%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP130^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : 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 08:06:52 AM UTC 2026
% Result : Theorem 15.56s 4.51s
% Output : Refutation 16.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 320
% Syntax : Number of formulae : 642 ( 318 unt; 0 typ; 0 def)
% Number of atoms : 1678 ( 570 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 4685 ( 156 ~; 44 |; 76 &;3727 @)
% ( 0 <=>; 682 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 11 con; 0-2 aty)
% Number of variables : 1326 ( 14 ^;1262 !; 50 ?;1326 :)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(zero_zero_int_decl,type,
zero_zero_int: int ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(ring_1_of_int_int_decl,type,
ring_1_of_int_int: int > int ).
thf(ring_1_of_int_real_decl,type,
ring_1_of_int_real: int > real ).
thf(suc_decl,type,
suc: nat > nat ).
thf(nthRoo1352626670d_root_decl,type,
nthRoo1352626670d_root: nat > nat > $o ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_real_decl,type,
ord_less_real: real > real > $o ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(power_power_int_decl,type,
power_power_int: int > nat > int ).
thf(power_power_nat_decl,type,
power_power_nat: nat > nat > nat ).
thf(power_power_real_decl,type,
power_power_real: real > nat > real ).
thf(divide_divide_int_decl,type,
divide_divide_int: int > int > int ).
thf(divide_divide_nat_decl,type,
divide_divide_nat: nat > nat > nat ).
thf(divide_divide_real_decl,type,
divide_divide_real: real > real > real ).
thf(ny_decl,type,
ny: real ).
thf(na_decl,type,
na: int ).
thf(p_decl,type,
p: nat ).
thf(pm_decl,type,
pm: nat ).
thf(x_decl,type,
x: int ).
thf(y_decl,type,
y: int ).
thf(ya_decl,type,
ya: int ).
thf(288,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_less__SucI) ).
thf(1322,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',fact_274_divide__less__cancel) ).
thf(1036,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)],[206]) ).
thf(309,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ B ) ) @ ( power_power_int @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_power__le__imp__le__base) ).
thf(1411,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ B ) ) @ ( power_power_int @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(90,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_zero__reorient) ).
thf(629,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_4_of__int__power__less__of__int__cancel__iff) ).
thf(760,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)],[129]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) )
= ( ord_less_eq_int @ B @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_neg__imp__zdiv__nonneg__iff) ).
thf(479,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) )
= ( ord_less_eq_int @ B @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(11,axiom,
( ( ring_1_of_int_int @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_of__int__0) ).
thf(347,plain,
( ( ring_1_of_int_int @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(204,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_zero__less__Suc) ).
thf(1031,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(168,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_inc__induct) ).
thf(893,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(217,axiom,
ord_less_nat @ zero_zero_nat @ pm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_pm0) ).
thf(1083,plain,
ord_less_nat @ zero_zero_nat @ pm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',fact_164_power__eq__iff__eq__base) ).
thf(777,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)],[135]) ).
thf(13,axiom,
! [A: int] :
( ( zero_zero_int
= ( ring_1_of_int_int @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_of__int__0__eq__iff) ).
thf(352,plain,
! [A: int] :
( ( zero_zero_int
= ( ring_1_of_int_int @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(246,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/sandbox2/benchmark/theBenchmark.p',fact_107_of__int__0__le__iff) ).
thf(1200,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)],[246]) ).
thf(279,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_lift__Suc__mono__less__iff) ).
thf(1290,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(212,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Suc__less__eq2) ).
thf(1068,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',fact_102_power__mono__iff) ).
thf(1443,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)],[317]) ).
thf(123,axiom,
ord_less_eq_int @ zero_zero_int @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_y_H0) ).
thf(741,plain,
ord_less_eq_int @ zero_zero_int @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',fact_282_divide__nonneg__neg) ).
thf(878,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)],[163]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',fact_71_power__eq__0__iff) ).
thf(597,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)],[82]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_le__imp__less__Suc) ).
thf(873,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(43,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ex__least__nat__le) ).
thf(449,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(230,axiom,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_less__eq__Suc__le) ).
thf(1142,plain,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(270,axiom,
! [A: real] :
? [B: int] : ( ord_less_real @ ( ring_1_of_int_real @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ex__of__int__less) ).
thf(1269,plain,
! [A: real] :
? [B: int] : ( ord_less_real @ ( ring_1_of_int_real @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( nthRoo1352626670d_root @ A @ B )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_fixed__root_Op0) ).
thf(384,plain,
! [A: nat,B: nat] :
( ( nthRoo1352626670d_root @ A @ B )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(67,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_nat__less__le) ).
thf(550,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',fact_11_of__int__less__iff) ).
thf(1233,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)],[259]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',fact_281_divide__le__cancel) ).
thf(814,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)],[147]) ).
thf(268,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_lift__Suc__mono__le) ).
thf(1260,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(170,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_lift__Suc__mono__le) ).
thf(913,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(236,axiom,
! [A: real,B: nat,C: real] :
( ( ( power_power_real @ A @ ( suc @ B ) )
= ( power_power_real @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_power__inject__base) ).
thf(1164,plain,
! [A: real,B: nat,C: real] :
( ( ( power_power_real @ A @ ( suc @ B ) )
= ( power_power_real @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',fact_37_of__int__0__less__iff) ).
thf(797,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)],[141]) ).
thf(227,axiom,
! [A: nat,B: real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ A )
= B )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ A )
= B ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_realpow__pos__nth__unique) ).
thf(1127,plain,
! [A: nat,B: real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ A )
= B )
& ! [D: real] :
( ( ( ord_less_real @ zero_zero_real @ D )
& ( ( power_power_real @ D @ A )
= B ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(155,axiom,
! [A: nat] :
( ( power_power_int @ zero_zero_int @ ( suc @ A ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_power__0__Suc) ).
thf(841,plain,
! [A: nat] :
( ( power_power_int @ zero_zero_int @ ( suc @ A ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(299,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_nat_OdiscI) ).
thf(1359,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(25,axiom,
x = y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_x) ).
thf(389,plain,
x = y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(278,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/sandbox2/benchmark/theBenchmark.p',fact_269_divide__neg__neg) ).
thf(1287,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)],[278]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_291_div__le__mono) ).
thf(570,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)],[74]) ).
thf(313,axiom,
na != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n00) ).
thf(1430,plain,
na != zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',fact_268_divide__le__0__iff) ).
thf(719,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)],[116]) ).
thf(10,axiom,
! [A: int] :
( ( divide_divide_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_bits__div__0) ).
thf(344,plain,
! [A: int] :
( ( divide_divide_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',fact_276_divide__strict__right__mono) ).
thf(817,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)],[148]) ).
thf(93,axiom,
! [A: real] :
( ( divide_divide_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_division__ring__divide__zero) ).
thf(638,plain,
! [A: real] :
( ( divide_divide_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',fact_70_power__eq__0__iff) ).
thf(1087,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)],[219]) ).
thf(232,axiom,
! [A: int,B: int] :
( ( ( ring_1_of_int_real @ A )
= ( ring_1_of_int_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_of__int__eq__iff) ).
thf(1147,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)],[232]) ).
thf(264,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_lift__Suc__antimono__le) ).
thf(1247,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_111_of__int__power__le__of__int__cancel__iff) ).
thf(881,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)],[164]) ).
thf(36,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__nat__zero__code) ).
thf(421,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(160,axiom,
! [A: nat,B: nat] :
( ( nthRoo1352626670d_root @ A @ B )
=> ( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_fixed__root_Op) ).
thf(870,plain,
! [A: nat,B: nat] :
( ( nthRoo1352626670d_root @ A @ B )
=> ( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(319,axiom,
( p
= ( suc @ pm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_p) ).
thf(1450,plain,
( p
= ( suc @ pm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',fact_3_of__int__power__less__of__int__cancel__iff) ).
thf(1373,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)],[301]) ).
thf(200,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ A @ ( suc @ B ) )
= ( power_power_nat @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_power__inject__base) ).
thf(1020,plain,
! [A: nat,B: nat,C: nat] :
( ( ( power_power_nat @ A @ ( suc @ B ) )
= ( power_power_nat @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(144,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_less__eq__nat_Osimps_I1_J) ).
thf(806,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(276,axiom,
ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ na ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_n0) ).
thf(1283,plain,
ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ na ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(228,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_not__less__eq) ).
thf(1136,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Suc__le__D) ).
thf(834,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(131,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_le__zero__eq) ).
thf(766,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_287_div__pos__pos__trivial) ).
thf(734,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)],[121]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',fact_169_power__mono) ).
thf(774,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)],[134]) ).
thf(96,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_neq0__conv) ).
thf(660,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',fact_280_frac__less2) ).
thf(1433,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)],[314]) ).
thf(262,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_not__less__eq__eq) ).
thf(1242,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_less__Suc__eq__0__disj) ).
thf(1169,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_35_of__int__less__0__iff) ).
thf(397,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)],[28]) ).
thf(318,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_real @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_lift__Suc__mono__less) ).
thf(1447,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_real @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',fact_272_divide__pos__pos) ).
thf(956,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)],[181]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',fact_168_power__mono) ).
thf(1074,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)],[214]) ).
thf(249,axiom,
! [A: real] :
? [B: int] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_ex__le__of__int) ).
thf(1206,plain,
! [A: real] :
? [B: int] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(22,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ C @ B ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_power__less__imp__less__base) ).
thf(380,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)],[22]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',fact_163_power__eq__iff__eq__base) ).
thf(512,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)],[59]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_170_power__mono) ).
thf(678,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)],[103]) ).
thf(283,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ A )
=> ( ord_less_nat @ B @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_power__gt__expt) ).
thf(1306,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ A )
=> ( ord_less_nat @ B @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(234,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_less__Suc__induct) ).
thf(1153,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(210,axiom,
nthRoo1352626670d_root @ p @ pm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_fixed__root__axioms) ).
thf(1047,plain,
nthRoo1352626670d_root @ p @ pm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Suc__lessD) ).
thf(1274,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(254,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ B ) ) @ ( power_power_nat @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_power__le__imp__le__base) ).
thf(1223,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ B ) ) @ ( power_power_nat @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(293,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_less__Suc0) ).
thf(1343,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(208,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_linordered__field__no__lb) ).
thf(1042,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(297,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_linordered__field__no__ub) ).
thf(1355,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(252,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_lift__Suc__mono__less) ).
thf(1217,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(149,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Zero__neq__Suc) ).
thf(820,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(71,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_bot__nat__0_Oextremum__unique) ).
thf(561,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(37,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_power__strict__mono) ).
thf(424,plain,
! [A: int,B: int,C: nat] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_int @ ( power_power_int @ A @ C ) @ ( power_power_int @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
= ( ( ord_less_eq_int @ B @ A )
& ( ord_less_int @ zero_zero_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_nonneg1__imp__zdiv__pos__iff) ).
thf(429,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
= ( ( ord_less_eq_int @ B @ A )
& ( ord_less_int @ zero_zero_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(138,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_zero__less__iff__neq__zero) ).
thf(788,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(158,axiom,
~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_not_I2_J) ).
thf(862,plain,
~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_8_of__int__eq__of__int__power__cancel__iff) ).
thf(349,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)],[12]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',fact_275_zero__less__divide__iff) ).
thf(916,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)],[171]) ).
thf(16,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_less__not__refl) ).
thf(361,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(89,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_less__not__refl3) ).
thf(625,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(5,axiom,
! [A: int] :
( ( divide_divide_int @ zero_zero_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_div__0) ).
thf(329,plain,
! [A: int] :
( ( divide_divide_int @ zero_zero_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(98,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_div__le__dividend) ).
thf(665,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(53,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_not__gr0) ).
thf(493,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',fact_263_divide__nonpos__nonneg) ).
thf(757,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)],[128]) ).
thf(244,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_All__less__Suc) ).
thf(1195,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(113,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_bot__nat__0_Onot__eq__extremum) ).
thf(710,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(197,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_gr0__implies__Suc) ).
thf(1012,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_le__neq__implies__less) ).
thf(583,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(62,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_less__zeroE) ).
thf(522,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_eq__imp__le) ).
thf(697,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(86,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_le__0__eq) ).
thf(615,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(290,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_zero__induct) ).
thf(1328,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(225,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_less__Suc__eq__le) ).
thf(1121,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(256,axiom,
! [A: real,B: nat,C: real] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_power__less__imp__less__base) ).
thf(1227,plain,
! [A: real,B: nat,C: real] :
( ( ord_less_real @ ( power_power_real @ A @ B ) @ ( power_power_real @ C @ B ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',fact_161_power__eq__imp__eq__base) ).
thf(725,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)],[118]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',fact_106_of__int__le__0__iff) ).
thf(403,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)],[30]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_le__less__Suc__eq) ).
thf(1096,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(195,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_lift__Suc__mono__less__iff) ).
thf(1006,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(55,axiom,
! [A: real,B: real] :
( ( ( divide_divide_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_divide__eq__0__iff) ).
thf(499,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)],[55]) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',fact_5_of__int__power) ).
thf(989,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)],[190]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_nat__neq__iff) ).
thf(519,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',fact_2_of__int__less__of__int__power__cancel__iff) ).
thf(742,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)],[124]) ).
thf(165,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_gr0__conv__Suc) ).
thf(884,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Suc__le__eq) ).
thf(1028,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_gr__implies__not0) ).
thf(554,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',fact_262_divide__nonpos__nonpos) ).
thf(476,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)],[48]) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',fact_159_power__eq__imp__eq__base) ).
thf(1039,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)],[207]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_linorder__neqE__nat) ).
thf(547,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(289,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Suc__neq__Zero) ).
thf(1324,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(269,axiom,
! [A: nat,B: real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_realpow__pos__nth) ).
thf(1263,plain,
! [A: nat,B: real] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(110,axiom,
p != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_p0) ).
thf(701,plain,
p != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',fact_34_of__int__less__0__iff) ).
thf(1150,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)],[233]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',fact_277_divide__strict__right__mono__neg) ).
thf(1297,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)],[281]) ).
thf(122,axiom,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_div__by__0) ).
thf(738,plain,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(321,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Suc__lessE) ).
thf(1456,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_165_zero__le__power) ).
thf(1192,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)],[243]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_128_nat__power__less__imp__less) ).
thf(371,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)],[19]) ).
thf(307,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_transitive__stepwise__le) ).
thf(1393,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(88,axiom,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_zero__reorient) ).
thf(622,plain,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',fact_162_power__eq__iff__eq__base) ).
thf(837,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)],[154]) ).
thf(223,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_real @ zero_zero_real @ A )
= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_zero__power) ).
thf(1099,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)],[223]) ).
thf(188,axiom,
ord_less_real @ zero_zero_real @ ny,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_NY0) ).
thf(985,plain,
ord_less_real @ zero_zero_real @ ny,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(179,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_nat__induct__at__least) ).
thf(938,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(58,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ ( divide_divide_int @ B @ A ) @ zero_zero_int )
= ( ord_less_int @ B @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_pos__imp__zdiv__neg__iff) ).
thf(508,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ ( divide_divide_int @ B @ A ) @ zero_zero_int )
= ( ord_less_int @ B @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',fact_108_of__int__0__le__iff) ).
thf(541,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)],[64]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',fact_56_of__int__pos) ).
thf(1167,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)],[237]) ).
thf(174,axiom,
! [A: int] :
( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_power__Suc0__right) ).
thf(926,plain,
! [A: int] :
( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) )
= ( ( ord_less_eq_nat @ B @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_div__greater__zero__iff) ).
thf(558,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) )
= ( ( ord_less_eq_nat @ B @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_less__antisym) ).
thf(1071,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',fact_278_frac__le) ).
thf(953,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)],[180]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( B = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_nat__power__eq__Suc__0__iff) ).
thf(1185,plain,
! [A: nat,B: nat] :
( ( ( power_power_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( B = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(140,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_zero__reorient) ).
thf(794,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(79,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_not__gr__zero) ).
thf(586,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(274,axiom,
! [A: real,B: nat,C: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ B ) ) @ ( power_power_real @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_power__le__imp__le__base) ).
thf(1278,plain,
! [A: real,B: nat,C: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ B ) ) @ ( power_power_real @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',fact_266_zero__le__divide__iff) ).
thf(412,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)],[33]) ).
thf(185,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_nat__induct) ).
thf(965,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(87,axiom,
! [A: int,B: nat] :
( ( A != zero_zero_int )
=> ( ( power_power_int @ A @ B )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_power__not__zero) ).
thf(618,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)],[87]) ).
thf(150,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_old_Onat_Odistinct_I2_J) ).
thf(824,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(125,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_int @ zero_zero_int @ A )
= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_zero__power) ).
thf(745,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)],[125]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ B )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_power__not__zero) ).
thf(573,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)],[75]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_less__imp__le__nat) ).
thf(689,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(306,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_nat_Odistinct_I1_J) ).
thf(1389,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(226,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_less__SucE) ).
thf(1124,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(267,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 )
=> ( ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) )
= ( ord_less_eq_real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_compare__pow__le__iff) ).
thf(1256,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 )
=> ( ( ord_less_eq_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) )
= ( ord_less_eq_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(162,axiom,
( ( ord_less_int @ zero_zero_int @ ya )
| ( ya = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062) ).
thf(875,plain,
( ( ord_less_int @ zero_zero_int @ ya )
| ( ya = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(76,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 )
=> ( ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) )
= ( ord_less_eq_int @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_compare__pow__le__iff) ).
thf(577,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 )
=> ( ( ord_less_eq_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) )
= ( ord_less_eq_int @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(94,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_infinite__descent0) ).
thf(641,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(23,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_bot__nat__0_Oextremum) ).
thf(382,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(271,axiom,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= zero_zero_real )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_of__int__eq__0__iff) ).
thf(1271,plain,
! [A: int] :
( ( ( ring_1_of_int_real @ A )
= zero_zero_real )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_293_Euclidean__Division_Odiv__eq__0__iff) ).
thf(713,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)],[114]) ).
thf(261,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/sandbox2/benchmark/theBenchmark.p',fact_36_of__int__0__less__iff) ).
thf(1239,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)],[261]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',fact_103_power__mono__iff) ).
thf(466,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)],[45]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',fact_10_of__int__power__eq__of__int__cancel__iff) ).
thf(335,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)],[7]) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',fact_75_zero__less__power) ).
thf(1090,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)],[220]) ).
thf(172,axiom,
! [A: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ A ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_power__0__Suc) ).
thf(919,plain,
! [A: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ A ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_261_divide__right__mono__neg) ).
thf(704,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)],[111]) ).
thf(26,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__irrefl__nat) ).
thf(391,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(229,axiom,
! [A: nat] :
( ( divide_divide_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_div__by__Suc__0) ).
thf(1139,plain,
! [A: nat] :
( ( divide_divide_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(31,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_le__trans) ).
thf(406,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',fact_100_of__int__le__iff) ).
thf(831,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)],[152]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_gr__implies__not__zero) ).
thf(784,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(35,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_le__refl) ).
thf(419,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(211,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_strict__inc__induct) ).
thf(1048,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(295,axiom,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ A @ ( suc @ B ) )
= ( power_power_int @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_power__inject__base) ).
thf(1349,plain,
! [A: int,B: nat,C: int] :
( ( ( power_power_int @ A @ ( suc @ B ) )
= ( power_power_int @ C @ ( suc @ B ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(21,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_bot__nat__0_Oextremum__strict) ).
thf(377,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fact_209_divide__cancel__right) ).
thf(567,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)],[73]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',fact_279_frac__less) ).
thf(1144,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)],[231]) ).
thf(240,axiom,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_exists__least__lemma) ).
thf(1175,plain,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_286_div__neg__neg__trivial) ).
thf(681,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)],[104]) ).
thf(308,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_le__Suc__eq) ).
thf(1408,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(302,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Suc__mono) ).
thf(1376,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(316,axiom,
! [A: real,B: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ B )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_power__not__zero) ).
thf(1439,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)],[316]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_less__Suc__eq) ).
thf(890,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',fact_1_of__int__less__of__int__power__cancel__iff) ).
thf(811,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)],[146]) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',fact_136_power__divide) ).
thf(1080,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)],[216]) ).
thf(291,axiom,
ord_less_eq_int @ na @ ( power_power_int @ ya @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85__C1_Oprems_C_I1_J) ).
thf(1339,plain,
ord_less_eq_int @ na @ ( power_power_int @ ya @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(3,axiom,
! [A: int,B: int] :
( ( ( ring_1_of_int_int @ A )
= ( ring_1_of_int_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_of__int__eq__iff) ).
thf(323,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)],[3]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_264_divide__nonneg__nonpos) ).
thf(483,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)],[50]) ).
thf(157,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_ex__least__nat__less) ).
thf(848,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(184,axiom,
ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ ya ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_y0) ).
thf(964,plain,
ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ ya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',fact_57_of__int__pos) ).
thf(769,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)],[132]) ).
thf(100,axiom,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_div__0) ).
thf(668,plain,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(304,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_old_Onat_Odistinct_I1_J) ).
thf(1381,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(177,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_lift__Suc__antimono__le) ).
thf(932,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_int @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_int @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(18,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) )
= ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_pos__imp__zdiv__pos__iff) ).
thf(367,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) )
= ( ord_less_eq_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,axiom,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_power__less__imp__less__base) ).
thf(552,plain,
! [A: int,B: nat,C: int] :
( ( ord_less_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ C @ B ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(245,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Suc__less__SucD) ).
thf(1198,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(182,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_Suc__leD) ).
thf(959,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Suc__less__eq) ).
thf(1015,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_not__less__less__Suc__eq) ).
thf(1000,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(224,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_dec__induct) ).
thf(1102,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_112_of__int__power__le__of__int__cancel__iff) ).
thf(505,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)],[57]) ).
thf(173,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( nthRoo1352626670d_root @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_fixed__root_Ointro) ).
thf(922,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( nthRoo1352626670d_root @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(95,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_zero__le) ).
thf(658,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(169,axiom,
ord_less_int @ ( power_power_int @ y @ p ) @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_yyn_H) ).
thf(912,plain,
ord_less_int @ ( power_power_int @ y @ p ) @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(105,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 )
=> ( ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) )
= ( ord_less_int @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_compare__pow__less__iff) ).
thf(685,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 )
=> ( ( ord_less_int @ ( power_power_int @ B @ A ) @ ( power_power_int @ C @ A ) )
= ( ord_less_int @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(209,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_less__trans__Suc) ).
thf(1044,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_172_of__int__nonneg) ).
thf(695,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)],[108]) ).
thf(263,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Suc__div__le__mono) ).
thf(1245,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(27,axiom,
! [A: real] :
( ( divide_divide_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_div__0) ).
thf(394,plain,
! [A: real] :
( ( divide_divide_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(189,axiom,
ya != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_y00) ).
thf(986,plain,
ya != zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(300,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq_nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_full__nat__induct) ).
thf(1364,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq_nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(265,axiom,
pm != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82__092_060open_062pm_A_061_A0_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
thf(1250,plain,
pm != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(310,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
thf(1413,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(117,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( power_power_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_zero__power) ).
thf(722,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)],[117]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_nat__le__linear) ).
thf(663,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_nat__zero__less__power__iff) ).
thf(374,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)],[20]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_167_zero__le__power) ).
thf(516,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)],[60]) ).
thf(292,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_power__Suc0__right) ).
thf(1340,plain,
! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(199,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_le__SucI) ).
thf(1018,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',fact_12_of__int__less__iff) ).
thf(355,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)],[14]) ).
thf(127,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_div__neg__pos__less0) ).
thf(754,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( divide_divide_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_div__less) ).
thf(490,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)],[52]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_div__positive) ).
thf(675,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(247,axiom,
ord_less_eq_int @ zero_zero_int @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27__C1_Oprems_C_I3_J) ).
thf(1203,plain,
ord_less_eq_int @ zero_zero_int @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(250,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_real @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_lift__Suc__mono__less__iff) ).
thf(1208,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_real @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_211_divide__cancel__left) ).
thf(589,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)],[80]) ).
thf(63,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Nat_Oex__has__greatest__nat) ).
thf(525,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',fact_9_of__int__power__eq__of__int__cancel__iff) ).
thf(1003,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)],[194]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',fact_109_of__int__le__of__int__power__cancel__iff) ).
thf(1025,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)],[202]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Suc__lessI) ).
thf(887,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(255,axiom,
( ny
= ( divide_divide_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ pm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_NY__def) ).
thf(1225,plain,
( ny
= ( divide_divide_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ pm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(112,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_not__less__zero) ).
thf(707,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(32,axiom,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_bits__div__0) ).
thf(409,plain,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(258,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Ex__less__Suc2) ).
thf(1230,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(139,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_power__strict__mono) ).
thf(791,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( power_power_nat @ A @ C ) @ ( power_power_nat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(242,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_n__not__Suc__n) ).
thf(1188,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(56,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_zdiv__mono2) ).
thf(502,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(44,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_not__less0) ).
thf(463,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',fact_284_divide__nonpos__neg) ).
thf(1317,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)],[286]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',fact_6_of__int__power) ).
thf(338,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)],[8]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',fact_312_unique__euclidean__semiring__numeral__class_Odiv__less) ).
thf(470,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)],[46]) ).
thf(145,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_div__nonpos__pos__le0) ).
thf(808,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(253,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_All__less__Suc2) ).
thf(1220,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(65,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_gr__zeroI) ).
thf(544,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(282,axiom,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ ( suc @ B ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_realpow__pos__nth2) ).
thf(1300,plain,
! [A: real,B: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ( power_power_real @ C @ ( suc @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(320,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_old_Onat_Oexhaust) ).
thf(1452,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(201,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_lessI) ).
thf(1023,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',fact_283_divide__nonneg__pos) ).
thf(1284,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)],[277]) ).
thf(83,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_gr0I) ).
thf(600,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(312,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Suc__n__not__le__n) ).
thf(1427,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_72_power__eq__0__iff) ).
thf(446,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)],[42]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',fact_77_zero__less__power) ).
thf(612,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)],[85]) ).
thf(218,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_lift__Suc__antimono__le) ).
thf(1084,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_real @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_real @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(176,axiom,
ord_less_int @ na @ ( power_power_int @ ya @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_yyn) ).
thf(931,plain,
ord_less_int @ na @ ( power_power_int @ ya @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(101,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_pos__imp__zdiv__nonneg__iff) ).
thf(671,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Nat_OlessE) ).
thf(976,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(77,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le__eq__less__or__eq) ).
thf(581,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(196,axiom,
( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_of__int__0) ).
thf(1010,plain,
( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(156,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Zero__not__Suc) ).
thf(844,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_267_divide__right__mono) ).
thf(771,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)],[133]) ).
thf(273,axiom,
! [A: real] :
? [B: int] : ( ord_less_real @ A @ ( ring_1_of_int_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ex__less__of__int) ).
thf(1276,plain,
! [A: real] :
? [B: int] : ( ord_less_real @ A @ ( ring_1_of_int_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(266,axiom,
! [A: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ A )
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_power__Suc__0) ).
thf(1253,plain,
! [A: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ A )
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_less__or__eq__imp__le) ).
thf(748,plain,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(91,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_bot__nat__0_Oextremum__uniqueI) ).
thf(632,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(120,axiom,
! [A: real] :
( ( divide_divide_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_div__by__0) ).
thf(731,plain,
! [A: real] :
( ( divide_divide_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(136,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_div__positive) ).
thf(781,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(192,axiom,
~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_not_I1_J) ).
thf(995,plain,
~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(183,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_int @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_lift__Suc__mono__less) ).
thf(961,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_int @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(305,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 )
=> ( ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) )
= ( ord_less_real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_compare__pow__less__iff) ).
thf(1385,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 )
=> ( ( ord_less_real @ ( power_power_real @ B @ A ) @ ( power_power_real @ C @ A ) )
= ( ord_less_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(40,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_infinite__descent) ).
thf(433,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',fact_171_of__int__nonneg) ).
thf(929,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)],[175]) ).
thf(215,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ A )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_nat__one__le__power) ).
thf(1077,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ A )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(251,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Suc__inject) ).
thf(1212,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(130,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( divide_divide_nat @ C @ B ) @ ( divide_divide_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_div__le__mono2) ).
thf(763,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( divide_divide_nat @ C @ B ) @ ( divide_divide_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(284,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_diff__induct) ).
thf(1309,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(99,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_less__eq__int__code_I1_J) ).
thf(667,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(280,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Ex__less__Suc) ).
thf(1294,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_le__antisym) ).
thf(716,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(235,axiom,
! [A: nat] :
( ( power_power_real @ zero_zero_real @ ( suc @ A ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_power__0__Suc) ).
thf(1161,plain,
! [A: nat] :
( ( power_power_real @ zero_zero_real @ ( suc @ A ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',fact_110_of__int__le__of__int__power__cancel__iff) ).
thf(800,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)],[142]) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',fact_271_divide__pos__neg) ).
thf(1280,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)],[275]) ).
thf(257,axiom,
ord_less_eq_int @ zero_zero_int @ ya,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__C1_Oprems_C_I2_J) ).
thf(1229,plain,
ord_less_eq_int @ zero_zero_int @ ya,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_273_divide__less__0__iff) ).
thf(867,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)],[159]) ).
thf(84,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_nat__less__induct) ).
thf(603,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',fact_166_zero__le__power) ).
thf(564,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)],[72]) ).
thf(315,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Onat_Oinject) ).
thf(1436,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',fact_101_of__int__le__iff) ).
thf(326,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)],[4]) ).
thf(285,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/sandbox2/benchmark/theBenchmark.p',fact_285_divide__nonpos__pos) ).
thf(1314,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)],[285]) ).
thf(9,axiom,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_of__int__eq__0__iff) ).
thf(341,plain,
! [A: int] :
( ( ( ring_1_of_int_int @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: int] :
( ( divide_divide_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_bits__div__by__0) ).
thf(358,plain,
! [A: int] :
( ( divide_divide_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(151,axiom,
! [A: real,B: real,C: nat] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_power__strict__mono) ).
thf(828,plain,
! [A: real,B: real,C: nat] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_real @ ( power_power_real @ A @ C ) @ ( power_power_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(92,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ C )
=> ( ord_less_eq_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_zdiv__mono1) ).
thf(635,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ zero_zero_int @ C )
=> ( ord_less_eq_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',fact_270_divide__neg__pos) ).
thf(1346,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)],[294]) ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_less__not__refl2) ).
thf(415,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(239,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_lift__Suc__mono__le) ).
thf(1172,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(47,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_le0) ).
thf(474,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Suc__le__mono) ).
thf(1033,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_linorder__neqE__linordered__idom) ).
thf(400,plain,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',fact_7_of__int__eq__of__int__power__cancel__iff) ).
thf(1093,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)],[221]) ).
thf(119,axiom,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_bits__div__by__0) ).
thf(728,plain,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(260,axiom,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( ord_less_real @ A @ B )
=> ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_linorder__neqE__linordered__idom) ).
thf(1236,plain,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( ord_less_real @ A @ B )
=> ( ord_less_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',fact_105_of__int__le__0__iff) ).
thf(1352,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)],[296]) ).
thf(6,axiom,
! [A: int] :
( ( divide_divide_int @ A @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_div__by__0) ).
thf(332,plain,
! [A: int] :
( ( divide_divide_int @ A @ zero_zero_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__int__code_I1_J) ).
thf(427,plain,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(303,axiom,
! [A: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ A ) )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_of__int__0__eq__iff) ).
thf(1378,plain,
! [A: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ A ) )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(298,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Suc__leI) ).
thf(1357,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(191,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_not0__implies__Suc) ).
thf(992,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(187,axiom,
! [A: real] :
( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_power__Suc0__right) ).
thf(982,plain,
! [A: real] :
( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ B )
=> ( ( divide_divide_nat @ A @ B )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_unique__euclidean__semiring__numeral__class_Odiv__less) ).
thf(691,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ B )
=> ( ( divide_divide_nat @ A @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',fact_104_power__mono__iff) ).
thf(442,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)],[41]) ).
thf(1,conjecture,
ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(322,plain,
~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ ( divide_divide_int @ B @ A ) @ zero_zero_int )
= ( ord_less_int @ zero_zero_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_neg__imp__zdiv__neg__iff) ).
thf(486,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ ( divide_divide_int @ B @ A ) @ zero_zero_int )
= ( ord_less_int @ zero_zero_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',fact_160_power__eq__imp__eq__base) ).
thf(803,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)],[143]) ).
thf(287,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Suc__le__lessD) ).
thf(1320,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(178,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_le__SucE) ).
thf(935,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(311,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_old_Onat_Oinducts) ).
thf(1416,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(248,axiom,
( nthRoo1352626670d_root
= ( ^ [A: nat,B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_fixed__root__def) ).
thf(1204,plain,
( nthRoo1352626670d_root
= ( ^ [A: nat,B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(81,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_less__mono__imp__le__mono) ).
thf(592,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',fact_265_divide__nonneg__nonneg) ).
thf(496,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)],[54]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',fact_76_zero__less__power) ).
thf(364,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)],[17]) ).
thf(1472,plain,
$false,
inference(e,[status(thm)],[1322,1036,1411,629,760,479,347,1031,893,1083,777,352,1200,1290,1068,1443,741,878,597,873,449,1142,1269,384,550,1233,814,1260,913,1164,797,1127,841,1359,389,1287,570,1430,719,344,817,638,1087,1147,1247,881,421,870,1450,1373,1020,806,1283,1136,834,766,734,774,660,1433,1242,1169,397,1447,956,1074,1206,380,512,678,1306,1153,1047,1274,1223,1343,1042,1355,1217,820,561,424,429,788,862,349,916,361,625,329,665,493,757,1195,710,1012,583,522,697,615,1328,1121,1227,725,403,1096,1006,499,989,519,742,884,1028,554,476,1039,547,1324,1263,701,1150,1297,738,1456,1192,371,1393,622,837,1099,985,938,508,541,1167,926,558,1071,953,1185,794,586,1278,412,965,618,824,745,573,689,1389,1124,1256,875,577,641,382,1271,713,1239,466,335,1090,919,704,391,1139,406,831,784,419,1048,1349,377,567,1144,1175,681,1408,1376,1439,890,811,1080,1339,323,483,848,964,769,668,1381,932,367,552,1198,959,1015,1000,1102,505,922,658,912,685,1044,695,1245,394,986,1364,1250,1413,722,663,374,516,1340,1018,355,754,490,675,1203,1208,589,525,1003,1025,887,1225,707,409,1230,791,1188,502,463,1317,338,470,808,1220,544,1300,1452,1023,1284,600,1427,446,612,1084,931,671,976,581,1010,844,771,1276,1253,748,632,731,781,995,961,1385,433,929,1077,1212,763,1309,667,1294,716,1161,800,1280,1229,867,603,564,1436,326,1314,341,358,828,635,1346,415,1172,474,1033,400,1093,728,1236,1352,332,427,1378,1357,992,982,691,442,322,486,803,1320,935,1416,1204,592,496,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP130^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % 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
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:58:01 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.14/1.19 % [INFO] Parsing done (411ms).
% 2.46/1.21 % [INFO] Running in sequential loop mode.
% 3.35/1.59 % [INFO] eprover registered as external prover.
% 3.67/1.60 % [INFO] Scanning for conjecture ...
% 3.87/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 319 axioms. Running axiom selection ...
% 4.09/1.89 % [INFO] Axiom selection finished. Selected 319 axioms (removed 0 axioms).
% 5.30/2.16 % [INFO] Problem is higher-order (TPTP THF).
% 5.30/2.18 % [INFO] Type checking passed.
% 5.30/2.19 % [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 ...
% 15.56/4.50 % External prover 'e' found a proof!
% 15.56/4.50 % [INFO] Killing All external provers ...
% 15.56/4.50 % Time passed: 4160ms (effective reasoning time: 3289ms)
% 15.56/4.50 % 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)>
% 15.56/4.51 % Axioms used in derivation (319): fact_318_div__nonpos__pos__le0, fact_173_power__less__imp__less__base, fact_92_less__nat__zero__code, fact_214_bot__nat__0_Oextremum, fact_315_pos__imp__zdiv__nonneg__iff, fact_313_unique__euclidean__semiring__numeral__class_Odiv__less, fact_303_linorder__neqE__linordered__idom, fact_227_transitive__stepwise__le, fact_248_ex__least__nat__le, fact_236_Suc__leD, fact_3_of__int__power__less__of__int__cancel__iff, fact_165_zero__le__power, fact_195_power__not__zero, fact_295_div__greater__zero__iff, fact_9_of__int__power__eq__of__int__cancel__iff, fact_241_less__imp__le__nat, fact_64_lift__Suc__mono__less, fact_220_le__antisym, fact_193_zero__less__iff__neq__zero, fact_159_power__eq__imp__eq__base, fact_149_Zero__neq__Suc, fact_180_power__inject__base, fact_98_zero__less__Suc, fact_48_less__Suc__eq, fact_204_compare__pow__le__iff, fact_57_of__int__pos, fact_316_neg__imp__zdiv__nonneg__iff, fact_253_Suc__le__lessD, fact_244_fixed__root_Ointro, fact_91_neq0__conv, fact_97_power__Suc0__right, fact_229_full__nat__induct, fact_52_Suc__lessI, fact_215_le0, fact_259_linordered__field__no__lb, fact_74_realpow__pos__nth2, fact_154_less__Suc__eq__0__disj, fact_42_less__trans__Suc, fact_255_less__Suc__eq__le, fact_119_less__not__refl2, fact_66_power__0__Suc, fact_135_zero__le, fact_7_of__int__eq__of__int__power__cancel__iff, fact_211_divide__cancel__left, fact_124_infinite__descent, fact_179_power__inject__base, fact_2_of__int__less__of__int__power__cancel__iff, fact_41_less__Suc__induct, fact_79_ex__of__int__less, fact_225_le__0__eq, fact_175_power__less__imp__less__base, fact_198_zero__power, fact_37_of__int__0__less__iff, fact_114_not__gr0, fact_250_Suc__le__eq, fact_22_Suc__mono, fact_274_divide__less__cancel, fact_262_divide__nonpos__nonpos, fact_137_ex__le__of__int, fact_287_div__pos__pos__trivial, fact_294_Suc__div__le__mono, fact_127_bot__nat__0_Oextremum__strict, fact_263_divide__nonpos__nonneg, fact_171_of__int__nonneg, fact_189_zero__reorient, fact_45_Suc__less__eq2, fact_299_div__by__0, fact_282_divide__nonneg__neg, fact_26__C1_Oprems_C_I2_J, fact_163_power__eq__iff__eq__base, fact_292_div__le__dividend, fact_317_pos__imp__zdiv__pos__iff, fact_152_old_Onat_Oinducts, fact_267_divide__right__mono, fact_222_Nat_Oex__has__greatest__nat, fact_21_Suc__less__eq, fact_68_power__0__Suc, fact_103_power__mono__iff, fact_108_of__int__0__le__iff, fact_265_divide__nonneg__nonneg, fact_166_zero__le__power, fact_279_frac__less, fact_55_Nat_OlessE, fact_105_of__int__le__0__iff, fact_36_of__int__0__less__iff, fact_60_lift__Suc__mono__less__iff, fact_100_of__int__le__iff, fact_203_compare__pow__less__iff, fact_270_divide__neg__pos, fact_240_le__eq__less__or__eq, fact_208_bits__div__by__0, fact_258_linordered__field__no__ub, fact_216_Suc__le__mono, fact_14_y0, fact_169_power__mono, fact_285_divide__nonpos__pos, fact_237_less__mono__imp__le__mono, fact_102_power__mono__iff, fact_284_divide__nonpos__neg, fact_199_zero__power, fact_209_divide__cancel__right, fact_99_less__Suc0, fact_63_lift__Suc__mono__less, fact_90_power__Suc__0, fact_93_bot__nat__0_Onot__eq__extremum, fact_88_le__zero__eq, fact_5_of__int__power, fact_62_lift__Suc__mono__less__iff, fact_123_nat__less__induct, fact_125_infinite__descent0, fact_261_divide__right__mono__neg, fact_87_fixed__root__axioms, fact_67_power__0__Suc, fact_251_dec__induct, fact_278_frac__le, fact_268_divide__le__0__iff, fact_6_of__int__power, fact_213_bits__div__0, fact_291_div__le__mono, fact_297_div__by__0, fact_254_le__less__Suc__eq, fact_43_Suc__less__SucD, fact_289_div__by__Suc__0, fact_309_div__neg__pos__less0, fact_186_realpow__pos__nth__unique, fact_191_not__less__zero, fact_112_of__int__power__le__of__int__cancel__iff, fact_185_realpow__pos__nth, fact_178_power__strict__mono, fact_27__C1_Oprems_C_I3_J, fact_206_division__ring__divide__zero, fact_164_power__eq__iff__eq__base, fact_15_of__int__eq__iff, fact_223_bot__nat__0_Oextremum__uniqueI, fact_219_eq__imp__le, fact_314_nonneg1__imp__zdiv__pos__iff, fact_109_of__int__le__of__int__power__cancel__iff, fact_290_div__less, fact_260_ex__least__nat__less, fact_78_NY__def, fact_210_divide__eq__0__iff, fact_162_power__eq__iff__eq__base, fact_58_n__not__Suc__n, fact_132_lift__Suc__mono__le, fact_85__C1_Oprems_C_I1_J, fact_266_zero__le__divide__iff, fact_156_All__less__Suc2, fact_288_x, fact_157_gr0__conv__Suc, fact_138_exists__least__lemma, fact_107_of__int__0__le__iff, fact_23_lessI, fact_181_power__inject__base, fact_133_lift__Suc__mono__le, fact_32_of__int__eq__0__iff, fact_72_power__eq__0__iff, fact_120_less__not__refl3, fact_39_not__less__less__Suc__eq, fact_256_less__eq__Suc__le, fact_75_zero__less__power, fact_101_of__int__le__iff, fact_56_of__int__pos, fact_61_lift__Suc__mono__less__iff, fact_242_nat__less__le, fact_235_le__SucE, fact_110_of__int__le__of__int__power__cancel__iff, fact_82__092_060open_062pm_A_061_A0_A_092_060Longrightarrow_062_AFalse_092_060close_062, fact_144_nat_OdiscI, fact_161_power__eq__imp__eq__base, fact_51_less__SucE, fact_301_div__0, fact_148_Suc__neq__Zero, fact_49_Ex__less__Suc, fact_196_power__not__zero, fact_147_zero__induct, fact_69_NY0, fact_257_le__imp__less__Suc, fact_224_bot__nat__0_Oextremum__unique, fact_33_of__int__eq__0__iff, fact_35_of__int__less__0__iff, fact_94_nat__zero__less__power__iff, fact_281_divide__le__cancel, fact_73_not__gr__zero, fact_134_lift__Suc__mono__le, fact_160_power__eq__imp__eq__base, fact_205_compare__pow__le__iff, fact_272_divide__pos__pos, fact_174_power__less__imp__less__base, fact_113_gr0I, fact_136_power__divide, fact_128_nat__power__less__imp__less, fact_140_less__eq__int__code_I1_J, fact_141_nat_Odistinct_I1_J, fact_177_power__strict__mono, fact_95_power__Suc0__right, fact_307_pos__imp__zdiv__neg__iff, fact_269_divide__neg__neg, fact_194_power__not__zero, fact_245_fixed__root__def, fact_280_frac__less2, fact_122_less__irrefl__nat, fact_1_of__int__less__of__int__power__cancel__iff, fact_77_zero__less__power, fact_118_less__not__refl, fact_302_div__0, fact_130_lift__Suc__antimono__le, fact_271_divide__pos__neg, fact_139_power__gt__expt, fact_8_of__int__eq__of__int__power__cancel__iff, fact_293_Euclidean__Division_Odiv__eq__0__iff, fact_38_less__int__code_I1_J, fact_50_less__SucI, fact_231_Suc__n__not__le__n, fact_12_of__int__less__iff, fact_17_nat_Oinject, fact_168_power__mono, fact_28_of__int__0, fact_192_gr__implies__not__zero, fact_202_compare__pow__less__iff, fact_25_not_I2_J, fact_65_lift__Suc__mono__less, fact_89_nat__power__eq__Suc__0__iff, fact_217_le__refl, fact_218_le__trans, fact_296_div__le__mono2, fact_207_bits__div__by__0, fact_311_div__positive, fact_187_zero__reorient, fact_310_div__positive, fact_221_nat__le__linear, fact_34_of__int__less__0__iff, fact_46_All__less__Suc, fact_83_p0, fact_249_Suc__leI, fact_167_zero__le__power, fact_19_y00, fact_312_unique__euclidean__semiring__numeral__class_Odiv__less, fact_247_nat__one__le__power, fact_143_old_Onat_Odistinct_I1_J, fact_121_gr__implies__not0, fact_76_zero__less__power, fact_273_divide__less__0__iff, fact_106_of__int__le__0__iff, fact_233_Suc__le__D, fact_53_Suc__lessE, fact_239_less__or__eq__imp__le, fact_170_power__mono, fact_40_strict__inc__induct, fact_13_n0, fact_29_of__int__0, fact_230_not__less__eq__eq, fact_276_divide__strict__right__mono, fact_4_of__int__power__less__of__int__cancel__iff, fact_11_of__int__less__iff, fact_155_gr0__implies__Suc, fact_117_nat__neq__iff, fact_150_Zero__not__Suc, fact_10_of__int__power__eq__of__int__cancel__iff, fact_308_neg__imp__zdiv__neg__iff, fact_264_divide__nonneg__nonpos, fact_176_power__strict__mono, fact_31_of__int__0__eq__iff, fact_96_power__Suc0__right, fact_238_le__neq__implies__less, fact_81_yyn, fact_234_le__SucI, fact_47_not__less__eq, fact_30_of__int__0__eq__iff, fact_182_power__le__imp__le__base, fact_306_zdiv__mono2, fact_252_inc__induct, fact_84_pm0, fact_246_fixed__root_Op, fact_184_power__le__imp__le__base, fact_200_yyn_H, fact_304_linorder__neqE__linordered__idom, fact_129_lift__Suc__antimono__le, fact_131_lift__Suc__antimono__le, fact_18_old_Onat_Oinject, fact_59_Suc__inject, fact_80_ex__less__of__int, fact_0_n00, fact_277_divide__strict__right__mono__neg, fact_158_Ex__less__Suc2, fact_183_power__le__imp__le__base, fact_300_div__0, fact_243_fixed__root_Op0, fact_188_zero__reorient, fact_44_less__antisym, fact_151_old_Onat_Oexhaust, fact_115_not__less0, fact_283_divide__nonneg__pos, fact_228_nat__induct__at__least, fact_16_of__int__eq__iff, fact_201_y_H0, fact_24_not_I1_J, fact_146_diff__induct, fact_153_not0__implies__Suc, fact_86_p, fact_305_zdiv__mono1, fact_111_of__int__power__le__of__int__cancel__iff, fact_226_less__eq__nat_Osimps_I1_J, fact_197_zero__power, fact_54_Suc__lessD, fact_145_nat__induct, fact_70_power__eq__0__iff, fact_116_less__zeroE, fact_71_power__eq__0__iff, fact_298_div__by__0, fact_104_power__mono__iff, fact_126_linorder__neqE__nat, fact_275_zero__less__divide__iff, fact_172_of__int__nonneg, fact_142_old_Onat_Odistinct_I2_J, fact_286_div__neg__neg__trivial, fact_190_gr__zeroI, fact_212_bits__div__0, fact_232_le__Suc__eq, fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062
% 15.56/4.51 % No. of inferences in proof: 642
% 15.56/4.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4160 ms resp. 3289 ms w/o parsing
% 16.51/4.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.51/4.77 % [INFO] Killing All external provers ...
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