real_decl,type,
divide_divide_real: real > real > real ).
thf(collect_real_decl,type,
collect_real: ( real > $o ) > set_real ).
thf(member_int_decl,type,
member_int: int > set_int > $o ).
thf(member_real_decl,type,
member_real: real > set_real > $o ).
thf(a_decl,type,
a: real ).
thf(m_decl,type,
m: real ).
thf(a2_decl,type,
a2: int ).
thf(b_decl,type,
b: int ).
thf(n_decl,type,
n: nat ).
thf(p_decl,type,
p: poly_real ).
thf(roots_decl,type,
roots: set_real ).
thf(thesis_decl,type,
thesis: $o ).
thf(x_decl,type,
x: real ).
thf(178,axiom,
! [A: poly_real,B: poly_real] :
( ! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_poly__eqI) ).
thf(892,plain,
! [A: poly_real,B: poly_real] :
( ! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(317,axiom,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( divide_divide_real @ A @ B ) @ C )
= ( divide_divide_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_power__divide) ).
thf(1337,plain,
! [A: real,B: real,C: nat] :
( ( power_power_real @ ( divide_divide_real @ A @ B ) @ C )
= ( divide_divide_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_self__le__power) ).
thf(629,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(62,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_power__inject__exp) ).
thf(518,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(193,axiom,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= one_one_real )
= ( A = one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_of__int__eq__1__iff) ).
thf(941,plain,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= one_one_real )
= ( A = one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(142,axiom,
! [A: int] :
( ( ord_le1180086932y_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_of__int__0__le__iff) ).
thf(777,plain,
! [A: int] :
( ( ord_le1180086932y_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(244,axiom,
( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_of__int__0) ).
thf(1110,plain,
( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(50,axiom,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_of__int__eq__0__iff) ).
thf(481,plain,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(286,axiom,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ field_1537545994s_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_algebraic__altdef) ).
thf(1237,plain,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ field_1537545994s_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(162,axiom,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_power__one__right) ).
thf(846,plain,
! [A: int] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(199,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_divide__pos__neg) ).
thf(962,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(45,axiom,
member_int @ zero_zero_int @ ring_1_Ints_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Ints__0) ).
thf(468,plain,
member_int @ zero_zero_int @ ring_1_Ints_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(274,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ one_one_real @ C )
=> ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_power__increasing) ).
thf(1200,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ one_one_real @ C )
=> ( ord_less_eq_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(260,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_divide__nonpos__nonpos) ).
thf(1158,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(212,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ B @ zero_zero_real ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_divide__less__0__iff) ).
thf(1005,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ B @ zero_zero_real ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(340,axiom,
ord_less_eq_real @ ( divide_divide_real @ a @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ) @ ( divide_divide_real @ a @ one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163__092_060open_062A_A_P_Areal__of__int_Ab_A_094_An_A_092_060le_062_AA_A_P_A1_092_060close_062) ).
thf(1406,plain,
ord_less_eq_real @ ( divide_divide_real @ a @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ) @ ( divide_divide_real @ a @ one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( divide_divide_nat @ A @ B )
= A )
= ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_div__eq__dividend__iff) ).
thf(683,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( divide_divide_nat @ A @ B )
= A )
= ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(233,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_divide__neg__pos) ).
thf(1073,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(35,axiom,
! [A: poly_int] :
( ( ( coeff_int @ A @ ( degree_int @ A ) )
= zero_zero_int )
= ( A = zero_zero_poly_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_leading__coeff__0__iff) ).
thf(440,plain,
! [A: poly_int] :
( ( ( coeff_int @ A @ ( degree_int @ A ) )
= zero_zero_int )
= ( A = zero_zero_poly_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(224,axiom,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ! [C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ord_less_real @ ( divide_divide_real @ A @ ( power_power_real @ ( ring_1_of_int_real @ D ) @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ C ) @ ( ring_1_of_int_real @ D ) ) ) ) ) )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_that) ).
thf(1041,plain,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ! [C: int,D: int] :
( ( ord_less_int @ zero_zero_int @ D )
=> ( ord_less_real @ ( divide_divide_real @ A @ ( power_power_real @ ( ring_1_of_int_real @ D ) @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ C ) @ ( ring_1_of_int_real @ D ) ) ) ) ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(129,axiom,
! [A: poly_real,B: poly_real,C: nat] :
( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_le1180086932y_real @ ( power_2108872382y_real @ A @ C ) @ ( power_2108872382y_real @ B @ C ) )
= ( ord_le1180086932y_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_power__mono__iff) ).
thf(730,plain,
! [A: poly_real,B: poly_real,C: nat] :
( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_le1180086932y_real @ ( power_2108872382y_real @ A @ C ) @ ( power_2108872382y_real @ B @ C ) )
= ( ord_le1180086932y_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(303,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= one_one_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_power__0__left) ).
thf(1290,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)],[303]) ).
thf(171,axiom,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_power__one) ).
thf(873,plain,
! [A: nat] :
( ( power_power_int @ one_one_int @ A )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(38,axiom,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_int @ A )
= ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__int__power__eq__of__int__cancel__iff) ).
thf(449,plain,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_int @ A )
= ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(255,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_real @ ( divide_divide_real @ A @ D ) @ ( divide_divide_real @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_frac__less) ).
thf(1142,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_real @ ( divide_divide_real @ A @ D ) @ ( divide_divide_real @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(15,axiom,
! [A: int] :
( ( zero_zero_int
= ( ring_1_of_int_int @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_of__int__0__eq__iff) ).
thf(379,plain,
! [A: int] :
( ( zero_zero_int
= ( ring_1_of_int_int @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(47,axiom,
! [A: poly_poly_real,B: nat] :
( ( ord_less_nat @ ( degree_poly_real @ A ) @ B )
=> ( ( coeff_poly_real @ A @ B )
= zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_coeff__eq__0) ).
thf(472,plain,
! [A: poly_poly_real,B: nat] :
( ( ord_less_nat @ ( degree_poly_real @ A ) @ B )
=> ( ( coeff_poly_real @ A @ B )
= zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(153,axiom,
( ( ring_11511526659y_real @ zero_zero_int )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_of__int__0) ).
thf(814,plain,
( ( ring_11511526659y_real @ zero_zero_int )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(294,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_power__increasing__iff) ).
thf(1260,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(230,axiom,
! [A: real,B: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_real @ one_one_real @ ( power_power_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_one__less__power) ).
thf(1063,plain,
! [A: real,B: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_real @ one_one_real @ ( power_power_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(323,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_divide__neg__neg) ).
thf(1354,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(282,axiom,
! [A: real,B: nat] :
( ( ord_less_eq_real @ one_one_real @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_real @ A @ ( power_power_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_self__le__power) ).
thf(1222,plain,
! [A: real,B: nat] :
( ( ord_less_eq_real @ one_one_real @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_real @ A @ ( power_power_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(262,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
= ( ( ord_less_eq_real @ zero_zero_real @ A )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_zero__le__divide__abs__iff) ).
thf(1164,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
= ( ( ord_less_eq_real @ zero_zero_real @ A )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(148,axiom,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( ( A != zero_zero_int )
=> ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Ints__nonzero__abs__ge1) ).
thf(797,plain,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( ( A != zero_zero_int )
=> ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(319,axiom,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_real @ A )
= ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_of__int__power__eq__of__int__cancel__iff) ).
thf(1342,plain,
! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int_real @ A )
= ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( A
= ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(134,axiom,
! [A: int] :
( ( zero_zero_poly_real
= ( ring_11511526659y_real @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_of__int__0__eq__iff) ).
thf(747,plain,
! [A: int] :
( ( zero_zero_poly_real
= ( ring_11511526659y_real @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(241,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_divide__less__eq__1__neg) ).
thf(1095,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(335,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_divide__nonneg__nonpos) ).
thf(1391,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(175,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_le1180086932y_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_of__int__nonneg) ).
thf(885,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_le1180086932y_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(225,axiom,
! [A: poly_real] :
( ( ( coeff_real @ A @ ( degree_real @ A ) )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_leading__coeff__0__iff) ).
thf(1046,plain,
! [A: poly_real] :
( ( ( coeff_real @ A @ ( degree_real @ A ) )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(18,axiom,
! [A: poly_int,B: nat] :
( ( coeff_int @ ( power_power_poly_int @ A @ B ) @ ( degree_int @ ( power_power_poly_int @ A @ B ) ) )
= ( power_power_int @ ( coeff_int @ A @ ( degree_int @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_lead__coeff__power) ).
thf(389,plain,
! [A: poly_int,B: nat] :
( ( coeff_int @ ( power_power_poly_int @ A @ B ) @ ( degree_int @ ( power_power_poly_int @ A @ B ) ) )
= ( power_power_int @ ( coeff_int @ A @ ( degree_int @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(302,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_power__less__imp__less__exp) ).
thf(1287,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_one__less__power) ).
thf(504,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(295,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_divide__le__0__iff) ).
thf(1264,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1,conjecture,
ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(344,plain,
~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_div__le__dividend) ).
thf(542,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(228,axiom,
! [A: real] :
( ( member_real @ A @ field_1537545994s_real )
=> ~ ! [B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( A
!= ( divide_divide_real @ ( ring_1_of_int_real @ B ) @ ( ring_1_of_int_real @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_Liouville__Numbers__Misc_ORats__cases_H) ).
thf(1055,plain,
! [A: real] :
( ( member_real @ A @ field_1537545994s_real )
=> ~ ! [B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ C )
=> ( A
!= ( divide_divide_real @ ( ring_1_of_int_real @ B ) @ ( ring_1_of_int_real @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(127,axiom,
! [A: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_of__int__less__0__iff) ).
thf(724,plain,
! [A: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(7,axiom,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_poly__0) ).
thf(357,plain,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(271,axiom,
( ( ring_1_of_int_real @ one_one_int )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_of__int__1) ).
thf(1191,plain,
( ( ring_1_of_int_real @ one_one_int )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(331,axiom,
! [A: real,B: real,C: real] :
( ( ( divide_divide_real @ A @ B )
= ( divide_divide_real @ C @ B ) )
= ( ( B = zero_zero_real )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_divide__cancel__right) ).
thf(1379,plain,
! [A: real,B: real,C: real] :
( ( ( divide_divide_real @ A @ B )
= ( divide_divide_real @ C @ B ) )
= ( ( B = zero_zero_real )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(238,axiom,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) @ ( divide_divide_real @ a @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_ab) ).
thf(1087,plain,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) @ ( divide_divide_real @ a @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(312,axiom,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ ( poly_real2 @ C @ A ) @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ B ) )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_poly__IVT__pos) ).
thf(1319,plain,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ ( poly_real2 @ C @ A ) @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ B ) )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(215,axiom,
! [A: real,B: real] :
( ( ( divide_divide_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_divide__eq__0__iff) ).
thf(1013,plain,
! [A: real,B: real] :
( ( ( divide_divide_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(26,axiom,
! [A: poly_nat,B: nat] :
( ( coeff_nat @ ( power_power_poly_nat @ A @ B ) @ zero_zero_nat )
= ( power_power_nat @ ( coeff_nat @ A @ zero_zero_nat ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_coeff__0__power) ).
thf(416,plain,
! [A: poly_nat,B: nat] :
( ( coeff_nat @ ( power_power_poly_nat @ A @ B ) @ zero_zero_nat )
= ( power_power_nat @ ( coeff_nat @ A @ zero_zero_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(246,axiom,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( ( coeff_real @ A @ ( degree_real @ A ) )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_leading__coeff__neq__0) ).
thf(1115,plain,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( ( coeff_real @ A @ ( degree_real @ A ) )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(48,axiom,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= one_one_int )
= ( A = one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_of__int__eq__1__iff) ).
thf(475,plain,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= one_one_int )
= ( A = one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(137,axiom,
! [A: nat] :
( ( coeff_real @ zero_zero_poly_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_coeff__0) ).
thf(756,plain,
! [A: nat] :
( ( coeff_real @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(14,axiom,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_power__one__right) ).
thf(376,plain,
! [A: nat] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(316,axiom,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_power__one__right) ).
thf(1334,plain,
! [A: real] :
( ( power_power_real @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(258,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_power__decreasing__iff) ).
thf(1151,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ( ord_less_eq_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(151,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_power__increasing__iff) ).
thf(806,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(329,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_divide__nonpos__nonneg) ).
thf(1373,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(36,axiom,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_power__one) ).
thf(443,plain,
! [A: nat] :
( ( power_power_nat @ one_one_nat @ A )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(253,axiom,
! [A: real] :
( ( zero_zero_real
= ( divide_divide_real @ one_one_real @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_zero__eq__1__divide__iff) ).
thf(1136,plain,
! [A: real] :
( ( zero_zero_real
= ( divide_divide_real @ one_one_real @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(158,axiom,
~ ( member_real @ x @ roots ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37__092_060open_062x_A_092_060notin_062_Aroots_092_060close_062) ).
thf(834,plain,
~ ( member_real @ x @ roots ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(4,axiom,
! [A: nat] :
( ( coeff_nat @ zero_zero_poly_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_coeff__0) ).
thf(348,plain,
! [A: nat] :
( ( coeff_nat @ zero_zero_poly_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(80,axiom,
! [A: int,B: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_int @ one_one_int @ ( power_power_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_one__less__power) ).
thf(574,plain,
! [A: int,B: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_int @ one_one_int @ ( power_power_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(116,axiom,
! [A: poly_real,B: nat,C: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ A )
=> ( ( ord_less_poly_real @ A @ one_one_poly_real )
=> ( ( ord_le1180086932y_real @ ( power_2108872382y_real @ A @ B ) @ ( power_2108872382y_real @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_power__decreasing__iff) ).
thf(687,plain,
! [A: poly_real,B: nat,C: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ A )
=> ( ( ord_less_poly_real @ A @ one_one_poly_real )
=> ( ( ord_le1180086932y_real @ ( power_2108872382y_real @ A @ B ) @ ( power_2108872382y_real @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(130,axiom,
! [A: int] :
( ( ord_le1180086932y_real @ ( ring_11511526659y_real @ A ) @ zero_zero_poly_real )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_of__int__le__0__iff) ).
thf(734,plain,
! [A: int] :
( ( ord_le1180086932y_real @ ( ring_11511526659y_real @ A ) @ zero_zero_poly_real )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(336,axiom,
! [A: poly_real,B: nat] :
( ( ( coeff_real @ A @ B )
!= zero_zero_real )
=> ( ord_less_eq_nat @ B @ ( degree_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_le__degree) ).
thf(1394,plain,
! [A: poly_real,B: nat] :
( ( ( coeff_real @ A @ B )
!= zero_zero_real )
=> ( ord_less_eq_nat @ B @ ( degree_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(322,axiom,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_poly__eq__poly__eq__iff) ).
thf(1351,plain,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(58,axiom,
~ ( member_real @ x @ field_1537545994s_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_irrationsl) ).
thf(507,plain,
~ ( member_real @ x @ field_1537545994s_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(24,axiom,
( ( ring_1_of_int_int @ one_one_int )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_of__int__1) ).
thf(411,plain,
( ( ring_1_of_int_int @ one_one_int )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(320,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_divide__nonpos__pos) ).
thf(1345,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(288,axiom,
! [A: int] :
( ( coeff_real @ ( ring_11511526659y_real @ A ) @ ( degree_real @ ( ring_11511526659y_real @ A ) ) )
= ( ring_1_of_int_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_lead__coeff__of__int) ).
thf(1242,plain,
! [A: int] :
( ( coeff_real @ ( ring_11511526659y_real @ A ) @ ( degree_real @ ( ring_11511526659y_real @ A ) ) )
= ( ring_1_of_int_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(163,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( ord_less_int @ A @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_of__int__power__less__of__int__cancel__iff) ).
thf(849,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( ord_less_int @ A @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(60,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_zero__power) ).
thf(512,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(112,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_linordered__field__no__lb) ).
thf(678,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(307,axiom,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__int__1__le__iff) ).
thf(1306,plain,
! [A: int] :
( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_power__strict__increasing__iff) ).
thf(810,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(11,axiom,
! [A: poly_nat,B: nat] :
( ( ord_less_eq_nat @ ( degree_nat @ A ) @ B )
=> ( ( ( coeff_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_poly_nat )
| ( ord_less_nat @ ( degree_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_eq__zero__or__degree__less) ).
thf(366,plain,
! [A: poly_nat,B: nat] :
( ( ord_less_eq_nat @ ( degree_nat @ A ) @ B )
=> ( ( ( coeff_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_poly_nat )
| ( ord_less_nat @ ( degree_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(67,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_of__int__le__1__iff) ).
thf(534,plain,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
= ( ord_less_eq_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(124,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_2108872382y_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_zero__power) ).
thf(714,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_2108872382y_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(276,axiom,
! [A: nat,B: real,C: real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ( power_power_real @ B @ A )
= ( power_power_real @ C @ A ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_power__eq__iff__eq__base) ).
thf(1206,plain,
! [A: nat,B: real,C: real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ( power_power_real @ B @ A )
= ( power_power_real @ C @ A ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(39,axiom,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Ints__abs) ).
thf(452,plain,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(298,axiom,
! [A: int,B: int] :
( ( ( ring_1_of_int_real @ A )
= ( ring_1_of_int_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_of__int__eq__iff) ).
thf(1274,plain,
! [A: int,B: int] :
( ( ( ring_1_of_int_real @ A )
= ( ring_1_of_int_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(198,axiom,
! [A: nat,B: poly_real] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_real @ B @ C )
= zero_zero_real ) )
=> ( ord_less_eq_nat @ ( degree_real @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_degree__le) ).
thf(957,plain,
! [A: nat,B: poly_real] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_real @ B @ C )
= zero_zero_real ) )
=> ( ord_less_eq_nat @ ( degree_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(240,axiom,
! [A: poly_real,B: real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( algebraic_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_algebraicI) ).
thf(1091,plain,
! [A: poly_real,B: real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( algebraic_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(157,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= one_one_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_power__0__left) ).
thf(825,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)],[157]) ).
thf(218,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_eq_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_divide__le__eq__1__pos) ).
thf(1021,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_eq_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(292,axiom,
ord_less_real @ a @ one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_A__less_I1_J) ).
thf(1255,plain,
ord_less_real @ a @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(167,axiom,
! [A: int] :
( ( ord_less_int @ ( abs_abs_int @ A ) @ one_one_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zabs__less__one__iff) ).
thf(862,plain,
! [A: int] :
( ( ord_less_int @ ( abs_abs_int @ A ) @ one_one_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(265,axiom,
ord_less_int @ zero_zero_int @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_b) ).
thf(1174,plain,
ord_less_int @ zero_zero_int @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(19,axiom,
! [A: poly_nat,B: nat] :
( ( ( coeff_nat @ A @ B )
!= zero_zero_nat )
=> ( ord_less_eq_nat @ B @ ( degree_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_le__degree) ).
thf(392,plain,
! [A: poly_nat,B: nat] :
( ( ( coeff_nat @ A @ B )
!= zero_zero_nat )
=> ( ord_less_eq_nat @ B @ ( degree_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_of__int__less__iff) ).
thf(424,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(328,axiom,
! [A: int] :
( ( degree_real @ ( ring_11511526659y_real @ A ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_degree__of__int) ).
thf(1370,plain,
! [A: int] :
( ( degree_real @ ( ring_11511526659y_real @ A ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(280,axiom,
! [A: real] :
( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_divide__less__0__1__iff) ).
thf(1217,plain,
! [A: real] :
( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_power__eq__imp__eq__base) ).
thf(598,plain,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ A @ B )
= ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(51,axiom,
! [A: poly_poly_real] :
( ( A != zero_z1423781445y_real )
=> ( ( coeff_poly_real @ A @ ( degree_poly_real @ A ) )
!= zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_leading__coeff__neq__0) ).
thf(484,plain,
! [A: poly_poly_real] :
( ( A != zero_z1423781445y_real )
=> ( ( coeff_poly_real @ A @ ( degree_poly_real @ A ) )
!= zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(173,axiom,
! [A: poly_poly_real] :
( ( poly_poly_real2 @ A @ zero_zero_poly_real )
= ( coeff_poly_real @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_poly__0__coeff__0) ).
thf(879,plain,
! [A: poly_poly_real] :
( ( poly_poly_real2 @ A @ zero_zero_poly_real )
= ( coeff_poly_real @ A @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(164,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ B @ A )
=> ( ( divide_divide_int @ A @ B )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_div__neg__neg__trivial) ).
thf(852,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ B @ A )
=> ( ( divide_divide_int @ A @ B )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(108,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ one_one_nat @ C )
=> ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_power__strict__increasing) ).
thf(665,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ one_one_nat @ C )
=> ( ord_less_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_power__not__zero) ).
thf(461,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(235,axiom,
! [A: nat] : ( member_real @ ( coeff_real @ p @ A ) @ ring_1_Ints_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_p_I1_J) ).
thf(1079,plain,
! [A: nat] : ( member_real @ ( coeff_real @ p @ A ) @ ring_1_Ints_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(41,axiom,
( ( coeff_nat @ one_one_poly_nat @ ( degree_nat @ one_one_poly_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_lead__coeff__1) ).
thf(456,plain,
( ( coeff_nat @ one_one_poly_nat @ ( degree_nat @ one_one_poly_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_zero__less__power) ).
thf(583,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(63,axiom,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mem__Collect__eq) ).
thf(522,plain,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(54,axiom,
! [A: poly_poly_real,B: nat] :
( ( ord_less_eq_nat @ ( degree_poly_real @ A ) @ B )
=> ( ( ( coeff_poly_real @ A @ B )
= zero_zero_poly_real )
=> ( ( A = zero_z1423781445y_real )
| ( ord_less_nat @ ( degree_poly_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_eq__zero__or__degree__less) ).
thf(493,plain,
! [A: poly_poly_real,B: nat] :
( ( ord_less_eq_nat @ ( degree_poly_real @ A ) @ B )
=> ( ( ( coeff_poly_real @ A @ B )
= zero_zero_poly_real )
=> ( ( A = zero_z1423781445y_real )
| ( ord_less_nat @ ( degree_poly_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(277,axiom,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( ( A != zero_zero_real )
=> ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Ints__nonzero__abs__ge1) ).
thf(1210,plain,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( ( A != zero_zero_real )
=> ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(114,axiom,
algebraic_real @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(682,plain,
algebraic_real @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(341,axiom,
! [A: int,B: real] :
( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_real @ one_one_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_of__int__lessD) ).
thf(1407,plain,
! [A: int,B: real] :
( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_real @ one_one_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(73,axiom,
member_real @ zero_zero_real @ ring_1_Ints_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Ints__0) ).
thf(551,plain,
member_real @ zero_zero_real @ ring_1_Ints_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(250,axiom,
! [A: poly_real] :
( ( ! [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_poly__all__0__iff__0) ).
thf(1128,plain,
! [A: poly_real] :
( ( ! [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(119,axiom,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( ( ord_less_int @ ( abs_abs_int @ A ) @ one_one_int )
=> ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Ints__nonzero__abs__less1) ).
thf(697,plain,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( ( ord_less_int @ ( abs_abs_int @ A ) @ one_one_int )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(105,axiom,
! [A: int] :
( ( ord_less_poly_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_of__int__0__less__iff) ).
thf(650,plain,
! [A: int] :
( ( ord_less_poly_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(284,axiom,
! [A: poly_real,B: nat] :
( ( coeff_real @ ( power_2108872382y_real @ A @ B ) @ zero_zero_nat )
= ( power_power_real @ ( coeff_real @ A @ zero_zero_nat ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_coeff__0__power) ).
thf(1227,plain,
! [A: poly_real,B: nat] :
( ( coeff_real @ ( power_2108872382y_real @ A @ B ) @ zero_zero_nat )
= ( power_power_real @ ( coeff_real @ A @ zero_zero_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(204,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_less__divide__eq__1__neg) ).
thf(980,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(86,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_of__int__nonneg) ).
thf(593,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(56,axiom,
! [A: int,B: int > $o] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( ! [C: int] : ( B @ ( ring_1_of_int_int @ C ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Ints__induct) ).
thf(499,plain,
! [A: int,B: int > $o] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( ! [C: int] : ( B @ ( ring_1_of_int_int @ C ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(337,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ ( divide_divide_real @ C @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ C ) )
& ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ C @ A ) )
& ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_divide__less__cancel) ).
thf(1397,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ ( divide_divide_real @ C @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ C ) )
& ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ C @ A ) )
& ( B != zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(144,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_power__strict__increasing__iff) ).
thf(783,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(247,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ( power_power_real @ A @ B )
= ( power_power_real @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_power__inject__exp) ).
thf(1118,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ( power_power_real @ A @ B )
= ( power_power_real @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(314,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ B @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_zero__less__divide__iff) ).
thf(1329,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ B @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(220,axiom,
! [A: nat,B: poly_real] :
( ( ord_less_nat @ A @ ( degree_real @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_real @ B @ C )
!= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_less__degree__imp) ).
thf(1028,plain,
! [A: nat,B: poly_real] :
( ( ord_less_nat @ A @ ( degree_real @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_real @ B @ C )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(325,axiom,
! [A: real,B: real,C: real] :
( ( ( divide_divide_real @ A @ B )
= ( divide_divide_real @ A @ C ) )
= ( ( A = zero_zero_real )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_divide__cancel__left) ).
thf(1361,plain,
! [A: real,B: real,C: real] :
( ( ( divide_divide_real @ A @ B )
= ( divide_divide_real @ A @ C ) )
= ( ( A = zero_zero_real )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(136,axiom,
! [A: poly_real,B: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ ( power_2108872382y_real @ ( abs_abs_poly_real @ A ) @ B ) )
= ( ( A != zero_zero_poly_real )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_zero__less__power__abs__iff) ).
thf(753,plain,
! [A: poly_real,B: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ ( power_2108872382y_real @ ( abs_abs_poly_real @ A ) @ B ) )
= ( ( A != zero_zero_poly_real )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(68,axiom,
( ( coeff_real @ zero_zero_poly_real )
= ( ^ [A: nat] : zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_zero__poly_Orep__eq) ).
thf(537,plain,
( ( coeff_real @ zero_zero_poly_real )
= ( ^ [A: nat] : zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(279,axiom,
! [A: real,B: real] :
( ( ( divide_divide_real @ A @ B )
= one_one_real )
= ( ( B != zero_zero_real )
& ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_divide__eq__eq__1) ).
thf(1214,plain,
! [A: real,B: real] :
( ( ( divide_divide_real @ A @ B )
= one_one_real )
= ( ( B != zero_zero_real )
& ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(216,axiom,
( ( poly_real2 @ p @ x )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p_I3_J) ).
thf(1016,plain,
( ( poly_real2 @ p @ x )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(259,axiom,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_int @ one_one_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_of__int__1__less__iff) ).
thf(1155,plain,
! [A: int] :
( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_int @ one_one_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(122,axiom,
! [A: nat,B: poly_int] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_int @ B @ C )
= zero_zero_int ) )
=> ( ord_less_eq_nat @ ( degree_int @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_degree__le) ).
thf(706,plain,
! [A: nat,B: poly_int] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_int @ B @ C )
= zero_zero_int ) )
=> ( ord_less_eq_nat @ ( degree_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(96,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ( power_power_int @ A @ B )
= ( power_power_int @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_power__inject__exp) ).
thf(622,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ( power_power_int @ A @ B )
= ( power_power_int @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(104,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_of__int__le__0__iff) ).
thf(647,plain,
! [A: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(242,axiom,
~ ! [A: poly_real] :
( ! [B: nat] : ( member_real @ ( coeff_real @ A @ B ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( poly_real2 @ A @ x )
!= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062) ).
thf(1099,plain,
~ ! [A: poly_real] :
( ! [B: nat] : ( member_real @ ( coeff_real @ A @ B ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( poly_real2 @ A @ x )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(332,axiom,
! [A: real,B: nat] :
( ( abs_abs_real @ ( power_power_real @ A @ B ) )
= ( power_power_real @ ( abs_abs_real @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_power__abs) ).
thf(1382,plain,
! [A: real,B: nat] :
( ( abs_abs_real @ ( power_power_real @ A @ B ) )
= ( power_power_real @ ( abs_abs_real @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(251,axiom,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( member_real @ ( abs_abs_real @ A ) @ ring_1_Ints_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Ints__abs) ).
thf(1131,plain,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( member_real @ ( abs_abs_real @ A ) @ ring_1_Ints_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(229,axiom,
! [A: int,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_eq_real @ one_one_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_of__int__leD) ).
thf(1060,plain,
! [A: int,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_eq_real @ one_one_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(205,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_zero__less__divide__1__iff) ).
thf(984,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(211,axiom,
! [A: int,B: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_of__int__less__iff) ).
thf(1002,plain,
! [A: int,B: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(13,axiom,
! [A: nat,B: poly_nat] :
( ( ord_less_nat @ A @ ( degree_nat @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_nat @ B @ C )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_less__degree__imp) ).
thf(371,plain,
! [A: nat,B: poly_nat] :
( ( ord_less_nat @ A @ ( degree_nat @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_nat @ B @ C )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(61,axiom,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_power__eq__0__iff) ).
thf(515,plain,
! [A: int,B: nat] :
( ( ( power_power_int @ A @ B )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(290,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_divide__strict__right__mono__neg) ).
thf(1249,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(192,axiom,
! [A: real,B: nat] :
( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ B )
= ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_power__one__over) ).
thf(938,plain,
! [A: real,B: nat] :
( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ B )
= ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(8,axiom,
( ( coeff_poly_real @ zero_z1423781445y_real )
= ( ^ [A: nat] : zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zero__poly_Orep__eq) ).
thf(360,plain,
( ( coeff_poly_real @ zero_z1423781445y_real )
= ( ^ [A: nat] : zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,axiom,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ ( ring_1_of_int_int @ A ) @ B )
= ( ring_1_of_int_int @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_of__int__eq__of__int__power__cancel__iff) ).
thf(398,plain,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ ( ring_1_of_int_int @ A ) @ B )
= ( ring_1_of_int_int @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(263,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_power__strict__decreasing__iff) ).
thf(1167,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ A @ one_one_real )
=> ( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(269,axiom,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_power__eq__0__iff) ).
thf(1185,plain,
! [A: real,B: nat] :
( ( ( power_power_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(107,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_of__int__0__less__iff) ).
thf(662,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(188,axiom,
! [A: real,B: real,C: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_power__mono) ).
thf(926,plain,
! [A: real,B: real,C: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_nat__zero__less__power__iff) ).
thf(794,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)],[147]) ).
thf(84,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_of__int__less__of__int__power__cancel__iff) ).
thf(586,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(183,axiom,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( divide_divide_real @ A @ A )
= zero_zero_real ) )
& ( ( A != zero_zero_real )
=> ( ( divide_divide_real @ A @ A )
= one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_divide__self__if) ).
thf(906,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( divide_divide_real @ A @ A )
= zero_zero_real ) )
& ( ( A != zero_zero_real )
=> ( ( divide_divide_real @ A @ A )
= one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(31,axiom,
member_int @ one_one_int @ ring_1_Ints_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Ints__1) ).
thf(430,plain,
member_int @ one_one_int @ ring_1_Ints_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(165,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_one__le__power) ).
thf(856,plain,
! [A: int,B: nat] :
( ( ord_less_eq_int @ one_one_int @ A )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(305,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_divide__strict__right__mono) ).
thf(1301,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(89,axiom,
! [A: poly_real,B: poly_real] :
( ( ( coeff_real @ A )
= ( coeff_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_coeff__inject) ).
thf(601,plain,
! [A: poly_real,B: poly_real] :
( ( ( coeff_real @ A )
= ( coeff_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(200,axiom,
! [A: poly_real,B: nat,C: real] :
( ( poly_real2 @ ( power_2108872382y_real @ A @ B ) @ C )
= ( power_power_real @ ( poly_real2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_poly__power) ).
thf(965,plain,
! [A: poly_real,B: nat,C: real] :
( ( poly_real2 @ ( power_2108872382y_real @ A @ B ) @ C )
= ( power_power_real @ ( poly_real2 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(135,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_of__int__power__le__of__int__cancel__iff) ).
thf(750,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(155,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_of__int__0__le__iff) ).
thf(819,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(202,axiom,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= zero_zero_real )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_of__int__eq__0__iff) ).
thf(975,plain,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= zero_zero_real )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(118,axiom,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Collect__mem__eq) ).
thf(694,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(334,axiom,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_of__int__0__less__iff) ).
thf(1388,plain,
! [A: int] :
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(339,axiom,
! [A: real] :
( ( A != x )
=> ( ( ( poly_real2 @ p @ A )
= zero_zero_real )
=> ( ord_less_real @ a @ ( abs_abs_real @ ( minus_minus_real @ A @ x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_A__less_I3_J) ).
thf(1403,plain,
! [A: real] :
( ( A != x )
=> ( ( ( poly_real2 @ p @ A )
= zero_zero_real )
=> ( ord_less_real @ a @ ( abs_abs_real @ ( minus_minus_real @ A @ x ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(293,axiom,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ~ ! [B: int] :
( A
!= ( ring_1_of_int_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Ints__cases) ).
thf(1256,plain,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ~ ! [B: int] :
( A
!= ( ring_1_of_int_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(25,axiom,
! [A: int,B: nat] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( member_int @ ( power_power_int @ A @ B ) @ ring_1_Ints_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Ints__power) ).
thf(413,plain,
! [A: int,B: nat] :
( ( member_int @ A @ ring_1_Ints_int )
=> ( member_int @ ( power_power_int @ A @ B ) @ ring_1_Ints_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(161,axiom,
! [A: poly_real,B: nat] :
( ( ( power_2108872382y_real @ A @ B )
= zero_zero_poly_real )
= ( ( A = zero_zero_poly_real )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_power__eq__0__iff) ).
thf(843,plain,
! [A: poly_real,B: nat] :
( ( ( power_2108872382y_real @ A @ B )
= zero_zero_poly_real )
= ( ( A = zero_zero_poly_real )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(249,axiom,
! [A: int,B: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ A @ B ) )
= ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_of__int__power) ).
thf(1125,plain,
! [A: int,B: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ A @ B ) )
= ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(81,axiom,
! [A: poly_real,B: nat] :
( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ord_le1180086932y_real @ zero_zero_poly_real @ ( power_2108872382y_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_zero__le__power) ).
thf(577,plain,
! [A: poly_real,B: nat] :
( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ord_le1180086932y_real @ zero_zero_poly_real @ ( power_2108872382y_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(123,axiom,
! [A: poly_real,B: poly_real,C: nat] :
( ( ord_le1180086932y_real @ A @ B )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ord_le1180086932y_real @ ( power_2108872382y_real @ A @ C ) @ ( power_2108872382y_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_power__mono) ).
thf(711,plain,
! [A: poly_real,B: poly_real,C: nat] :
( ( ord_le1180086932y_real @ A @ B )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ord_le1180086932y_real @ ( power_2108872382y_real @ A @ C ) @ ( power_2108872382y_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(254,axiom,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_power__one) ).
thf(1139,plain,
! [A: nat] :
( ( power_power_real @ one_one_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(16,axiom,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ~ ! [B: int] :
( A
!= ( ring_1_of_int_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Ints__cases) ).
thf(382,plain,
! [A: int] :
( ( member_int @ A @ ring_1_Ints_int )
=> ~ ! [B: int] :
( A
!= ( ring_1_of_int_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(297,axiom,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_zero__less__power) ).
thf(1271,plain,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(309,axiom,
( n
= ( degree_real @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_n__def) ).
thf(1312,plain,
( n
= ( degree_real @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(145,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( divide_divide_int @ A @ B )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_div__pos__pos__trivial) ).
thf(787,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ B )
=> ( ( divide_divide_int @ A @ B )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(243,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__int__power__le__of__int__cancel__iff) ).
thf(1107,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( ord_less_eq_int @ A @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(287,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_of__int__le__0__iff) ).
thf(1239,plain,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ zero_zero_real )
= ( ord_less_eq_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(315,axiom,
( ( degree_real @ one_one_poly_real )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_degree__1) ).
thf(1332,plain,
( ( degree_real @ one_one_poly_real )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(186,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_zero__le__divide__iff) ).
thf(919,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
= ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(195,axiom,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ B ) )
= ( ( A != zero_zero_real )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_zero__less__power__abs__iff) ).
thf(947,plain,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ B ) )
= ( ( A != zero_zero_real )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(90,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_power__decreasing__iff) ).
thf(604,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(23,axiom,
! [A: nat,B: poly_int] :
( ( ord_less_nat @ A @ ( degree_int @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_int @ B @ C )
!= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_less__degree__imp) ).
thf(406,plain,
! [A: nat,B: poly_int] :
( ( ord_less_nat @ A @ ( degree_int @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_int @ B @ C )
!= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,axiom,
( ( coeff_int @ zero_zero_poly_int )
= ( ^ [A: nat] : zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_zero__poly_Orep__eq) ).
thf(362,plain,
( ( coeff_int @ zero_zero_poly_int )
= ( ^ [A: nat] : zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(131,axiom,
! [A: int,B: nat] :
( ( abs_abs_int @ ( power_power_int @ A @ B ) )
= ( power_power_int @ ( abs_abs_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_power__abs) ).
thf(737,plain,
! [A: int,B: nat] :
( ( abs_abs_int @ ( power_power_int @ A @ B ) )
= ( power_power_int @ ( abs_abs_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(248,axiom,
! [A: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ zero_zero_real )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_of__int__less__0__iff) ).
thf(1122,plain,
! [A: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ zero_zero_real )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(330,axiom,
! [A: int,B: nat,C: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ A ) @ B )
= ( ring_1_of_int_real @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_of__int__eq__of__int__power__cancel__iff) ).
thf(1376,plain,
! [A: int,B: nat,C: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ A ) @ B )
= ( ring_1_of_int_real @ C ) )
= ( ( power_power_int @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(266,axiom,
! [A: real,B: real > $o] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( ! [C: int] : ( B @ ( ring_1_of_int_real @ C ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Ints__induct) ).
thf(1175,plain,
! [A: real,B: real > $o] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( ! [C: int] : ( B @ ( ring_1_of_int_real @ C ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(214,axiom,
( ( degree_real @ zero_zero_poly_real )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_degree__0) ).
thf(1011,plain,
( ( degree_real @ zero_zero_poly_real )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(27,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_of__int__le__iff) ).
thf(419,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(207,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_zero__power) ).
thf(990,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(209,axiom,
! [A: poly_real,B: nat] :
( ( ord_less_eq_nat @ ( degree_real @ A ) @ B )
=> ( ( ( coeff_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_poly_real )
| ( ord_less_nat @ ( degree_real @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_eq__zero__or__degree__less) ).
thf(996,plain,
! [A: poly_real,B: nat] :
( ( ord_less_eq_nat @ ( degree_real @ A ) @ B )
=> ( ( ( coeff_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_poly_real )
| ( ord_less_nat @ ( degree_real @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(59,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_of__int__1__le__iff) ).
thf(509,plain,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_eq_int @ one_one_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(33,axiom,
! [A: poly_nat,B: nat] :
( ( coeff_nat @ ( power_power_poly_nat @ A @ B ) @ ( degree_nat @ ( power_power_poly_nat @ A @ B ) ) )
= ( power_power_nat @ ( coeff_nat @ A @ ( degree_nat @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_lead__coeff__power) ).
thf(434,plain,
! [A: poly_nat,B: nat] :
( ( coeff_nat @ ( power_power_poly_nat @ A @ B ) @ ( degree_nat @ ( power_power_poly_nat @ A @ B ) ) )
= ( power_power_nat @ ( coeff_nat @ A @ ( degree_nat @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(177,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_power__less__imp__less__base) ).
thf(890,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)],[177]) ).
thf(154,axiom,
! [A: int] :
( ( ord_less_poly_real @ ( ring_11511526659y_real @ A ) @ zero_zero_poly_real )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_of__int__less__0__iff) ).
thf(816,plain,
! [A: int] :
( ( ord_less_poly_real @ ( ring_11511526659y_real @ A ) @ zero_zero_poly_real )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_power__mono__iff) ).
thf(609,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(120,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_zero__power) ).
thf(700,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(179,axiom,
ord_less_real @ zero_zero_real @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_M__pos) ).
thf(895,plain,
ord_less_real @ zero_zero_real @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(109,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_int @ one_one_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_of__int__lessD) ).
thf(668,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_int @ one_one_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(190,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_divide__nonneg__pos) ).
thf(932,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(245,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_divide__right__mono__neg) ).
thf(1112,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(3,axiom,
! [A: nat] :
( ( coeff_int @ zero_zero_poly_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_coeff__0) ).
thf(345,plain,
! [A: nat] :
( ( coeff_int @ zero_zero_poly_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(74,axiom,
! [A: nat,B: int,C: int] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ( power_power_int @ B @ A )
= ( power_power_int @ C @ A ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_power__eq__iff__eq__base) ).
thf(552,plain,
! [A: nat,B: int,C: int] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ( power_power_int @ B @ A )
= ( power_power_int @ C @ A ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(97,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_eq_int @ one_one_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_of__int__leD) ).
thf(626,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) @ B )
=> ( ( A = zero_zero_int )
| ( ord_less_eq_int @ one_one_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(184,axiom,
! [A: real,B: nat] :
( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_one__le__power) ).
thf(915,plain,
! [A: real,B: nat] :
( ( ord_less_eq_real @ one_one_real @ A )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(264,axiom,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_power__0) ).
thf(1171,plain,
! [A: real] :
( ( power_power_real @ A @ zero_zero_nat )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(289,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_less__divide__eq__1__pos) ).
thf(1245,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(143,axiom,
! [A: int,B: nat] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_zero__less__power) ).
thf(780,plain,
! [A: int,B: nat] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(91,axiom,
ord_less_real @ zero_zero_real @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_A__pos) ).
thf(608,plain,
ord_less_real @ zero_zero_real @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(77,axiom,
! [A: nat,B: poly_poly_real] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_poly_real @ B @ C )
= zero_zero_poly_real ) )
=> ( ord_less_eq_nat @ ( degree_poly_real @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_degree__le) ).
thf(563,plain,
! [A: nat,B: poly_poly_real] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_poly_real @ B @ C )
= zero_zero_poly_real ) )
=> ( ord_less_eq_nat @ ( degree_poly_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(326,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_divide__le__0__1__iff) ).
thf(1364,plain,
! [A: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(32,axiom,
! [A: poly_nat,B: nat] :
( ( ord_less_nat @ ( degree_nat @ A ) @ B )
=> ( ( coeff_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_coeff__eq__0) ).
thf(431,plain,
! [A: poly_nat,B: nat] :
( ( ord_less_nat @ ( degree_nat @ A ) @ B )
=> ( ( coeff_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(106,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_2108872382y_real @ zero_zero_poly_real @ A )
= one_one_poly_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_2108872382y_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_power__0__left) ).
thf(653,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_2108872382y_real @ zero_zero_poly_real @ A )
= one_one_poly_real ) )
& ( ( A != zero_zero_nat )
=> ( ( power_2108872382y_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(187,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_divide__le__eq__1__neg) ).
thf(922,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(278,axiom,
member_real @ one_one_real @ ring_1_Ints_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Ints__1) ).
thf(1213,plain,
member_real @ one_one_real @ ring_1_Ints_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(139,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( divide_divide_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_div__less) ).
thf(768,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( divide_divide_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(231,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( abs_abs_real @ ( divide_divide_real @ B @ A ) )
= ( divide_divide_real @ ( abs_abs_real @ B ) @ ( abs_abs_real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_nonzero__abs__divide) ).
thf(1066,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( abs_abs_real @ ( divide_divide_real @ B @ A ) )
= ( divide_divide_real @ ( abs_abs_real @ B ) @ ( abs_abs_real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(169,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_int @ one_one_int @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_int @ A @ ( power_power_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_self__le__power) ).
thf(868,plain,
! [A: int,B: nat] :
( ( ord_less_eq_int @ one_one_int @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_int @ A @ ( power_power_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(126,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_linordered__field__no__ub) ).
thf(722,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(222,axiom,
! [A: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
= ( ord_less_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_of__int__less__1__iff) ).
thf(1034,plain,
! [A: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
= ( ord_less_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(306,axiom,
! [A: int] : ( member_real @ ( ring_1_of_int_real @ A ) @ ring_1_Ints_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Ints__of__int) ).
thf(1304,plain,
! [A: int] : ( member_real @ ( ring_1_of_int_real @ A ) @ ring_1_Ints_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(113,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_poly_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_of__int__pos) ).
thf(680,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_poly_real @ zero_zero_poly_real @ ( ring_11511526659y_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(72,axiom,
! [A: int,B: nat] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ B ) )
= ( ( A != zero_zero_int )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_zero__less__power__abs__iff) ).
thf(548,plain,
! [A: int,B: nat] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ B ) )
= ( ( A != zero_zero_int )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(299,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_divide__nonpos__neg) ).
thf(1277,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(52,axiom,
! [A: poly_poly_real] :
( ( ( coeff_poly_real @ A @ ( degree_poly_real @ A ) )
= zero_zero_poly_real )
= ( A = zero_z1423781445y_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_leading__coeff__0__iff) ).
thf(487,plain,
! [A: poly_poly_real] :
( ( ( coeff_poly_real @ A @ ( degree_poly_real @ A ) )
= zero_zero_poly_real )
= ( A = zero_z1423781445y_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(236,axiom,
! [A: real,B: real] :
( ( one_one_real
= ( divide_divide_real @ A @ B ) )
= ( ( B != zero_zero_real )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_one__eq__divide__iff) ).
thf(1081,plain,
! [A: real,B: real] :
( ( one_one_real
= ( divide_divide_real @ A @ B ) )
= ( ( B != zero_zero_real )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_div__le__mono) ).
thf(617,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(318,axiom,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_algebraic__def) ).
thf(1340,plain,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ( power_power_nat @ B @ A )
= ( power_power_nat @ C @ A ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_power__eq__iff__eq__base) ).
thf(836,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ( power_power_nat @ B @ A )
= ( power_power_nat @ C @ A ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(226,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( ord_less_int @ A @ ( power_power_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_of__int__power__less__of__int__cancel__iff) ).
thf(1049,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ C ) )
= ( ord_less_int @ A @ ( power_power_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(343,axiom,
! [A: real,B: real] :
( ( one_one_real
= ( divide_divide_real @ A @ B ) )
= ( ( B != zero_zero_real )
& ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_eq__divide__eq__1) ).
thf(1413,plain,
! [A: real,B: real] :
( ( one_one_real
= ( divide_divide_real @ A @ B ) )
= ( ( B != zero_zero_real )
& ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(234,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( divide_divide_real @ A @ D ) @ ( divide_divide_real @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_frac__less2) ).
thf(1076,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( divide_divide_real @ A @ D ) @ ( divide_divide_real @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(53,axiom,
! [A: poly_poly_real,B: nat] :
( ( ( coeff_poly_real @ A @ B )
!= zero_zero_poly_real )
=> ( ord_less_eq_nat @ B @ ( degree_poly_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_le__degree) ).
thf(490,plain,
! [A: poly_poly_real,B: nat] :
( ( ( coeff_poly_real @ A @ B )
!= zero_zero_poly_real )
=> ( ord_less_eq_nat @ B @ ( degree_poly_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(111,axiom,
! [A: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_of__int__less__1__iff) ).
thf(675,plain,
! [A: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(275,axiom,
! [A: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ A ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_of__int__abs) ).
thf(1203,plain,
! [A: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ A ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(85,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_power__strict__decreasing__iff) ).
thf(589,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ one_one_int )
=> ( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(66,axiom,
! [A: poly_real] :
( ( divide1727078534y_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_divide__poly__0) ).
thf(531,plain,
! [A: poly_real] :
( ( divide1727078534y_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(194,axiom,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( divide_divide_real @ A @ A )
= one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_divide__self) ).
thf(944,plain,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( divide_divide_real @ A @ A )
= one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(256,axiom,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_of__int__le__iff) ).
thf(1145,plain,
! [A: int,B: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
= ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(217,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_zero__le__divide__1__iff) ).
thf(1018,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(201,axiom,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ A ) )
=> ( ( ord_less_real @ ( poly_real2 @ C @ B ) @ zero_zero_real )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_poly__IVT__neg) ).
thf(968,plain,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ A ) )
=> ( ( ord_less_real @ ( poly_real2 @ C @ B ) @ zero_zero_real )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(42,axiom,
! [A: poly_int,B: nat] :
( ( ord_less_eq_nat @ ( degree_int @ A ) @ B )
=> ( ( ( coeff_int @ A @ B )
= zero_zero_int )
=> ( ( A = zero_zero_poly_int )
| ( ord_less_nat @ ( degree_int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_eq__zero__or__degree__less) ).
thf(458,plain,
! [A: poly_int,B: nat] :
( ( ord_less_eq_nat @ ( degree_int @ A ) @ B )
=> ( ( ( coeff_int @ A @ B )
= zero_zero_int )
=> ( ( A = zero_zero_poly_int )
| ( ord_less_nat @ ( degree_int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(268,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_eq_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_le__divide__eq__1__neg) ).
thf(1181,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_eq_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(64,axiom,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_power__0) ).
thf(525,plain,
! [A: int] :
( ( power_power_int @ A @ zero_zero_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ one_one_nat @ C )
=> ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_power__increasing) ).
thf(580,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ one_one_nat @ C )
=> ( ord_less_eq_nat @ ( power_power_nat @ C @ A ) @ ( power_power_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(102,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_power__strict__decreasing__iff) ).
thf(640,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(219,axiom,
! [A: poly_real,B: poly_real] :
( ( ord_less_nat @ ( degree_real @ A ) @ ( degree_real @ B ) )
=> ( ( divide1727078534y_real @ A @ B )
= zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_div__poly__less) ).
thf(1025,plain,
! [A: poly_real,B: poly_real] :
( ( ord_less_nat @ ( degree_real @ A ) @ ( degree_real @ B ) )
=> ( ( divide1727078534y_real @ A @ B )
= zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(232,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ ( divide_divide_real @ C @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ C ) )
& ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_divide__le__cancel) ).
thf(1070,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ ( divide_divide_real @ C @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ C ) )
& ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(176,axiom,
! [A: poly_real,B: nat,C: poly_real] :
( ( ( power_2108872382y_real @ A @ B )
= ( power_2108872382y_real @ C @ B ) )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_power__eq__imp__eq__base) ).
thf(887,plain,
! [A: poly_real,B: nat,C: poly_real] :
( ( ( power_2108872382y_real @ A @ B )
= ( power_2108872382y_real @ C @ B ) )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ A )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(296,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( ( divide_divide_real @ B @ A )
= one_one_real )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_right__inverse__eq) ).
thf(1267,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( ( divide_divide_real @ B @ A )
= one_one_real )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(285,axiom,
! [A: real] :
( ( algebraic_real @ A )
=> ~ ! [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
=> ( ( B != zero_zero_poly_real )
=> ( ( poly_real2 @ B @ A )
!= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_algebraicE) ).
thf(1230,plain,
! [A: real] :
( ( algebraic_real @ A )
=> ~ ! [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
=> ( ( B != zero_zero_poly_real )
=> ( ( poly_real2 @ B @ A )
!= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(208,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_divide__pos__pos) ).
thf(993,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(283,axiom,
! [A: poly_real] :
( ( ord_less_real @ zero_zero_real @ ( coeff_real @ A @ ( degree_real @ A ) ) )
=> ? [B: real] :
! [C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( coeff_real @ A @ ( degree_real @ A ) ) @ ( poly_real2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_poly__pinfty__gt__lc) ).
thf(1225,plain,
! [A: poly_real] :
( ( ord_less_real @ zero_zero_real @ ( coeff_real @ A @ ( degree_real @ A ) ) )
=> ? [B: real] :
! [C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( coeff_real @ A @ ( degree_real @ A ) ) @ ( poly_real2 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(338,axiom,
! [A: real,B: nat] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_zero__le__power) ).
thf(1400,plain,
! [A: real,B: nat] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(197,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_divide__nonneg__nonneg) ).
thf(954,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(291,axiom,
! [A: real,B: real] :
( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
= ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_abs__divide) ).
thf(1252,plain,
! [A: real,B: real] :
( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
= ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(146,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_int @ one_one_int @ C )
=> ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_power__increasing) ).
thf(791,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_int @ one_one_int @ C )
=> ( ord_less_eq_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(270,axiom,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_of__int__le__1__iff) ).
thf(1188,plain,
! [A: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
= ( ord_less_eq_int @ A @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(125,axiom,
! [A: nat,B: poly_nat] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_nat @ B @ C )
= zero_zero_nat ) )
=> ( ord_less_eq_nat @ ( degree_nat @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_degree__le) ).
thf(717,plain,
! [A: nat,B: poly_nat] :
( ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( ( coeff_nat @ B @ C )
= zero_zero_nat ) )
=> ( ord_less_eq_nat @ ( degree_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(160,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_power__eq__0__iff) ).
thf(840,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(281,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_of__int__pos) ).
thf(1220,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(71,axiom,
! [A: int,B: nat] :
( ( A != zero_zero_int )
=> ( ( power_power_int @ A @ B )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_power__not__zero) ).
thf(544,plain,
! [A: int,B: nat] :
( ( A != zero_zero_int )
=> ( ( power_power_int @ A @ B )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(133,axiom,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_int @ one_one_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_of__int__1__less__iff) ).
thf(744,plain,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
= ( ord_less_int @ one_one_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(121,axiom,
! [A: poly_int,B: nat] :
( ( coeff_int @ ( power_power_poly_int @ A @ B ) @ zero_zero_nat )
= ( power_power_int @ ( coeff_int @ A @ zero_zero_nat ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_coeff__0__power) ).
thf(703,plain,
! [A: poly_int,B: nat] :
( ( coeff_int @ ( power_power_poly_int @ A @ B ) @ zero_zero_nat )
= ( power_power_int @ ( coeff_int @ A @ zero_zero_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(93,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_power__increasing__iff) ).
thf(613,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(301,axiom,
! [A: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_of__int__0__eq__iff) ).
thf(1284,plain,
! [A: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(227,axiom,
! [A: real,B: nat] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( member_real @ ( power_power_real @ A @ B ) @ ring_1_Ints_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Ints__power) ).
thf(1052,plain,
! [A: real,B: nat] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( member_real @ ( power_power_real @ A @ B ) @ ring_1_Ints_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_power__less__imp__less__exp) ).
thf(727,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(213,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
= ( ( ord_less_eq_real @ A @ zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_divide__le__0__abs__iff) ).
thf(1008,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
= ( ( ord_less_eq_real @ A @ zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( divide_divide_nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_div__less__dividend) ).
thf(595,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ one_one_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( divide_divide_nat @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(172,axiom,
! [A: poly_real,B: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ A )
=> ( ord_less_poly_real @ zero_zero_poly_real @ ( power_2108872382y_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_zero__less__power) ).
thf(876,plain,
! [A: poly_real,B: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ A )
=> ( ord_less_poly_real @ zero_zero_poly_real @ ( power_2108872382y_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(166,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_of__int__le__of__int__power__cancel__iff) ).
thf(859,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) @ ( ring_1_of_int_int @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(203,axiom,
( ( coeff_real @ one_one_poly_real @ ( degree_real @ one_one_poly_real ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_lead__coeff__1) ).
thf(978,plain,
( ( coeff_real @ one_one_poly_real @ ( degree_real @ one_one_poly_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(17,axiom,
! [A: int] :
( ( ring_1_of_int_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_of__int__abs) ).
thf(386,plain,
! [A: int] :
( ( ring_1_of_int_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(37,axiom,
! [A: poly_int,B: nat] :
( ( ( coeff_int @ A @ B )
!= zero_zero_int )
=> ( ord_less_eq_nat @ B @ ( degree_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_le__degree) ).
thf(446,plain,
! [A: poly_int,B: nat] :
( ( ( coeff_int @ A @ B )
!= zero_zero_int )
=> ( ord_less_eq_nat @ B @ ( degree_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(79,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_power__mono) ).
thf(571,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(44,axiom,
! [A: poly_nat] :
( ( A != zero_zero_poly_nat )
=> ( ( coeff_nat @ A @ ( degree_nat @ A ) )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_leading__coeff__neq__0) ).
thf(465,plain,
! [A: poly_nat] :
( ( A != zero_zero_poly_nat )
=> ( ( coeff_nat @ A @ ( degree_nat @ A ) )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(267,axiom,
ord_less_eq_real @ a @ one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171__092_060open_062A_A_092_060le_062_A1_092_060close_062) ).
thf(1180,plain,
ord_less_eq_real @ a @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(75,axiom,
! [A: poly_real,B: nat,C: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ A )
=> ( ( ord_less_poly_real @ A @ one_one_poly_real )
=> ( ( ord_less_poly_real @ ( power_2108872382y_real @ A @ B ) @ ( power_2108872382y_real @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_power__strict__decreasing__iff) ).
thf(556,plain,
! [A: poly_real,B: nat,C: nat] :
( ( ord_less_poly_real @ zero_zero_poly_real @ A )
=> ( ( ord_less_poly_real @ A @ one_one_poly_real )
=> ( ( ord_less_poly_real @ ( power_2108872382y_real @ A @ B ) @ ( power_2108872382y_real @ A @ C ) )
= ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(69,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_int__one__le__iff__zero__less) ).
thf(539,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)],[69]) ).
thf(110,axiom,
! [A: nat,B: poly_real,C: poly_real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ B )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ C )
=> ( ( ( power_2108872382y_real @ B @ A )
= ( power_2108872382y_real @ C @ A ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_power__eq__iff__eq__base) ).
thf(671,plain,
! [A: nat,B: poly_real,C: poly_real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ B )
=> ( ( ord_le1180086932y_real @ zero_zero_poly_real @ C )
=> ( ( ( power_2108872382y_real @ B @ A )
= ( power_2108872382y_real @ C @ A ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(182,axiom,
! [A: real] :
( ( divide_divide_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_division__ring__divide__zero) ).
thf(903,plain,
! [A: real] :
( ( divide_divide_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(138,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= one_one_int ) )
& ( ( A != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_power__0__left) ).
thf(759,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)],[138]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_power__decreasing__iff) ).
thf(771,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(311,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_of__int__less__of__int__power__cancel__iff) ).
thf(1316,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(237,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ A )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( divide_divide_real @ B @ D ) @ ( divide_divide_real @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_frac__le) ).
thf(1084,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ A )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( divide_divide_real @ B @ D ) @ ( divide_divide_real @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(313,axiom,
! [A: real] :
( ( poly_real2 @ one_one_poly_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_poly__1) ).
thf(1326,plain,
! [A: real] :
( ( poly_real2 @ one_one_poly_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(333,axiom,
! [A: nat,B: nat,C: real] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_real @ one_one_real @ C )
=> ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_power__strict__increasing) ).
thf(1385,plain,
! [A: nat,B: nat,C: real] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_real @ one_one_real @ C )
=> ( ord_less_real @ ( power_power_real @ C @ A ) @ ( power_power_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(180,axiom,
p != zero_zero_poly_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_p_I2_J) ).
thf(896,plain,
p != zero_zero_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(5,axiom,
! [A: nat] :
( ( coeff_poly_real @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_coeff__0) ).
thf(351,plain,
! [A: nat] :
( ( coeff_poly_real @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(99,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_power__mono) ).
thf(632,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(22,axiom,
! [A: nat,B: poly_poly_real] :
( ( ord_less_nat @ A @ ( degree_poly_real @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_poly_real @ B @ C )
!= zero_zero_poly_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_less__degree__imp) ).
thf(401,plain,
! [A: nat,B: poly_poly_real] :
( ( ord_less_nat @ A @ ( degree_poly_real @ B ) )
=> ? [C: nat] :
( ( ord_less_nat @ A @ C )
& ( ( coeff_poly_real @ B @ C )
!= zero_zero_poly_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ( divide_divide_nat @ A @ B )
= zero_zero_nat )
= ( ( ord_less_nat @ A @ B )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_Euclidean__Division_Odiv__eq__0__iff) ).
thf(568,plain,
! [A: nat,B: nat] :
( ( ( divide_divide_nat @ A @ B )
= zero_zero_nat )
= ( ( ord_less_nat @ A @ B )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(189,axiom,
( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
!= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_no__root) ).
thf(929,plain,
( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
!= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(272,axiom,
! [A: poly_real,B: int,C: int] :
( ! [D: nat] : ( member_real @ ( coeff_real @ A @ D ) @ ring_1_Ints_real )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( poly_real2 @ A @ ( divide_divide_real @ ( ring_1_of_int_real @ C ) @ ( ring_1_of_int_real @ B ) ) )
!= zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ ( degree_real @ A ) ) ) @ ( abs_abs_real @ ( poly_real2 @ A @ ( divide_divide_real @ ( ring_1_of_int_real @ C ) @ ( ring_1_of_int_real @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_int__poly__rat__no__root__ge) ).
thf(1193,plain,
! [A: poly_real,B: int,C: int] :
( ! [D: nat] : ( member_real @ ( coeff_real @ A @ D ) @ ring_1_Ints_real )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ( poly_real2 @ A @ ( divide_divide_real @ ( ring_1_of_int_real @ C ) @ ( ring_1_of_int_real @ B ) ) )
!= zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ ( degree_real @ A ) ) ) @ ( abs_abs_real @ ( poly_real2 @ A @ ( divide_divide_real @ ( ring_1_of_int_real @ C ) @ ( ring_1_of_int_real @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(49,axiom,
! [A: int,B: nat] :
( ( ring_1_of_int_int @ ( power_power_int @ A @ B ) )
= ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_of__int__power) ).
thf(478,plain,
! [A: int,B: nat] :
( ( ring_1_of_int_int @ ( power_power_int @ A @ B ) )
= ( power_power_int @ ( ring_1_of_int_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(181,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_divide__less__eq__1__pos) ).
thf(899,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
= ( ord_less_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(308,axiom,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( ( ord_less_real @ ( abs_abs_real @ A ) @ one_one_real )
=> ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Ints__nonzero__abs__less1) ).
thf(1309,plain,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( ( ord_less_real @ ( abs_abs_real @ A ) @ one_one_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(261,axiom,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_of__int__0__le__iff) ).
thf(1161,plain,
! [A: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(149,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_zero__le__power) ).
thf(800,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(252,axiom,
! [A: real] :
( ( ( divide_divide_real @ one_one_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_one__divide__eq__0__iff) ).
thf(1133,plain,
! [A: real] :
( ( ( divide_divide_real @ one_one_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(321,axiom,
! [A: real,B: real] :
( ( ( divide_divide_real @ A @ B )
= one_one_real )
= ( ( B != zero_zero_real )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_divide__eq__1__iff) ).
thf(1348,plain,
! [A: real,B: real] :
( ( ( divide_divide_real @ A @ B )
= one_one_real )
= ( ( B != zero_zero_real )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(300,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_le__divide__eq__1__pos) ).
thf(1280,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
= ( ord_less_eq_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(196,axiom,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_power__strict__increasing__iff) ).
thf(950,plain,
! [A: real,B: nat,C: nat] :
( ( ord_less_real @ one_one_real @ A )
=> ( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(257,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_of__int__le__of__int__power__cancel__iff) ).
thf(1148,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ A ) @ B ) @ ( ring_1_of_int_real @ C ) )
= ( ord_less_eq_int @ ( power_power_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(28,axiom,
( ( coeff_int @ one_one_poly_int @ ( degree_int @ one_one_poly_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_lead__coeff__1) ).
thf(422,plain,
( ( coeff_int @ one_one_poly_int @ ( degree_int @ one_one_poly_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(168,axiom,
! [A: int,B: nat] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_zero__le__power) ).
thf(865,plain,
! [A: int,B: nat] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(210,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_divide__nonneg__neg) ).
thf(999,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(95,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_of__int__pos) ).
thf(620,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(185,axiom,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_ab_H) ).
thf(918,plain,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(310,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_of__int__nonneg) ).
thf(1314,plain,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(34,axiom,
! [A: poly_int,B: nat] :
( ( ord_less_nat @ ( degree_int @ A ) @ B )
=> ( ( coeff_int @ A @ B )
= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_coeff__eq__0) ).
thf(437,plain,
! [A: poly_int,B: nat] :
( ( ord_less_nat @ ( degree_int @ A ) @ B )
=> ( ( coeff_int @ A @ B )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(342,axiom,
! [A: poly_real,B: nat] :
( ( ord_less_nat @ ( degree_real @ A ) @ B )
=> ( ( coeff_real @ A @ B )
= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_coeff__eq__0) ).
thf(1410,plain,
! [A: poly_real,B: nat] :
( ( ord_less_nat @ ( degree_real @ A ) @ B )
=> ( ( coeff_real @ A @ B )
= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(100,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) )
= ( ord_less_eq_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_power__mono__iff) ).
thf(635,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) )
= ( ord_less_eq_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(221,axiom,
ord_less_real @ a @ ( divide_divide_real @ one_one_real @ m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_A__less_I2_J) ).
thf(1033,plain,
ord_less_real @ a @ ( divide_divide_real @ one_one_real @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(273,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_divide__right__mono) ).
thf(1197,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(20,axiom,
! [A: poly_nat] :
( ( ( coeff_nat @ A @ ( degree_nat @ A ) )
= zero_zero_nat )
= ( A = zero_zero_poly_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_leading__coeff__0__iff) ).
thf(395,plain,
! [A: poly_nat] :
( ( ( coeff_nat @ A @ ( degree_nat @ A ) )
= zero_zero_nat )
= ( A = zero_zero_poly_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(132,axiom,
! [A: poly_real,B: nat] :
( ( A != zero_zero_poly_real )
=> ( ( power_2108872382y_real @ A @ B )
!= zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_power__not__zero) ).
thf(740,plain,
! [A: poly_real,B: nat] :
( ( A != zero_zero_poly_real )
=> ( ( power_2108872382y_real @ A @ B )
!= zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(206,axiom,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_poly__0) ).
thf(987,plain,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(30,axiom,
! [A: int] :
( ( coeff_int @ ( ring_12102921859ly_int @ A ) @ ( degree_int @ ( ring_12102921859ly_int @ A ) ) )
= ( ring_1_of_int_int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_lead__coeff__of__int) ).
thf(427,plain,
! [A: int] :
( ( coeff_int @ ( ring_12102921859ly_int @ A ) @ ( degree_int @ ( ring_12102921859ly_int @ A ) ) )
= ( ring_1_of_int_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_nat__power__less__imp__less) ).
thf(528,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(103,axiom,
! [A: nat,B: nat,C: int] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_int @ one_one_int @ C )
=> ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_power__strict__increasing) ).
thf(644,plain,
! [A: nat,B: nat,C: int] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_int @ one_one_int @ C )
=> ( ord_less_int @ ( power_power_int @ C @ A ) @ ( power_power_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(324,axiom,
! [A: real,B: real,C: nat] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) )
= ( ord_less_eq_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_power__mono__iff) ).
thf(1357,plain,
! [A: real,B: real,C: nat] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) )
= ( ord_less_eq_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_one__le__power) ).
thf(822,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(304,axiom,
~ ( ord_less_real @ ( divide_divide_real @ a @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ) @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224__092_060open_062_092_060not_062_AA_A_P_Areal__of__int_Ab_A_094_An_A_060_A_092_060bar_062x_A_N_Areal__of__int_Aa_A_P_Areal__of__int_Ab_092_060bar_062_092_060close_062) ).
thf(1299,plain,
~ ( ord_less_real @ ( divide_divide_real @ a @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ) @ ( abs_abs_real @ ( minus_minus_real @ x @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(117,axiom,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ A @ B )
= ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_power__eq__imp__eq__base) ).
thf(691,plain,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ A @ B )
= ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(170,axiom,
( ( (=) @ poly_real )
= ( ^ [A: poly_real,B: poly_real] :
! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_poly__eq__iff) ).
thf(871,plain,
( ( (=) @ poly_real )
= ( ^ [A: poly_real,B: poly_real] :
! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(12,axiom,
( ( ring_1_of_int_int @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_of__int__0) ).
thf(369,plain,
( ( ring_1_of_int_int @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(150,axiom,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_power__0) ).
thf(803,plain,
! [A: nat] :
( ( power_power_nat @ A @ zero_zero_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(6,axiom,
! [A: poly_poly_real] :
( ( ! [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) )
= ( A = zero_z1423781445y_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_poly__all__0__iff__0) ).
thf(354,plain,
! [A: poly_poly_real] :
( ( ! [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) )
= ( A = zero_z1423781445y_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(191,axiom,
! [A: real,B: nat,C: real] :
( ( ( power_power_real @ A @ B )
= ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_power__eq__imp__eq__base) ).
thf(935,plain,
! [A: real,B: nat,C: real] :
( ( ( power_power_real @ A @ B )
= ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(101,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_less__eq__int__code_I1_J) ).
thf(639,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(239,axiom,
! [A: poly_real,B: nat] :
( ( coeff_real @ ( power_2108872382y_real @ A @ B ) @ ( degree_real @ ( power_2108872382y_real @ A @ B ) ) )
= ( power_power_real @ ( coeff_real @ A @ ( degree_real @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_lead__coeff__power) ).
thf(1088,plain,
! [A: poly_real,B: nat] :
( ( coeff_real @ ( power_2108872382y_real @ A @ B ) @ ( degree_real @ ( power_2108872382y_real @ A @ B ) ) )
= ( power_power_real @ ( coeff_real @ A @ ( degree_real @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(10,axiom,
( ( coeff_nat @ zero_zero_poly_nat )
= ( ^ [A: nat] : zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_zero__poly_Orep__eq) ).
thf(364,plain,
( ( coeff_nat @ zero_zero_poly_nat )
= ( ^ [A: nat] : zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(174,axiom,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_power__less__imp__less__exp) ).
thf(882,plain,
! [A: int,B: nat,C: nat] :
( ( ord_less_int @ one_one_int @ A )
=> ( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(46,axiom,
! [A: poly_int] :
( ( A != zero_zero_poly_int )
=> ( ( coeff_int @ A @ ( degree_int @ A ) )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_leading__coeff__neq__0) ).
thf(469,plain,
! [A: poly_int] :
( ( A != zero_zero_poly_int )
=> ( ( coeff_int @ A @ ( degree_int @ A ) )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(327,axiom,
! [A: poly_real] :
( ( poly_real2 @ A @ zero_zero_real )
= ( coeff_real @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_poly__0__coeff__0) ).
thf(1367,plain,
! [A: poly_real] :
( ( poly_real2 @ A @ zero_zero_real )
= ( coeff_real @ A @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(223,axiom,
! [A: real,B: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ B )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_power__not__zero) ).
thf(1037,plain,
! [A: real,B: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ B )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(141,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_less__int__code_I1_J) ).
thf(775,plain,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(76,axiom,
! [A: int] :
( ( ( ring_11511526659y_real @ A )
= zero_zero_poly_real )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_of__int__eq__0__iff) ).
thf(560,plain,
! [A: int] :
( ( ( ring_11511526659y_real @ A )
= zero_zero_poly_real )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(55,axiom,
! [A: int,B: int] :
( ( ( ring_1_of_int_int @ A )
= ( ring_1_of_int_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_of__int__eq__iff) ).
thf(496,plain,
! [A: int,B: int] :
( ( ( ring_1_of_int_int @ A )
= ( ring_1_of_int_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(40,axiom,
! [A: int] : ( member_int @ ( ring_1_of_int_int @ A ) @ ring_1_Ints_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Ints__of__int) ).
thf(454,plain,
! [A: int] : ( member_int @ ( ring_1_of_int_int @ A ) @ ring_1_Ints_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1644,plain,
$false,
inference(e,[status(thm)],[892,1337,629,518,941,777,1110,481,1237,846,962,468,1200,1158,1005,1406,683,1073,440,1041,730,1290,873,449,1142,379,472,814,1260,1063,1354,1222,1164,797,1342,747,1095,1391,885,1046,389,1287,504,1264,344,542,1055,724,357,1191,1379,1087,1319,1013,416,1115,475,756,376,1334,1151,806,1373,443,1136,834,348,574,687,734,1394,1351,507,411,1345,1242,849,512,678,1306,810,366,534,714,1206,452,1274,957,1091,825,1021,1255,862,1174,392,424,1370,1217,598,484,879,852,665,461,1079,456,583,522,493,1210,682,1407,551,1128,697,650,1227,980,593,499,1397,783,1118,1329,1028,1361,753,537,1214,1016,1155,706,622,647,1099,1382,1131,1060,984,1002,371,515,1249,938,360,398,1167,1185,662,926,794,586,906,430,856,1301,601,965,750,819,975,694,1388,1403,1256,413,843,1125,577,711,1139,382,1271,1312,787,1107,1239,1332,919,947,604,406,362,737,1122,1376,1175,1011,419,990,996,509,434,890,816,609,700,895,668,932,1112,345,552,626,915,1171,1245,780,608,563,1364,431,653,922,1213,768,1066,868,722,1034,1304,680,548,1277,487,1081,617,1340,836,1049,1413,1076,490,675,1203,589,531,944,1145,1018,968,458,1181,525,580,640,1025,1070,887,1267,1230,993,1225,1400,954,1252,791,1188,717,840,1220,544,744,703,613,1284,1052,727,1008,595,876,859,978,386,446,571,465,1180,556,539,671,903,759,771,1316,1084,1326,1385,896,351,632,401,568,929,1193,478,899,1309,1161,800,1133,1348,1280,950,1148,422,865,999,620,918,1314,437,1410,635,1033,1197,395,740,987,427,528,644,1357,822,1299,691,871,369,803,354,935,639,1088,364,882,469,1367,1037,775,560,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP095^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n011.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:53:01 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.11/1.20 % [INFO] Parsing done (398ms).
% 2.41/1.21 % [INFO] Running in sequential loop mode.
% 3.17/1.59 % [INFO] eprover registered as external prover.
% 3.42/1.60 % [INFO] Scanning for conjecture ...
% 3.60/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ...
% 4.18/1.92 % [INFO] Axiom selection finished. Selected 341 axioms (removed 12 axioms).
% 5.03/2.16 % [INFO] Problem is higher-order (TPTP THF).
% 5.03/2.18 % [INFO] Type checking passed.
% 5.03/2.18 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 19.66/5.55 % External prover 'e' found a proof!
% 19.66/5.56 % [INFO] Killing All external provers ...
% 19.66/5.56 % Time passed: 5213ms (effective reasoning time: 4342ms)
% 19.66/5.56 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 19.66/5.56 % Axioms used in derivation (341): fact_321_power__increasing, fact_149_poly__eq__poly__eq__iff, fact_101_zero__poly_Orep__eq, fact_183_abs__divide, fact_312_power__0__left, fact_33_irrationsl, fact_2_p_I1_J, fact_140_of__int__nonneg, fact_261_degree__le, fact_92_mem__Collect__eq, fact_269_eq__zero__or__degree__less, fact_144_lead__coeff__power, fact_163__092_060open_062A_A_P_Areal__of__int_Ab_A_094_An_A_092_060le_062_AA_A_P_A1_092_060close_062, fact_136_Ints__cases, fact_29_of__int__1, fact_3_b, fact_188_divide__eq__eq__1, fact_313_power__0__left, fact_0_assms_I2_J, fact_5_no__root, fact_74_of__int__0__le__iff, fact_114_algebraicE, fact_15_poly__power, fact_173_power__one__right, fact_147_Ints__nonzero__abs__ge1, fact_302_divide__less__0__iff, fact_91_poly__eqI, fact_75_of__int__less__0__iff, fact_65_zabs__less__one__iff, fact_161_divide__le__eq__1__pos, fact_268_coeff__0__power, fact_189_eq__divide__eq__1, fact_315_power__0__left, fact_175_nat__zero__less__power__iff, fact_23_of__int__power, fact_276_power__not__zero, fact_306_divide__strict__right__mono__neg, fact_236_power__0, fact_133_Ints__induct, fact_150_of__int__lessD, fact_299_divide__neg__pos, fact_342_div__pos__pos__trivial, fact_174_power__one__right, fact_343_div__neg__neg__trivial, fact_157_power__decreasing__iff, fact_125_Ints__1, fact_250_poly__IVT__pos, fact_34_of__int__eq__iff, fact_90_less__eq__int__code_I1_J, fact_44_of__int__0, fact_104_le__degree, fact_243_power__eq__imp__eq__base, fact_100_zero__poly_Orep__eq, fact_215_power__strict__decreasing__iff, fact_194_power__inject__exp, fact_228_self__le__power, fact_277_power__divide, fact_186_divide__self, fact_148_Ints__nonzero__abs__ge1, fact_256_coeff__eq__0, fact_167_zero__le__divide__abs__iff, fact_152_of__int__leD, fact_77_of__int__less__0__iff, fact_348_div__eq__dividend__iff, fact_112_algebraic__def, fact_139_Ints__nonzero__abs__less1, fact_126_Ints__1, fact_181_power__one, fact_70_of__int__le__0__iff, fact_67_lead__coeff__1, fact_171__092_060open_062A_A_092_060le_062_A1_092_060close_062, fact_230_divide__poly__0, fact_294_zero__le__power, fact_280_power__abs, fact_292_power__mono, fact_307_zero__less__power, fact_288_divide__nonpos__nonpos, fact_320_power__increasing, fact_333_divide__le__cancel, fact_271_eq__zero__or__degree__less, fact_318_one__le__power, fact_262_degree__le, fact_120_leading__coeff__neq__0, fact_6_n__def, fact_154_int__poly__rat__no__root__ge, fact_13_of__int__le__1__iff, fact_253_coeff__eq__0, fact_93_Collect__mem__eq, fact_72_of__int__0__le__iff, fact_203_degree__1, fact_314_power__0__left, fact_18_poly__1, fact_310_zero__less__power, fact_11_of__int__1__le__iff, fact_241_power__eq__iff__eq__base, fact_103_coeff__inject, fact_223_power__increasing__iff, fact_22_of__int__abs, fact_200_power__eq__0__iff, fact_99_zero__poly_Orep__eq, fact_168_divide__le__0__abs__iff, fact_42_of__int__0__eq__iff, fact_177_divide__cancel__left, fact_296_zero__le__power, fact_83_of__int__1__less__iff, fact_264_degree__le, fact_71_of__int__le__0__iff, fact_69_of__int__le__0__iff, fact_141_of__int__nonneg, fact_176_divide__eq__0__iff, fact_331_frac__less, fact_316_one__le__power, fact_340_ab, fact_115_of__int__pos, fact_205_divide__le__0__1__iff, fact_206_zero__le__divide__1__iff, fact_244_power__eq__imp__eq__base, fact_229_self__le__power, fact_88_of__int__less__of__int__power__cancel__iff, fact_285_divide__nonneg__nonneg, fact_169_A__pos, fact_153_of__int__leD, fact_281_algebraic__altdef, fact_45_of__int__0, fact_79_of__int__0__less__iff, fact_64_leading__coeff__0__iff, fact_98_zero__poly_Orep__eq, fact_124_poly__all__0__iff__0, fact_195_power__strict__increasing__iff, fact_135_Ints__cases, fact_309_zero__less__power, fact_9_of__int__power__le__of__int__cancel__iff, fact_10_of__int__power__le__of__int__cancel__iff, fact_131_Ints__of__int, fact_62_leading__coeff__0__iff, fact_32_of__int__eq__1__iff, fact_305_divide__strict__right__mono, fact_51_coeff__0, fact_158_power__decreasing__iff, fact_25_of__int__eq__of__int__power__cancel__iff, fact_63_leading__coeff__0__iff, fact_265_Liouville__Numbers__Misc_ORats__cases_H, fact_48_of__int__le__iff, fact_344_M__pos, fact_255_coeff__eq__0, fact_323_power__less__imp__less__exp, fact_246_one__less__power, fact_346_A__less_I3_J, fact_273_power__not__zero, fact_162_divide__le__eq__1__neg, fact_326_power__strict__increasing, fact_322_power__less__imp__less__exp, fact_61_leading__coeff__0__iff, fact_121_leading__coeff__neq__0, fact_50_of__int__less__iff, fact_254_coeff__eq__0, fact_59_lead__coeff__of__int, fact_184_divide__eq__1__iff, fact_317_one__le__power, fact_279_power__abs, fact_303_divide__less__cancel, fact_248_one__less__power, fact_249_poly__IVT__neg, fact_282_divide__le__0__iff, fact_289_divide__right__mono__neg, fact_30_of__int__1, fact_60_lead__coeff__of__int, fact_237_power__0, fact_238_power__eq__iff__eq__base, fact_199_power__eq__0__iff, fact_46_of__int__0, fact_81_of__int__less__1__iff, fact_332_frac__less2, fact_286_divide__nonneg__nonpos, fact_68_lead__coeff__1, fact_28_of__int__power__eq__of__int__cancel__iff, fact_212_zero__less__divide__1__iff, fact_76_of__int__less__0__iff, fact_216_power__strict__decreasing__iff, fact_197_power__strict__increasing__iff, fact_102_int__one__le__iff__zero__less, fact_117_of__int__pos, fact_73_of__int__0__le__iff, fact_334_divide__nonneg__neg, fact_53_coeff__0, fact_132_Ints__of__int, fact_110_poly__0__coeff__0, fact_179_division__ring__divide__zero, fact_349_div__less__dividend, fact_180_power__one, fact_211_less__divide__eq__1__pos, fact_341_ab_H, fact_328_power__one__over, fact_231_zero__power, fact_220_power__mono__iff, fact_85_of__int__power__less__of__int__cancel__iff, fact_202_degree__0, fact_7_of__int__le__of__int__power__cancel__iff, fact_155_power__decreasing__iff, fact_300_divide__pos__neg, fact_324_power__less__imp__less__exp, fact_38_of__int__eq__0__iff, fact_82_of__int__less__1__iff, fact_258_less__degree__imp, fact_97_Ints__0, fact_49_of__int__less__iff, fact_350_Euclidean__Division_Odiv__eq__0__iff, fact_290_power__mono, fact_43_of__int__0__eq__iff, fact_116_of__int__pos, fact_36__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062, fact_257_less__degree__imp, fact_4_p_I3_J, fact_52_coeff__0, fact_295_zero__le__power, fact_232_zero__power, fact_159_le__divide__eq__1__pos, fact_338_power__less__imp__less__base, fact_119_leading__coeff__neq__0, fact_187_divide__self__if, fact_245_power__eq__imp__eq__base, fact_47_of__int__le__iff, fact_274_power__not__zero, fact_263_degree__le, fact_209_divide__less__eq__1__pos, fact_242_power__eq__imp__eq__base, fact_235_power__0, fact_27_of__int__power__eq__of__int__cancel__iff, fact_298_divide__neg__neg, fact_208_divide__less__eq__1__neg, fact_351_div__le__dividend, fact_213_power__strict__decreasing__iff, fact_335_divide__nonneg__pos, fact_182_power__one, fact_304_zero__less__divide__iff, fact_172_power__one__right, fact_39_of__int__eq__0__iff, fact_327_power__strict__increasing, fact_170_A__less_I1_J, fact_160_le__divide__eq__1__neg, fact_325_power__strict__increasing, fact_107_le__degree, fact_54_coeff__0, fact_96_Ints__0, fact_224__092_060open_062_092_060not_062_AA_A_P_Areal__of__int_Ab_A_094_An_A_060_A_092_060bar_062x_A_N_Areal__of__int_Aa_A_P_Areal__of__int_Ab_092_060bar_062_092_060close_062, fact_207_divide__less__0__1__iff, fact_330_frac__le, fact_164_zero__less__power__abs__iff, fact_14_of__int__le__1__iff, fact_12_of__int__1__le__iff, fact_8_of__int__le__of__int__power__cancel__iff, fact_129_Ints__abs, fact_113_algebraicI, fact_178_divide__cancel__right, fact_142_of__int__nonneg, fact_210_less__divide__eq__1__neg, fact_127_Ints__power, fact_143_lead__coeff__power, fact_214_power__strict__decreasing__iff, fact_247_one__less__power, fact_35_of__int__eq__iff, fact_106_le__degree, fact_240_power__eq__iff__eq__base, fact_192_power__inject__exp, fact_226_div__poly__less, fact_204_degree__of__int, fact_58_poly__0, fact_287_divide__nonpos__nonneg, fact_266_coeff__0__power, fact_87_of__int__less__of__int__power__cancel__iff, fact_329_nonzero__abs__divide, fact_227_self__le__power, fact_86_of__int__power__less__of__int__cancel__iff, fact_145_lead__coeff__power, fact_66_lead__coeff__1, fact_260_less__degree__imp, fact_283_divide__right__mono, fact_40_of__int__eq__0__iff, fact_198_power__eq__0__iff, fact_311_right__inverse__eq, fact_297_zero__le__power, fact_319_power__increasing, fact_234_zero__power, fact_191_zero__eq__1__divide__iff, fact_284_zero__le__divide__iff, fact_196_power__strict__increasing__iff, fact_41_of__int__0__eq__iff, fact_239_power__eq__iff__eq__base, fact_291_power__mono, fact_89_less__int__code_I1_J, fact_272_eq__zero__or__degree__less, fact_270_eq__zero__or__degree__less, fact_24_of__int__power, fact_339_A__less_I2_J, fact_37__092_060open_062x_A_092_060notin_062_Aroots_092_060close_062, fact_55_poly__0, fact_293_power__mono, fact_259_less__degree__imp, fact_336_divide__nonpos__neg, fact_308_zero__less__power, fact_352_div__le__mono, fact_345_div__less, fact_1_p_I2_J, fact_128_Ints__power, fact_301_divide__pos__pos, fact_278_poly__pinfty__gt__lc, fact_26_of__int__eq__of__int__power__cancel__iff, fact_347_that, fact_252_linordered__field__no__lb, fact_80_of__int__0__less__iff, fact_222_power__increasing__iff, fact_166_zero__less__power__abs__iff, fact_221_power__increasing__iff, fact_108_poly__0__coeff__0, fact_165_zero__less__power__abs__iff, fact_122_poly__all__0__iff__0, fact_219_power__mono__iff, fact_21_of__int__abs, fact_185_one__eq__divide__iff, fact_105_le__degree, fact_134_Ints__induct, fact_251_linordered__field__no__ub, fact_138_Ints__nonzero__abs__less1, fact_156_power__decreasing__iff, fact_78_of__int__0__less__iff, fact_217_power__mono__iff, fact_233_zero__power, fact_118_leading__coeff__neq__0, fact_94_poly__eq__iff, fact_275_power__not__zero, fact_84_of__int__1__less__iff, fact_193_power__inject__exp, fact_130_Ints__abs, fact_190_one__divide__eq__0__iff, fact_267_coeff__0__power, fact_31_of__int__eq__1__iff, fact_201_power__eq__0__iff, fact_337_divide__nonpos__pos, fact_218_power__mono__iff, fact_151_of__int__lessD, fact_225_nat__power__less__imp__less
% 19.66/5.56 % No. of inferences in proof: 686
% 19.66/5.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5213 ms resp. 4342 ms w/o parsing
% 21.13/5.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.13/5.82 % [INFO] Killing All external provers ...
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