%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM926_2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 : Sun Sep 27 08:10:27 AM UTC 2026
% Result : Theorem 232.11s 65.07s
% Output : Refutation 220.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 701
% Syntax : Number of formulae : 1723 ( 844 unt; 0 typ; 2 def)
% Number of atoms : 3873 (1697 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 16356 ( 584 ~; 324 |; 381 &;13720 @)
% ( 161 <=>;1186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 16 con; 0-3 aty)
% Number of variables : 3099 ( 0 ^;3070 !; 27 ?;3099 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(minus_minus_int_decl,type,
minus_minus_int: int > int > int ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(minus_minus_real_decl,type,
minus_minus_real: real > real > real ).
thf(one_one_int_decl,type,
one_one_int: int ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_real_decl,type,
one_one_real: real ).
thf(plus_plus_int_decl,type,
plus_plus_int: int > int > int ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_real_decl,type,
plus_plus_real: real > real > real ).
thf(times_times_int_decl,type,
times_times_int: int > int > int ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(times_times_real_decl,type,
times_times_real: real > real > real ).
thf(zero_zero_int_decl,type,
zero_zero_int: int ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(zcong_decl,type,
zcong: int > int > int > $o ).
thf(zprime_decl,type,
zprime: int > $o ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(min_decl,type,
min: int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_int_decl,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_decl,type,
number_number_of_nat: int > nat ).
thf(number267125858f_real_decl,type,
number267125858f_real: int > real ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_real_decl,type,
ord_less_real: real > real > $o ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(power_power_int_decl,type,
power_power_int: int > nat > int ).
thf(power_power_nat_decl,type,
power_power_nat: nat > nat > nat ).
thf(power_power_real_decl,type,
power_power_real: real > nat > real ).
thf(product_Pair_int_int_decl,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(legendre_decl,type,
legendre: int > int > int ).
thf(quadRes_decl,type,
quadRes: int > int > $o ).
thf(dvd_dvd_int_decl,type,
dvd_dvd_int: int > int > $o ).
thf(dvd_dvd_nat_decl,type,
dvd_dvd_nat: nat > nat > $o ).
thf(dvd_dvd_real_decl,type,
dvd_dvd_real: real > real > $o ).
thf(twoSqu512355103sum2sq_decl,type,
twoSqu512355103sum2sq: int > $o ).
thf(twoSqu2107342101sum2sq_decl,type,
twoSqu2107342101sum2sq: product_prod_int_int > int ).
thf(m_decl,type,
m: int ).
thf(s1_decl,type,
s1: int ).
thf(s_decl,type,
s: int ).
thf(t_decl,type,
t: int ).
thf(sk3_decl,type,
sk3: int ).
thf(sk11_decl,type,
sk11: int ).
thf(sk3_def,definition,
( sk3
= ( @+[A: int] :
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: int] :
( ! [B: int] :
( ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( B @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( B @ ord_less_int ) )
& ( B @ ( zero_zero_int @ ord_less_eq_int ) ) )
=> ( B = A ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ) ) ) ).
thf(247,axiom,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_real ) @ power_power_real ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) @ times_times_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(1665,plain,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_real ) @ power_power_real ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) @ times_times_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ dvd_dvd_nat ) )
& ( B @ ( A @ dvd_dvd_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_divides__antisym) ).
thf(809,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( B @ dvd_dvd_nat ) )
& ( B @ ( A @ dvd_dvd_nat ) ) ) )
& ( ( ( A @ ( B @ dvd_dvd_nat ) )
& ( B @ ( A @ dvd_dvd_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(186,axiom,
! [A: real,B: real] :
( ( zero_zero_real @ ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ord_less_eq_real ) )
<=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_sum__squares__le__zero__iff) ).
thf(1411,plain,
! [A: real,B: real] :
( ( ( ( B = zero_zero_real )
& ( A = zero_zero_real ) )
=> ( zero_zero_real @ ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ord_less_eq_real ) ) )
& ( ( zero_zero_real @ ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ord_less_eq_real ) )
=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(597,axiom,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( ( A @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ) )
& ( ( A = zero_zero_nat )
=> ( ( A @ ( zero_zero_int @ power_power_int ) )
= one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_power__0__left) ).
thf(3008,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( ( A @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ) )
& ( ( A = zero_zero_nat )
=> ( ( A @ ( zero_zero_int @ power_power_int ) )
= one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(410,axiom,
! [A: int] :
( ( min @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( min @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_rel__simps_I28_J) ).
thf(2263,plain,
! [A: int] :
( ( ( min @ ( A @ ord_less_eq_int ) )
=> ( min @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( min @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( min @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(147,axiom,
! [A: real,B: real,C: real] :
( ( B @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) )
= ( B @ ( C @ ( A @ plus_plus_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1237,plain,
! [A: real,B: real,C: real] :
( ( B @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) )
= ( B @ ( C @ ( A @ plus_plus_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( B @ times_times_nat ) @ ( one_one_nat @ ord_less_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_power__gt1__lemma) ).
thf(893,plain,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( B @ times_times_nat ) @ ( one_one_nat @ ord_less_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(335,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) @ ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( A @ ( E @ ord_less_int ) )
=> ( D @ ( B @ ord_less_eq_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_unique__quotient__lemma) ).
thf(1982,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) @ ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( A @ ( E @ ord_less_int ) )
=> ( D @ ( B @ ord_less_eq_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(329,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_rel__simps_I39_J) ).
thf(1956,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(305,axiom,
! [A: int] :
( ( one_one_int @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ zprime )
=> ( ( one_one_int @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ legendre ) )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_Legendre__1mod4) ).
thf(1879,plain,
! [A: int] :
( ( one_one_int @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ zprime )
=> ( ( one_one_int @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ legendre ) )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(261,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ ( one_one_int @ plus_plus_int ) @ times_times_int ) )
= ( A @ bit0 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_double__number__of__Bit0) ).
thf(1718,plain,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ ( one_one_int @ plus_plus_int ) @ times_times_int ) )
= ( A @ bit0 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(177,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( A != B )
& ( C = D ) )
=> ( ( A @ ( E @ times_times_real ) @ ( C @ plus_plus_real ) )
!= ( B @ ( E @ times_times_real ) @ ( D @ plus_plus_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_add__scale__eq__noteq) ).
thf(1369,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( E != zero_zero_real )
=> ( ( ( A != B )
& ( C = D ) )
=> ( ( A @ ( E @ times_times_real ) @ ( C @ plus_plus_real ) )
!= ( B @ ( E @ times_times_real ) @ ( D @ plus_plus_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(565,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_int ) @ power_power_int ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_power2__sum) ).
thf(2889,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_int ) @ power_power_int ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(139,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( D @ ( B @ times_times_nat ) @ ( C @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1190,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( D @ ( B @ times_times_nat ) @ ( C @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(422,axiom,
! [A: int,B: int,C: int] :
( ( ( B @ ( A @ minus_minus_int ) )
= C )
=> ( A
= ( B @ ( C @ plus_plus_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_Int2_Oaux1) ).
thf(2306,plain,
! [A: int,B: int,C: int] :
( ( ( B @ ( A @ minus_minus_int ) )
= C )
=> ( A
= ( B @ ( C @ plus_plus_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(17,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ times_times_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(760,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ times_times_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(224,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( B @ ( C @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1559,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( B @ ( C @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(114,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_power__one) ).
thf(1105,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(572,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_power__strict__increasing__iff) ).
thf(2921,plain,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( ( B @ ( A @ ord_less_nat ) )
=> ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_int ) ) )
& ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_int ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(93,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ power_power_nat ) )
= ( B @ ( C @ power_power_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( C @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_power__eq__imp__eq__base) ).
thf(1031,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ power_power_nat ) )
= ( B @ ( C @ power_power_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( C @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(273,axiom,
! [A: int] :
( ( min
= ( A @ bit1 ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_rel__simps_I43_J) ).
thf(1763,plain,
! [A: int] :
( ( ( min = A )
=> ( min
= ( A @ bit1 ) ) )
& ( ( min
= ( A @ bit1 ) )
=> ( min = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1764,plain,
( ! [A: int] :
( ( min = A )
=> ( min
= ( A @ bit1 ) ) )
& ! [A: int] :
( ( min
= ( A @ bit1 ) )
=> ( min = A ) ) ),
inference(miniscope,[status(thm)],[1763]) ).
thf(1765,plain,
! [B: int,A: int] :
( ( ( min
= ( B @ bit1 ) )
| ( min != B ) )
& ( ( min = A )
| ( min
!= ( A @ bit1 ) ) ) ),
inference(cnf,[status(esa)],[1764]) ).
thf(1767,plain,
! [A: int] :
( ( min
= ( A @ bit1 ) )
| ( min != A ) ),
inference(cnfConj,[status(thm)],[1765]) ).
thf(1769,plain,
! [A: int] :
( ( ( A @ bit1 )
= min )
| ( min != A ) ),
inference(lifteq,[status(thm)],[1767]) ).
thf(1770,plain,
( ( min @ bit1 )
= min ),
inference(simp,[status(thm)],[1769]) ).
thf(291,axiom,
pls @ bit1 @ bit1 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(1815,plain,
pls @ bit1 @ bit1 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(608,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_Pls__def) ).
thf(3056,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(3057,plain,
pls = zero_zero_int,
inference(lifteq,[status(thm)],[3056]) ).
thf(3812,plain,
zero_zero_int @ bit1 @ bit1 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ),
inference(rewrite,[status(thm)],[1815,3057]) ).
thf(693,axiom,
~ ( min @ ( pls @ ord_less_eq_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_rel__simps_I20_J) ).
thf(3383,plain,
~ ( min @ ( pls @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(3384,plain,
~ ( min @ ( pls @ ord_less_eq_int ) ),
inference(polarity_switch,[status(thm)],[3383]) ).
thf(3451,plain,
~ ( min @ ( zero_zero_int @ ord_less_eq_int ) ),
inference(rewrite,[status(thm)],[3384,3057]) ).
thf(3814,plain,
( ( ( zero_zero_int @ bit1 @ bit1 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3812,3451]) ).
thf(3815,plain,
( ( zero_zero_int @ bit1 @ bit1 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[3814]) ).
thf(3821,plain,
( ( ( zero_zero_int @ bit1 @ bit1 @ number_number_of_int )
!= min )
| ( zero_zero_int != zero_zero_int ) ),
inference(simp,[status(thm)],[3815]) ).
thf(3824,plain,
( ( zero_zero_int @ bit1 @ bit1 @ number_number_of_int )
!= min ),
inference(simp,[status(thm)],[3821]) ).
thf(3826,plain,
( ( ( zero_zero_int @ bit1 @ bit1 )
!= ( min @ bit1 ) )
| ( ( min @ number_number_of_int )
!= min ) ),
inference(paramod_ordered,[status(thm)],[1770,3824]) ).
thf(3830,plain,
( ( ( zero_zero_int @ bit1 )
!= min )
| ( ( min @ number_number_of_int )
!= min ) ),
inference(simp,[status(thm)],[3826]) ).
thf(490,axiom,
! [A: int,B: int] :
( ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_sum__squares__le__zero__iff) ).
thf(2595,plain,
! [A: int,B: int] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) ) )
& ( ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(475,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ power_power_int ) )
= ( C @ ( B @ ( A @ power_power_int ) @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_power__mult) ).
thf(2544,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ power_power_int ) )
= ( C @ ( B @ ( A @ power_power_int ) @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(70,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( B @ ( C @ ( A @ times_times_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(941,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( B @ ( C @ ( A @ times_times_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(414,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_zero__power2) ).
thf(2280,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(116,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( C @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ~ ( B @ ( A @ ( C @ zcong ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_zcong__not) ).
thf(1110,plain,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( C @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ~ ( B @ ( A @ ( C @ zcong ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(761,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ times_times_nat ) )
= zero_zero_nat ),
inference(cnf,[status(esa)],[760]) ).
thf(762,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ times_times_nat ) )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[761]) ).
thf(611,axiom,
! [A: int] :
( ( min @ ( A @ bit0 @ ord_less_int ) )
<=> ( min @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_rel__simps_I11_J) ).
thf(3072,plain,
! [A: int] :
( ( ( min @ ( A @ ord_less_eq_int ) )
=> ( min @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( min @ ( A @ bit0 @ ord_less_int ) )
=> ( min @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(306,axiom,
( ( pls @ number_number_of_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_semiring__numeral__0__eq__0) ).
thf(1882,plain,
( ( pls @ number_number_of_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(441,axiom,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ( B @ ( A @ times_times_int ) @ ( C @ dvd_dvd_int ) )
=> ( ( B @ ( C @ dvd_dvd_int ) )
| ( A @ ( C @ dvd_dvd_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_zprime__zdvd__zmult__better) ).
thf(2395,plain,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ( B @ ( A @ times_times_int ) @ ( C @ dvd_dvd_int ) )
=> ( ( B @ ( C @ dvd_dvd_int ) )
| ( A @ ( C @ dvd_dvd_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(195,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ plus_plus_nat ) @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) )
= ( D @ ( B @ plus_plus_nat ) @ ( C @ ( A @ plus_plus_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1443,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ plus_plus_nat ) @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) )
= ( D @ ( B @ plus_plus_nat ) @ ( C @ ( A @ plus_plus_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_eq_int ) )
=> ( ( A != B )
=> ( B @ ( A @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_order__le__neq__implies__less) ).
thf(739,plain,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_eq_int ) )
=> ( ( A != B )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(740,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_int ) )
| ( A = B )
| ~ ( B @ ( A @ ord_less_eq_int ) ) ),
inference(cnf,[status(esa)],[739]) ).
thf(741,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_int ) )
| ~ ( B @ ( A @ ord_less_eq_int ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[740]) ).
thf(143,axiom,
! [A: real,B: real] :
( ( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) )
= zero_zero_real )
<=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_sum__squares__eq__zero__iff) ).
thf(1205,plain,
! [A: real,B: real] :
( ( ( ( B = zero_zero_real )
& ( A = zero_zero_real ) )
=> ( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) )
= zero_zero_real )
=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(46,axiom,
~ ( min @ ( min @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_rel__simps_I7_J) ).
thf(878,plain,
~ ( min @ ( min @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(436,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ number_number_of_nat @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) )
= ( C @ number_number_of_nat @ ( B @ times_times_nat ) @ ( C @ number_number_of_nat @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_left__distrib__number__of) ).
thf(2363,plain,
! [A: nat,B: nat,C: int] :
( ( C @ number_number_of_nat @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) )
= ( C @ number_number_of_nat @ ( B @ times_times_nat ) @ ( C @ number_number_of_nat @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(362,axiom,
! [A: real,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ power_power_real ) @ power_power_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_power__even__eq) ).
thf(2077,plain,
! [A: real,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ power_power_real ) @ power_power_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(376,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( A != B )
& ( C = D ) )
=> ( ( A @ ( E @ times_times_int ) @ ( C @ plus_plus_int ) )
!= ( B @ ( E @ times_times_int ) @ ( D @ plus_plus_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq) ).
thf(2117,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E != zero_zero_int )
=> ( ( ( A != B )
& ( C = D ) )
=> ( ( A @ ( E @ times_times_int ) @ ( C @ plus_plus_int ) )
!= ( B @ ( E @ times_times_int ) @ ( D @ plus_plus_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(579,axiom,
pls @ ( pls @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I19_J) ).
thf(2940,plain,
pls @ ( pls @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(234,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( C @ ( A @ times_times_real ) )
= ( C @ ( B @ times_times_real ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_real__mult__right__cancel) ).
thf(1596,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( A = B )
=> ( ( C @ ( A @ times_times_real ) )
= ( C @ ( B @ times_times_real ) ) ) )
& ( ( ( C @ ( A @ times_times_real ) )
= ( C @ ( B @ times_times_real ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(403,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ times_times_int ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_semiring__mult__number__of) ).
thf(2231,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ times_times_int ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ times_times_nat ) )
= one_one_nat )
<=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_nat__mult__eq__one) ).
thf(1059,plain,
! [A: nat,B: nat] :
( ( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( ( B @ ( A @ times_times_nat ) )
= one_one_nat ) )
& ( ( ( B @ ( A @ times_times_nat ) )
= one_one_nat )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1060,plain,
( ! [A: nat,B: nat] :
( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( ( B @ ( A @ times_times_nat ) )
= one_one_nat ) )
& ! [A: nat,B: nat] :
( ( ( B @ ( A @ times_times_nat ) )
= one_one_nat )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(miniscope,[status(thm)],[1059]) ).
thf(1061,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( ( D @ ( C @ times_times_nat ) )
= one_one_nat )
| ( D != one_one_nat )
| ( C != one_one_nat ) )
& ( ( B = one_one_nat )
| ( ( B @ ( A @ times_times_nat ) )
!= one_one_nat ) )
& ( ( A = one_one_nat )
| ( ( B @ ( A @ times_times_nat ) )
!= one_one_nat ) ) ),
inference(cnf,[status(esa)],[1060]) ).
thf(1064,plain,
! [B: nat,A: nat] :
( ( ( B @ ( A @ times_times_nat ) )
= one_one_nat )
| ( B != one_one_nat )
| ( A != one_one_nat ) ),
inference(cnfConj,[status(thm)],[1061]) ).
thf(1067,plain,
! [B: nat,A: nat] :
( ( ( B @ ( A @ times_times_nat ) )
= one_one_nat )
| ( B != one_one_nat )
| ( A != one_one_nat ) ),
inference(lifteq,[status(thm)],[1064]) ).
thf(1068,plain,
( ( one_one_nat @ ( one_one_nat @ times_times_nat ) )
= one_one_nat ),
inference(simp,[status(thm)],[1067]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ dvd_dvd_nat ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_divides__ge) ).
thf(994,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ dvd_dvd_nat ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(632,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( B @ ( zero_zero_int @ ord_less_eq_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_q__pos__lemma) ).
thf(3153,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( B @ ( zero_zero_int @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(581,axiom,
! [A: int] :
( ( A @ ( pls @ number_number_of_int @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_add__numeral__0) ).
thf(2947,plain,
! [A: int] :
( ( A @ ( pls @ number_number_of_int @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(406,axiom,
! [A: int] :
( ( A @ number267125858f_real @ ( one_one_real @ plus_plus_real ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__special_I2_J) ).
thf(2248,plain,
! [A: int] :
( ( A @ number267125858f_real @ ( one_one_real @ plus_plus_real ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(509,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_add__Bit1__Bit0) ).
thf(2671,plain,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(343,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_add__Bit0__Bit0) ).
thf(2014,plain,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(264,axiom,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_one__add__one__is__two) ).
thf(1728,plain,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(622,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ord_less_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_rel__simps_I10_J) ).
thf(3108,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( pls @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( pls @ ( A @ bit0 @ ord_less_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(370,axiom,
min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ minus_minus_int ) @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ dvd_dvd_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(2099,plain,
min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ minus_minus_int ) @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ dvd_dvd_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(415,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ number_number_of_nat @ times_times_nat ) )
= ( C @ ( A @ number_number_of_nat @ times_times_nat ) @ ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_right__distrib__number__of) ).
thf(2282,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ number_number_of_nat @ times_times_nat ) )
= ( C @ ( A @ number_number_of_nat @ times_times_nat ) @ ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(375,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) ) )
=> ( ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( D @ ( F @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( D @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( D @ ord_less_eq_int ) )
=> ( E @ ( B @ ord_less_eq_int ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_zdiv__mono2__lemma) ).
thf(2114,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) ) )
=> ( ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( D @ ( F @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( D @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( D @ ord_less_eq_int ) )
=> ( E @ ( B @ ord_less_eq_int ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(154,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ power_power_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_power__0) ).
thf(1267,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ power_power_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1268,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ power_power_nat ) )
= one_one_nat ),
inference(cnf,[status(esa)],[1267]) ).
thf(1269,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ power_power_nat ) )
= one_one_nat ),
inference(lifteq,[status(thm)],[1268]) ).
thf(598,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( D @ ( C @ times_times_int ) @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(3017,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( D @ ( C @ times_times_int ) @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(249,axiom,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_semiring__numeral__1__eq__1) ).
thf(1671,plain,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(124,axiom,
zero_zero_int @ ( min @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_bin__less__0__simps_I2_J) ).
thf(1137,plain,
zero_zero_int @ ( min @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(163,axiom,
! [A: real,B: real,C: nat] :
( ( C @ ( B @ ( A @ times_times_real ) @ power_power_real ) )
= ( C @ ( B @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1310,plain,
! [A: real,B: real,C: nat] :
( ( C @ ( B @ ( A @ times_times_real ) @ power_power_real ) )
= ( C @ ( B @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(680,axiom,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_zadd__commute) ).
thf(3332,plain,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(571,axiom,
! [A: int,B: int] :
( ( B @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2918,plain,
! [A: int,B: int] :
( ( B @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(605,axiom,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_number__of__add) ).
thf(3044,plain,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(393,axiom,
! [A: int] :
( ( A @ bit1 @ number_number_of_int )
= ( A @ number_number_of_int @ ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_number__of__Bit1) ).
thf(2184,plain,
! [A: int] :
( ( A @ bit1 @ number_number_of_int )
= ( A @ number_number_of_int @ ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(339,axiom,
! [A: int,B: int,C: nat] :
( ( C @ ( B @ ( A @ times_times_int ) @ power_power_int ) )
= ( C @ ( B @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_power__mult__distrib) ).
thf(1999,plain,
! [A: int,B: int,C: nat] :
( ( C @ ( B @ ( A @ times_times_int ) @ power_power_int ) )
= ( C @ ( B @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(167,axiom,
! [A: real,B: real] :
( ( B @ ( A @ plus_plus_real ) )
= ( A @ ( B @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1327,plain,
! [A: real,B: real] :
( ( B @ ( A @ plus_plus_real ) )
= ( A @ ( B @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(454,axiom,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) )
= ( A @ ( B @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(2459,plain,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) )
= ( A @ ( B @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(242,axiom,
~ ! [A: int] :
~ ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) ).
thf(1640,plain,
~ ! [A: int] :
~ ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(568,axiom,
! [A: int] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_power__0__left__number__of) ).
thf(2901,plain,
! [A: int] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(386,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ number_number_of_int @ power_power_int ) )
= ( A @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power2__eq__square__number__of) ).
thf(2146,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ number_number_of_int @ power_power_int ) )
= ( A @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(435,axiom,
( ~ ( min @ number_number_of_int @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ quadRes ) )
=> ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ legendre ) )
!= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(2360,plain,
( ~ ( min @ number_number_of_int @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ quadRes ) )
=> ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ legendre ) )
!= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(484,axiom,
! [A: int] :
( ( zero_zero_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__special_I3_J) ).
thf(2575,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( zero_zero_real @ ( A @ number267125858f_real @ ord_less_eq_real ) ) )
& ( ( zero_zero_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(189,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ ord_less_eq_real ) )
<=> ( B @ ( A @ ord_less_eq_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_real__mult__le__cancel__iff1) ).
thf(1426,plain,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( ( B @ ( A @ ord_less_eq_real ) )
=> ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ ord_less_eq_real ) ) )
& ( ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(649,axiom,
! [A: int,B: int] :
( ( A @ bit0 )
!= ( B @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_rel__simps_I49_J) ).
thf(3217,plain,
! [A: int,B: int] :
( ( A @ bit0 )
!= ( B @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(6,axiom,
! [A: nat,B: nat,C: real,D: real] :
( ( D @ ( C @ dvd_dvd_real ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( D @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ dvd_dvd_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_dvd__power__le) ).
thf(715,plain,
! [A: nat,B: nat,C: real,D: real] :
( ( D @ ( C @ dvd_dvd_real ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( D @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ dvd_dvd_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(452,axiom,
! [A: int] :
( ( pls @ ( A @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add__Pls__right) ).
thf(2448,plain,
! [A: int] :
( ( pls @ ( A @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(682,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__number__of) ).
thf(3338,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(448,axiom,
! [A: int,B: int] :
( ( B @ zprime )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( one_one_int @ ( A @ ( A @ times_times_int ) @ zcong ) ) )
=> ( ( B @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ zcong ) ) )
| ( B @ ( one_one_int @ ( A @ zcong ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_zcong__square) ).
thf(2434,plain,
! [A: int,B: int] :
( ( B @ zprime )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( one_one_int @ ( A @ ( A @ times_times_int ) @ zcong ) ) )
=> ( ( B @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ zcong ) ) )
| ( B @ ( one_one_int @ ( A @ zcong ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(517,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= ( A @ ( A @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_power2__eq__square) ).
thf(2712,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= ( A @ ( A @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(496,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__int__code_I13_J) ).
thf(2627,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(390,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__eq__number__of__int__code) ).
thf(2168,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(272,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( one_one_int @ ( A @ ord_less_int ) )
=> ( B @ ( A @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ ord_less_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_power__strict__decreasing) ).
thf(1761,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( one_one_int @ ( A @ ord_less_int ) )
=> ( B @ ( A @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ ord_less_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(60,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_eq_int ) )
=> ( A @ ( B @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zle__trans) ).
thf(913,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_eq_int ) )
=> ( A @ ( B @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(681,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ minus_minus_int ) )
= ( B @ ( A @ minus_minus_int ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_diff__bin__simps_I9_J) ).
thf(3335,plain,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ minus_minus_int ) )
= ( B @ ( A @ minus_minus_int ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(521,axiom,
~ ! [A: int] :
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
!= ( A @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(2723,plain,
~ ! [A: int] :
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
!= ( A @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(350,axiom,
! [A: int,B: nat,C: int] :
( ( C @ zprime )
=> ( ( B @ ( A @ power_power_int ) @ ( C @ dvd_dvd_int ) )
=> ( A @ ( C @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_zprime__zdvd__power) ).
thf(2046,plain,
! [A: int,B: nat,C: int] :
( ( C @ zprime )
=> ( ( B @ ( A @ power_power_int ) @ ( C @ dvd_dvd_int ) )
=> ( A @ ( C @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(149,axiom,
! [A: real,B: real] :
( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_real ) )
<=> ( ( B != zero_zero_real )
| ( A != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_sum__squares__gt__zero__iff) ).
thf(1243,plain,
! [A: real,B: real] :
( ( ( ( B != zero_zero_real )
| ( A != zero_zero_real ) )
=> ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_real ) ) )
& ( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_real ) )
=> ( ( B != zero_zero_real )
| ( A != zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(387,axiom,
? [A: int] :
( ! [B: int] :
( ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( B @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( B @ ord_less_int ) )
& ( B @ ( zero_zero_int @ ord_less_eq_int ) ) )
=> ( B = A ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) ).
thf(2149,plain,
? [A: int] :
( ! [B: int] :
( ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( B @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( B @ ord_less_int ) )
& ( B @ ( zero_zero_int @ ord_less_eq_int ) ) )
=> ( B = A ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(2150,plain,
! [A: int] :
( ( ( A = sk11 )
| ~ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
| ~ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
| ~ ( A @ ( zero_zero_int @ ord_less_eq_int ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( sk11 @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( sk11 @ ord_less_int ) )
& ( sk11 @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(cnf,[status(esa)],[2149]) ).
thf(2151,plain,
sk11 @ ( zero_zero_int @ ord_less_eq_int ),
inference(cnfConj,[status(thm)],[2150]) ).
thf(4264,plain,
! [B: int,A: int] :
( ( ( sk11 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[2151,741]) ).
thf(4265,plain,
! [B: int,A: int] :
( ( ( sk11 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ( A = B ) ),
inference(simp,[status(thm)],[4264]) ).
thf(4266,plain,
( ( sk11 @ ( zero_zero_int @ ord_less_int ) )
| ( sk11 = zero_zero_int ) ),
inference(pattern_uni,[status(thm)],[4265:[bind(A,$thf( zero_zero_int )),bind(B,$thf( sk11 ))]]) ).
thf(5,axiom,
! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
<=> ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_real__le__eq__diff) ).
thf(709,plain,
! [A: real,B: real] :
( ( ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_real ) ) )
& ( ( B @ ( A @ ord_less_eq_real ) )
=> ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(239,axiom,
! [A: nat,B: int] :
( ( B @ number_number_of_nat @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
<=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
| ( ( B @ number_number_of_nat )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_zero__less__power__nat__eq__number__of) ).
thf(1613,plain,
! [A: nat,B: int] :
( ( ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
| ( ( B @ number_number_of_nat )
= zero_zero_nat ) )
=> ( B @ number_number_of_nat @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ) )
& ( ( B @ number_number_of_nat @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
| ( ( B @ number_number_of_nat )
= zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(341,axiom,
! [A: nat] :
( ( A @ ( one_one_int @ power_power_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_power__one) ).
thf(2008,plain,
! [A: nat] :
( ( A @ ( one_one_int @ power_power_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(2009,plain,
! [A: nat] :
( ( A @ ( one_one_int @ power_power_int ) )
= one_one_int ),
inference(cnf,[status(esa)],[2008]) ).
thf(2010,plain,
! [A: nat] :
( ( A @ ( one_one_int @ power_power_int ) )
= one_one_int ),
inference(lifteq,[status(thm)],[2009]) ).
thf(244,axiom,
( ( pls @ bit1 @ number_number_of_int )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).
thf(1650,plain,
( ( pls @ bit1 @ number_number_of_int )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(564,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( G @ ( F @ ( B @ times_times_int ) @ ( E @ minus_minus_int ) @ times_times_int ) @ ( D @ ( C @ ( B @ times_times_int ) @ ( A @ minus_minus_int ) @ times_times_int ) @ plus_plus_int ) )
= ( G @ ( F @ times_times_int ) @ ( D @ ( C @ times_times_int ) @ plus_plus_int ) @ ( B @ times_times_int ) @ ( G @ ( E @ times_times_int ) @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) @ minus_minus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_xzgcda__linear__aux1) ).
thf(2886,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( G @ ( F @ ( B @ times_times_int ) @ ( E @ minus_minus_int ) @ times_times_int ) @ ( D @ ( C @ ( B @ times_times_int ) @ ( A @ minus_minus_int ) @ times_times_int ) @ plus_plus_int ) )
= ( G @ ( F @ times_times_int ) @ ( D @ ( C @ times_times_int ) @ plus_plus_int ) @ ( B @ times_times_int ) @ ( G @ ( E @ times_times_int ) @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) @ minus_minus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(364,axiom,
! [A: real] :
( ( A @ ( pls @ number267125858f_real @ plus_plus_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_add__numeral__0) ).
thf(2082,plain,
! [A: real] :
( ( A @ ( pls @ number267125858f_real @ plus_plus_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(262,axiom,
! [A: int] :
( min
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_rel__simps_I42_J) ).
thf(1721,plain,
! [A: int] :
( min
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1722,plain,
~ ? [A: int] :
( min
= ( A @ bit0 ) ),
inference(miniscope,[status(thm)],[1721]) ).
thf(1723,plain,
! [A: int] :
( min
!= ( A @ bit0 ) ),
inference(cnf,[status(esa)],[1722]) ).
thf(1724,plain,
! [A: int] :
( ( A @ bit0 )
!= min ),
inference(lifteq,[status(thm)],[1723]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
<=> ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_less__bin__lemma) ).
thf(754,plain,
! [A: int,B: int] :
( ( ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(755,plain,
( ! [A: int,B: int] :
( ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) )
& ! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ) ),
inference(miniscope,[status(thm)],[754]) ).
thf(756,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( D @ ( C @ ord_less_int ) )
| ~ ( zero_zero_int @ ( D @ ( C @ minus_minus_int ) @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
| ~ ( B @ ( A @ ord_less_int ) ) ) ),
inference(cnf,[status(esa)],[755]) ).
thf(757,plain,
! [B: int,A: int] :
( ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
| ~ ( B @ ( A @ ord_less_int ) ) ),
inference(cnfConj,[status(thm)],[756]) ).
thf(5454,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( min @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1137,757]) ).
thf(5455,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( min @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5454]) ).
thf(5456,plain,
zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_int ),
inference(pattern_uni,[status(thm)],[5455:[bind(A,$thf( min )),bind(B,$thf( zero_zero_int ))]]) ).
thf(5519,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5456,757]) ).
thf(5520,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5519]) ).
thf(5521,plain,
zero_zero_int @ ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ),
inference(pattern_uni,[status(thm)],[5520:[bind(A,$thf( zero_zero_int @ ( min @ minus_minus_int ) )),bind(B,$thf( zero_zero_int ))]]) ).
thf(14,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
<=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(742,plain,
! [A: int,B: int] :
( ( ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) )
=> ( B @ ( A @ ord_less_int ) ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(743,plain,
( ! [A: int,B: int] :
( ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) )
=> ( B @ ( A @ ord_less_int ) ) )
& ! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ) ),
inference(miniscope,[status(thm)],[742]) ).
thf(744,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( D @ ( C @ ord_less_int ) )
| ( C = D )
| ~ ( D @ ( C @ ord_less_eq_int ) ) )
& ( ( A != B )
| ~ ( B @ ( A @ ord_less_int ) ) )
& ( ( B @ ( A @ ord_less_eq_int ) )
| ~ ( B @ ( A @ ord_less_int ) ) ) ),
inference(cnf,[status(esa)],[743]) ).
thf(745,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_eq_int ) )
| ~ ( B @ ( A @ ord_less_int ) ) ),
inference(cnfConj,[status(thm)],[744]) ).
thf(6100,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5521,745]) ).
thf(6101,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[6100]) ).
thf(6102,plain,
zero_zero_int @ ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) @ ord_less_eq_int ),
inference(pattern_uni,[status(thm)],[6101:[bind(A,$thf( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) )),bind(B,$thf( zero_zero_int ))]]) ).
thf(558,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ zcong ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_s) ).
thf(2869,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ zcong ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(689,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) )
<=> ~ ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ ord_less_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_le__number__of__eq__not__less) ).
thf(3370,plain,
! [A: int,B: int] :
( ( ~ ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ ord_less_nat ) )
=> ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) ) )
& ( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) )
=> ~ ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_power__mono) ).
thf(1095,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ ord_less_eq_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(269,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ bit1 @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_bin__less__0__simps_I4_J) ).
thf(1746,plain,
! [A: int] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ bit1 @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(54,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( one_one_real @ ord_less_real ) )
=> ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_power__strict__increasing) ).
thf(898,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( one_one_real @ ord_less_real ) )
=> ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(447,axiom,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(2432,plain,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(317,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( A @ times_times_int ) @ ( B @ plus_plus_int ) @ ( A @ dvd_dvd_int ) )
<=> ( B @ ( A @ dvd_dvd_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_zdvd__reduce) ).
thf(1914,plain,
! [A: int,B: int,C: int] :
( ( ( B @ ( A @ dvd_dvd_int ) )
=> ( C @ ( A @ times_times_int ) @ ( B @ plus_plus_int ) @ ( A @ dvd_dvd_int ) ) )
& ( ( C @ ( A @ times_times_int ) @ ( B @ plus_plus_int ) @ ( A @ dvd_dvd_int ) )
=> ( B @ ( A @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(77,axiom,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_power__0) ).
thf(971,plain,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(972,plain,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real ) )
= one_one_real ),
inference(cnf,[status(esa)],[971]) ).
thf(973,plain,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real ) )
= one_one_real ),
inference(lifteq,[status(thm)],[972]) ).
thf(49,axiom,
! [A: int] : ( A @ ( zero_zero_int @ ( A @ zcong ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_zcong__id) ).
thf(885,plain,
! [A: int] : ( A @ ( zero_zero_int @ ( A @ zcong ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(616,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zless__imp__add1__zle) ).
thf(3088,plain,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1046,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(443,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) )
<=> ( ~ ( B @ ( A @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_le__nat__number__of) ).
thf(2400,plain,
! [A: int,B: int] :
( ( ( ~ ( B @ ( A @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) )
=> ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) ) )
& ( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) )
=> ( ~ ( B @ ( A @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(546,axiom,
! [A: int,B: int] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_sum__power2__ge__zero) ).
thf(2825,plain,
! [A: int,B: int] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(313,axiom,
( ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ minus_minus_int ) )
= ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(1904,plain,
( ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ minus_minus_int ) )
= ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(214,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ord_less_eq_real ) )
=> ( ( A @ ( C @ ord_less_eq_real ) )
=> ( A @ ( B @ ord_less_eq_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_real__le__trans) ).
thf(1518,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ord_less_eq_real ) )
=> ( ( A @ ( C @ ord_less_eq_real ) )
=> ( A @ ( B @ ord_less_eq_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(240,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( A != B )
& ( C != D ) )
<=> ( ( B @ ( D @ times_times_int ) @ ( A @ ( C @ times_times_int ) @ plus_plus_int ) )
!= ( A @ ( D @ times_times_int ) @ ( B @ ( C @ times_times_int ) @ plus_plus_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_crossproduct__noteq) ).
thf(1623,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ( B @ ( D @ times_times_int ) @ ( A @ ( C @ times_times_int ) @ plus_plus_int ) )
!= ( A @ ( D @ times_times_int ) @ ( B @ ( C @ times_times_int ) @ plus_plus_int ) ) )
=> ( ( A != B )
& ( C != D ) ) )
& ( ( ( A != B )
& ( C != D ) )
=> ( ( B @ ( D @ times_times_int ) @ ( A @ ( C @ times_times_int ) @ plus_plus_int ) )
!= ( A @ ( D @ times_times_int ) @ ( B @ ( C @ times_times_int ) @ plus_plus_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(206,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ power_power_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1482,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ power_power_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(503,axiom,
! [A: nat,B: nat] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_power2__eq__imp__eq) ).
thf(2654,plain,
! [A: nat,B: nat] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(650,axiom,
! [A: int,B: int] :
( ( B @ ( A @ bit1 @ times_times_int ) )
= ( B @ ( B @ ( A @ times_times_int ) @ bit0 @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_mult__Bit1) ).
thf(3221,plain,
! [A: int,B: int] :
( ( B @ ( A @ bit1 @ times_times_int ) )
= ( B @ ( B @ ( A @ times_times_int ) @ bit0 @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(601,axiom,
! [A: int] :
( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( one_one_int @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_le__imp__0__less) ).
thf(3029,plain,
! [A: int] :
( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( one_one_int @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(628,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ zprime )
=> ( ( A @ ( C @ times_times_int ) @ ( B @ dvd_dvd_int ) )
=> ( ( A @ ( B @ dvd_dvd_int ) )
| ( C @ ( B @ dvd_dvd_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_zprime__zdvd__zmult) ).
thf(3131,plain,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ zprime )
=> ( ( A @ ( C @ times_times_int ) @ ( B @ dvd_dvd_int ) )
=> ( ( A @ ( B @ dvd_dvd_int ) )
| ( C @ ( B @ dvd_dvd_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) )
= ( C @ ( A @ plus_plus_nat ) @ ( B @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(717,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) )
= ( C @ ( A @ plus_plus_nat ) @ ( B @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(718,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) )
= ( C @ ( A @ plus_plus_nat ) @ ( B @ plus_plus_nat ) ) ),
inference(cnf,[status(esa)],[717]) ).
thf(719,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) )
= ( C @ ( A @ plus_plus_nat ) @ ( B @ plus_plus_nat ) ) ),
inference(lifteq,[status(thm)],[718]) ).
thf(24,axiom,
! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
<=> ( ( A = B )
| ( B @ ( A @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_less__eq__real__def) ).
thf(779,plain,
! [A: real,B: real] :
( ( ( ( A = B )
| ( B @ ( A @ ord_less_real ) ) )
=> ( B @ ( A @ ord_less_eq_real ) ) )
& ( ( B @ ( A @ ord_less_eq_real ) )
=> ( ( A = B )
| ( B @ ( A @ ord_less_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(780,plain,
( ! [A: real,B: real] :
( ( ( A = B )
| ( B @ ( A @ ord_less_real ) ) )
=> ( B @ ( A @ ord_less_eq_real ) ) )
& ! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
=> ( ( A = B )
| ( B @ ( A @ ord_less_real ) ) ) ) ),
inference(miniscope,[status(thm)],[779]) ).
thf(781,plain,
! [D: real,C: real,B: real,A: real] :
( ( ( D @ ( C @ ord_less_eq_real ) )
| ( C != D ) )
& ( ( D @ ( C @ ord_less_eq_real ) )
| ~ ( D @ ( C @ ord_less_real ) ) )
& ( ( A = B )
| ( B @ ( A @ ord_less_real ) )
| ~ ( B @ ( A @ ord_less_eq_real ) ) ) ),
inference(cnf,[status(esa)],[780]) ).
thf(782,plain,
! [B: real,A: real] :
( ( A = B )
| ( B @ ( A @ ord_less_real ) )
| ~ ( B @ ( A @ ord_less_eq_real ) ) ),
inference(cnfConj,[status(thm)],[781]) ).
thf(785,plain,
! [B: real,A: real] :
( ( B @ ( A @ ord_less_real ) )
| ~ ( B @ ( A @ ord_less_eq_real ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[782]) ).
thf(529,axiom,
! [A: int,B: nat,C: int] :
( ( C @ zprime )
=> ( ( B @ ( A @ power_power_int ) @ ( C @ dvd_dvd_int ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ dvd_dvd_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_zpower__zdvd__prop2) ).
thf(2755,plain,
! [A: int,B: nat,C: int] :
( ( C @ zprime )
=> ( ( B @ ( A @ power_power_int ) @ ( C @ dvd_dvd_int ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ dvd_dvd_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(303,axiom,
! [A: int,B: int,C: nat] :
( ( C @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( B @ ( A @ dvd_dvd_int ) )
=> ( C @ ( B @ power_power_int ) @ ( A @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_zpower__zdvd__prop1) ).
thf(1871,plain,
! [A: int,B: int,C: nat] :
( ( C @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( B @ ( A @ dvd_dvd_int ) )
=> ( C @ ( B @ power_power_int ) @ ( A @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(466,axiom,
! [A: int,B: int] :
( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
<=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_sum__squares__gt__zero__iff) ).
thf(2501,plain,
! [A: int,B: int] :
( ( ( ( B != zero_zero_int )
| ( A != zero_zero_int ) )
=> ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(62,axiom,
! [A: real,B: real] :
( ( A @ ( B @ ord_less_eq_real ) )
| ( B @ ( A @ ord_less_eq_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_real__le__linear) ).
thf(917,plain,
! [A: real,B: real] :
( ( A @ ( B @ ord_less_eq_real ) )
| ( B @ ( A @ ord_less_eq_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(627,axiom,
! [A: int] :
( ( min @ ( A @ bit1 @ ord_less_int ) )
<=> ( min @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_rel__simps_I13_J) ).
thf(3125,plain,
! [A: int] :
( ( ( min @ ( A @ ord_less_int ) )
=> ( min @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( min @ ( A @ bit1 @ ord_less_int ) )
=> ( min @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ plus_plus_nat ) ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_add__0__iff) ).
thf(1313,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( A
= ( B @ ( A @ plus_plus_nat ) ) ) )
& ( ( A
= ( B @ ( A @ plus_plus_nat ) ) )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(378,axiom,
pls @ bit1 @ bit0 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(2127,plain,
pls @ bit1 @ bit0 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(3833,plain,
zero_zero_int @ bit1 @ bit0 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ),
inference(rewrite,[status(thm)],[2127,3057]) ).
thf(3835,plain,
( ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3833,3451]) ).
thf(3836,plain,
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[3835]) ).
thf(3840,plain,
( ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_int )
!= min )
| ( zero_zero_int != zero_zero_int ) ),
inference(simp,[status(thm)],[3836]) ).
thf(3845,plain,
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_int )
!= min ),
inference(simp,[status(thm)],[3840]) ).
thf(67,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ power_power_real ) )
= ( C @ ( B @ ( A @ power_power_real ) @ power_power_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_power__mult) ).
thf(934,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ power_power_real ) )
= ( C @ ( B @ ( A @ power_power_real ) @ power_power_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(526,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__int__code_I16_J) ).
thf(2745,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(282,axiom,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ ord_less_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_power2__less__imp__less) ).
thf(1792,plain,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ ord_less_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(190,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ord_less_eq_real ) )
=> ( C @ ( A @ plus_plus_real ) @ ( B @ ( A @ plus_plus_real ) @ ord_less_eq_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_real__add__left__mono) ).
thf(1430,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ord_less_eq_real ) )
=> ( C @ ( A @ plus_plus_real ) @ ( B @ ( A @ plus_plus_real ) @ ord_less_eq_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(398,axiom,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_nat__1__add__1) ).
thf(2207,plain,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(2208,plain,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
inference(lifteq,[status(thm)],[2207]) ).
thf(5759,plain,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat ) ),
inference(rewrite,[status(thm)],[2208,3057]) ).
thf(411,axiom,
( ( pls @ number267125858f_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_semiring__numeral__0__eq__0) ).
thf(2269,plain,
( ( pls @ number267125858f_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(168,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1330,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(153,axiom,
! [A: real] :
( ( one_one_nat @ ( A @ power_power_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1264,plain,
! [A: real] :
( ( one_one_nat @ ( A @ power_power_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1,conjecture,
? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(701,plain,
~ ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(702,plain,
! [B: int,A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
!= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(cnf,[status(esa)],[701]) ).
thf(703,plain,
! [B: int,A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
!= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(lifteq,[status(thm)],[702]) ).
thf(3409,plain,
! [B: int,A: int] :
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
!= ( one_one_int @ ( m @ ( zero_zero_int @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(rewrite,[status(thm)],[703,3057]) ).
thf(3410,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) )
!= one_one_int )
| ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
!= ( m @ ( zero_zero_int @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) ) ) ),
inference(simp,[status(thm)],[3409]) ).
thf(198,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_eq_nat ) )
<=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_power__increasing__iff) ).
thf(1455,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_eq_nat ) ) )
& ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_eq_nat ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ times_times_nat ) )
= ( C @ ( A @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1132,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ times_times_nat ) )
= ( C @ ( A @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(555,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_rel__simps_I14_J) ).
thf(2857,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(352,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_semiring__mult__2) ).
thf(2049,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(258,axiom,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_power2__le__imp__le) ).
thf(1704,plain,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(237,axiom,
! [A: int,B: int,C: real] :
( ( C @ ( B @ number267125858f_real @ times_times_real ) @ ( A @ number267125858f_real @ times_times_real ) )
= ( C @ ( B @ ( A @ times_times_int ) @ number267125858f_real @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_mult__number__of__left) ).
thf(1609,plain,
! [A: int,B: int,C: real] :
( ( C @ ( B @ number267125858f_real @ times_times_real ) @ ( A @ number267125858f_real @ times_times_real ) )
= ( C @ ( B @ ( A @ times_times_int ) @ number267125858f_real @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(20,axiom,
! [A: real,B: real] :
( ( B @ ( A @ times_times_real ) )
= ( A @ ( B @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_real__mult__commute) ).
thf(768,plain,
! [A: real,B: real] :
( ( B @ ( A @ times_times_real ) )
= ( A @ ( B @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(769,plain,
! [B: real,A: real] :
( ( B @ ( A @ times_times_real ) )
= ( A @ ( B @ times_times_real ) ) ),
inference(cnf,[status(esa)],[768]) ).
thf(770,plain,
! [B: real,A: real] :
( ( B @ ( A @ times_times_real ) )
= ( A @ ( B @ times_times_real ) ) ),
inference(lifteq,[status(thm)],[769]) ).
thf(227,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_eq_nat ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_power__le__imp__le__exp) ).
thf(1568,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_eq_nat ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(274,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ times_times_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1771,plain,
! [A: int] :
( ( zero_zero_int @ ( A @ times_times_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1772,plain,
! [A: int] :
( ( zero_zero_int @ ( A @ times_times_int ) )
= zero_zero_int ),
inference(cnf,[status(esa)],[1771]) ).
thf(1773,plain,
! [A: int] :
( ( zero_zero_int @ ( A @ times_times_int ) )
= zero_zero_int ),
inference(lifteq,[status(thm)],[1772]) ).
thf(640,axiom,
! [A: int,B: int] :
( ( ( A @ bit0 )
= ( B @ bit0 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_rel__simps_I48_J) ).
thf(3180,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( ( A @ bit0 )
= ( B @ bit0 ) ) )
& ( ( ( A @ bit0 )
= ( B @ bit0 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(112,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( C @ ( B @ plus_plus_real ) @ ( A @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1100,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( C @ ( B @ plus_plus_real ) @ ( A @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
<=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_zero__less__power__nat__eq) ).
thf(1379,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
| ( B = zero_zero_nat ) )
=> ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ) )
& ( ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(694,axiom,
! [A: int] :
( ( A @ ( zero_zero_int @ times_times_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(3385,plain,
! [A: int] :
( ( A @ ( zero_zero_int @ times_times_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( B @ ( A @ dvd_dvd_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
| ( zero_zero_int @ ( B @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_zdvd__bounds) ).
thf(969,plain,
! [A: int,B: int] :
( ( B @ ( A @ dvd_dvd_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
| ( zero_zero_int @ ( B @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(229,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( one_one_real @ ( A @ ord_less_eq_real ) )
=> ( B @ ( A @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ ord_less_eq_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_power__decreasing) ).
thf(1572,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( one_one_real @ ( A @ ord_less_eq_real ) )
=> ( B @ ( A @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ ord_less_eq_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( one_one_nat @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_one__less__power) ).
thf(1115,plain,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( one_one_nat @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(575,axiom,
! [A: nat,B: int,C: int] :
( ( C @ ( B @ dvd_dvd_int ) )
=> ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ dvd_dvd_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_dvd__power__same) ).
thf(2929,plain,
! [A: nat,B: int,C: int] :
( ( C @ ( B @ dvd_dvd_int ) )
=> ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ dvd_dvd_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(210,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( B @ ( A @ ord_less_real ) )
=> ( B @ ( C @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_real__mult__less__mono2) ).
thf(1494,plain,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( B @ ( A @ ord_less_real ) )
=> ( B @ ( C @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(401,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J) ).
thf(2222,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(201,axiom,
! [A: nat,B: real,C: real] :
( ( C @ ( B @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( A @ ( C @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ ord_less_eq_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_power__mono) ).
thf(1465,plain,
! [A: nat,B: real,C: real] :
( ( C @ ( B @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( A @ ( C @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ ord_less_eq_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(367,axiom,
! [A: int,B: int] :
~ ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_not__sum__squares__lt__zero) ).
thf(2090,plain,
! [A: int,B: int] :
~ ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(178,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_Int2_Ozcong__zero) ).
thf(1373,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(409,axiom,
! [A: real,B: nat] :
( ( zero_zero_real @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) @ ord_less_eq_real ) )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_even__power__le__0__imp__0) ).
thf(2259,plain,
! [A: real,B: nat] :
( ( zero_zero_real @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) @ ord_less_eq_real ) )
=> ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(68,axiom,
! [A: nat,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ ord_less_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_power__strict__mono) ).
thf(937,plain,
! [A: nat,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ ord_less_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(417,axiom,
pls @ ( min @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_rel__simps_I23_J) ).
thf(2291,plain,
pls @ ( min @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(75,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ power_power_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_power__one__right) ).
thf(966,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ power_power_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(99,axiom,
! [A: nat,B: real,C: real] :
( ( C @ ( B @ ord_less_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ ord_less_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_power__strict__mono) ).
thf(1051,plain,
! [A: nat,B: real,C: real] :
( ( C @ ( B @ ord_less_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ ord_less_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(22,axiom,
! [A: int,B: int] : ( B @ ( A @ ( A @ zcong ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_zcong__refl) ).
thf(774,plain,
! [A: int,B: int] : ( B @ ( A @ ( A @ zcong ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(775,plain,
! [B: int,A: int] : ( B @ ( A @ ( A @ zcong ) ) ),
inference(cnf,[status(esa)],[774]) ).
thf(9,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
<=> ( A @ ( B @ dvd_dvd_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_zcong__zero__equiv__div) ).
thf(723,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ dvd_dvd_int ) )
=> ( B @ ( zero_zero_int @ ( A @ zcong ) ) ) )
& ( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ( A @ ( B @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(724,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ dvd_dvd_int ) )
=> ( B @ ( zero_zero_int @ ( A @ zcong ) ) ) )
& ! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ( A @ ( B @ dvd_dvd_int ) ) ) ),
inference(miniscope,[status(thm)],[723]) ).
thf(725,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( D @ ( zero_zero_int @ ( C @ zcong ) ) )
| ~ ( C @ ( D @ dvd_dvd_int ) ) )
& ( ( A @ ( B @ dvd_dvd_int ) )
| ~ ( B @ ( zero_zero_int @ ( A @ zcong ) ) ) ) ),
inference(cnf,[status(esa)],[724]) ).
thf(726,plain,
! [B: int,A: int] :
( ( A @ ( B @ dvd_dvd_int ) )
| ~ ( B @ ( zero_zero_int @ ( A @ zcong ) ) ) ),
inference(cnfConj,[status(thm)],[725]) ).
thf(6256,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( B @ ( A @ ( A @ zcong ) ) )
!= ( D @ ( zero_zero_int @ ( C @ zcong ) ) ) )
| ( C @ ( D @ dvd_dvd_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[775,726]) ).
thf(6257,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( B @ ( A @ ( A @ zcong ) ) )
!= ( D @ ( zero_zero_int @ ( C @ zcong ) ) ) )
| ( C @ ( D @ dvd_dvd_int ) ) ),
inference(simp,[status(thm)],[6256]) ).
thf(6258,plain,
! [A: int] : ( zero_zero_int @ ( A @ dvd_dvd_int ) ),
inference(pattern_uni,[status(thm)],[6257:[bind(A,$thf( zero_zero_int )),bind(B,$thf( B )),bind(C,$thf( zero_zero_int )),bind(D,$thf( B ))]]) ).
thf(6259,plain,
! [A: int] : ( zero_zero_int @ ( A @ dvd_dvd_int ) ),
inference(simp,[status(thm)],[6258]) ).
thf(582,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ dvd_dvd_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_le__imp__power__dvd) ).
thf(2950,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ dvd_dvd_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(405,axiom,
! [A: int,B: nat] :
( ( ( B @ ( A @ power_power_int ) )
= zero_zero_int )
<=> ( ( B != zero_zero_nat )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_power__eq__0__iff) ).
thf(2237,plain,
! [A: int,B: nat] :
( ( ( ( B != zero_zero_nat )
& ( A = zero_zero_int ) )
=> ( ( B @ ( A @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( B @ ( A @ power_power_int ) )
= zero_zero_int )
=> ( ( B != zero_zero_nat )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(161,axiom,
! [A: real,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_real @ ord_less_real ) )
=> ? [C: real] :
( ( ( B @ ( C @ power_power_real ) )
= A )
& ( C @ ( zero_zero_real @ ord_less_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_realpow__pos__nth) ).
thf(1302,plain,
! [A: real,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_real @ ord_less_real ) )
=> ? [C: real] :
( ( ( B @ ( C @ power_power_real ) )
= A )
& ( C @ ( zero_zero_real @ ord_less_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(246,axiom,
pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_pos2) ).
thf(1664,plain,
pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(539,axiom,
~ ( min @ ( pls @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_rel__simps_I3_J) ).
thf(2794,plain,
~ ( min @ ( pls @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(644,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__number__of__int__code) ).
thf(3199,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(5524,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5456,745]) ).
thf(5525,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[5524]) ).
thf(5526,plain,
zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_eq_int ),
inference(pattern_uni,[status(thm)],[5525:[bind(A,$thf( zero_zero_int @ ( min @ minus_minus_int ) )),bind(B,$thf( zero_zero_int ))]]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( ( A = one_one_nat )
| ( B @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_nat ) @ ( A @ dvd_dvd_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_dvd__power) ).
thf(789,plain,
! [A: nat,B: nat] :
( ( ( A = one_one_nat )
| ( B @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_nat ) @ ( A @ dvd_dvd_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(316,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ plus_plus_int ) @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( D @ ( B @ plus_plus_int ) @ ( C @ ( A @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1911,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ plus_plus_int ) @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( D @ ( B @ plus_plus_int ) @ ( C @ ( A @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(534,axiom,
! [A: int,B: int] :
( ( A @ ( B @ times_times_int ) @ ( A @ plus_plus_int ) )
= ( A @ ( one_one_int @ ( B @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2782,plain,
! [A: int,B: int] :
( ( A @ ( B @ times_times_int ) @ ( A @ plus_plus_int ) )
= ( A @ ( one_one_int @ ( B @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(453,axiom,
! [A: int] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_power__0__left__number__of) ).
thf(2451,plain,
! [A: int] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(404,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_int__0__neq__1) ).
thf(2234,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(2235,plain,
zero_zero_int != one_one_int,
inference(polarity_switch,[status(thm)],[2234]) ).
thf(2236,plain,
zero_zero_int != one_one_int,
inference(lifteq,[status(thm)],[2235]) ).
thf(299,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_rel__simps_I32_J) ).
thf(1858,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1641,plain,
~ ! [A: int] :
~ ( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(polarity_switch,[status(thm)],[1640]) ).
thf(1642,plain,
~ ~ ? [A: int] :
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( A @ ord_less_int ) )
& ( A @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(miniscope,[status(thm)],[1641]) ).
thf(1643,plain,
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( sk3 @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( sk3 @ ord_less_int ) )
& ( sk3 @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(cnf,[status(esa)],[1642]) ).
thf(1644,plain,
sk3 @ ( zero_zero_int @ ord_less_eq_int ),
inference(cnfConj,[status(thm)],[1643]) ).
thf(4145,plain,
! [B: int,A: int] :
( ( ( sk3 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[1644,741]) ).
thf(4146,plain,
! [B: int,A: int] :
( ( ( sk3 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ( A = B ) ),
inference(simp,[status(thm)],[4145]) ).
thf(4147,plain,
( ( sk3 @ ( zero_zero_int @ ord_less_int ) )
| ( sk3 = zero_zero_int ) ),
inference(pattern_uni,[status(thm)],[4146:[bind(A,$thf( zero_zero_int )),bind(B,$thf( sk3 ))]]) ).
thf(300,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( C @ ( A @ plus_plus_int ) @ ( B @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_zadd__left__mono) ).
thf(1864,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( C @ ( A @ plus_plus_int ) @ ( B @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(294,axiom,
! [A: int,B: int] :
( ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_eq__number__of) ).
thf(1828,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) ) )
& ( ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(573,axiom,
t @ ( one_one_int @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(2925,plain,
t @ ( one_one_int @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(330,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_rel__simps_I16_J) ).
thf(1960,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(29,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(806,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(344,axiom,
! [A: int,B: int,C: int] :
( ( zero_zero_int @ ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( zero_zero_int @ ( B @ ord_less_eq_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_q__neg__lemma) ).
thf(2017,plain,
! [A: int,B: int,C: int] :
( ( zero_zero_int @ ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( zero_zero_int @ ( B @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(57,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ plus_plus_real ) )
= ( C @ ( A @ plus_plus_real ) @ ( B @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(905,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ plus_plus_real ) )
= ( C @ ( A @ plus_plus_real ) @ ( B @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(587,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( B @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( D @ times_times_int ) @ ( A @ ( C @ times_times_int ) @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_zcong__zmult) ).
thf(2964,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( B @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( D @ times_times_int ) @ ( A @ ( C @ times_times_int ) @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_nat__power__eq__0__iff) ).
thf(1215,plain,
! [A: nat,B: nat] :
( ( ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) )
=> ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(308,axiom,
! [A: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_zero__eq__power2) ).
thf(1886,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(533,axiom,
! [A: real,B: int] :
( ( ( B @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real )
<=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_power__eq__0__iff__number__of) ).
thf(2772,plain,
! [A: real,B: int] :
( ( ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_real ) )
=> ( ( B @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real ) )
& ( ( ( B @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real )
=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(340,axiom,
! [A: int,B: int] :
( ( B @ ( A @ quadRes ) )
<=> ? [C: int] : ( A @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( C @ power_power_int ) @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_QuadRes__def) ).
thf(2002,plain,
! [A: int,B: int] :
( ( ? [C: int] : ( A @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( C @ power_power_int ) @ zcong ) ) )
=> ( B @ ( A @ quadRes ) ) )
& ( ( B @ ( A @ quadRes ) )
=> ? [C: int] : ( A @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( C @ power_power_int ) @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(499,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ ( A @ plus_plus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( A @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(2639,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ ( A @ plus_plus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( A @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(677,axiom,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ( A @ ( B @ times_times_int ) @ zcong ) ) )
=> ( ( C @ ( zero_zero_int @ ( A @ zcong ) ) )
| ( C @ ( zero_zero_int @ ( B @ zcong ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_zcong__zprime__prod__zero) ).
thf(3327,plain,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ( A @ ( B @ times_times_int ) @ zcong ) ) )
=> ( ( C @ ( zero_zero_int @ ( A @ zcong ) ) )
| ( C @ ( zero_zero_int @ ( B @ zcong ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(542,axiom,
! [A: int] :
( ( one_one_nat @ ( A @ power_power_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(2804,plain,
! [A: int] :
( ( one_one_nat @ ( A @ power_power_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(333,axiom,
! [A: int] :
( ( A @ bit0 )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_rel__simps_I45_J) ).
thf(1975,plain,
! [A: int] :
( ( A @ bit0 )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(297,axiom,
! [A: int] :
( ( A @ ( pls @ bit1 @ number_number_of_int @ times_times_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_mult__numeral__1) ).
thf(1843,plain,
! [A: int] :
( ( A @ ( pls @ bit1 @ number_number_of_int @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(356,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_int ) @ power_power_int ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zpower__zpower) ).
thf(2058,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_int ) @ power_power_int ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(284,axiom,
( one_one_real
= ( pls @ bit1 @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_semiring__norm_I110_J) ).
thf(1796,plain,
( one_one_real
= ( pls @ bit1 @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(471,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( B @ ( C @ times_times_int ) @ ( A @ zcong ) ) )
<=> ( E @ ( B @ ( D @ times_times_int ) @ ( A @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_zcong__zmult__prop1) ).
thf(2530,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( ( E @ ( B @ ( D @ times_times_int ) @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( C @ times_times_int ) @ ( A @ zcong ) ) ) )
& ( ( E @ ( B @ ( C @ times_times_int ) @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( D @ times_times_int ) @ ( A @ zcong ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( C @ ( A @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ dvd_dvd_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_divides__mul__l) ).
thf(1119,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( C @ ( A @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ dvd_dvd_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(446,axiom,
! [A: int] :
( ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_double__eq__0__iff) ).
thf(2424,plain,
! [A: int] :
( ( ( A = zero_zero_int )
=> ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int ) )
& ( ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(260,axiom,
( ( pls @ bit1 @ number267125858f_real )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_semiring__numeral__1__eq__1) ).
thf(1716,plain,
( ( pls @ bit1 @ number267125858f_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1717,plain,
( ( pls @ bit1 @ number267125858f_real )
= one_one_real ),
inference(lifteq,[status(thm)],[1716]) ).
thf(3676,plain,
( ( zero_zero_int @ bit1 @ number267125858f_real )
= one_one_real ),
inference(rewrite,[status(thm)],[1717,3057]) ).
thf(383,axiom,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2137,plain,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(372,axiom,
! [A: int] :
( ( A @ ( one_one_int @ times_times_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_zmult__1) ).
thf(2103,plain,
! [A: int] :
( ( A @ ( one_one_int @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(184,axiom,
! [A: real] :
( ( one_one_real @ ( A @ times_times_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1405,plain,
! [A: real] :
( ( one_one_real @ ( A @ times_times_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(255,axiom,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_eq_int ) )
=> ( A @ ( B @ power_power_int ) @ ( one_one_int @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_one__le__power) ).
thf(1697,plain,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_eq_int ) )
=> ( A @ ( B @ power_power_int ) @ ( one_one_int @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(39,axiom,
! [A: real] :
( ( A @ ( zero_zero_real @ plus_plus_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(849,plain,
! [A: real] :
( ( A @ ( zero_zero_real @ plus_plus_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(647,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) ) )
=> ( ( zero_zero_int @ ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) @ ord_less_int ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( F @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( D @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( D @ ord_less_eq_int ) )
=> ( B @ ( E @ ord_less_eq_int ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_zdiv__mono2__neg__lemma) ).
thf(3211,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int] :
( ( ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) ) )
=> ( ( zero_zero_int @ ( F @ ( E @ ( D @ times_times_int ) @ plus_plus_int ) @ ord_less_int ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( F @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( D @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( D @ ord_less_eq_int ) )
=> ( B @ ( E @ ord_less_eq_int ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(440,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(2392,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(519,axiom,
~ ( zero_zero_int @ ( pls @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_bin__less__0__simps_I1_J) ).
thf(2718,plain,
~ ( zero_zero_int @ ( pls @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(700,axiom,
one_one_int @ ( zero_zero_int @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_int__0__less__1) ).
thf(3406,plain,
one_one_int @ ( zero_zero_int @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(193,axiom,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_power__le__imp__le__exp) ).
thf(1438,plain,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(141,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_real__add__mult__distrib) ).
thf(1199,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(128,axiom,
! [A: real] :
( ( zero_zero_real @ ( A @ plus_plus_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1153,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ plus_plus_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(675,axiom,
! [A: int,B: int,C: real] :
( ( C @ ( B @ number267125858f_real @ plus_plus_real ) @ ( A @ number267125858f_real @ plus_plus_real ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ number267125858f_real @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_add__number__of__left) ).
thf(3318,plain,
! [A: int,B: int,C: real] :
( ( C @ ( B @ number267125858f_real @ plus_plus_real ) @ ( A @ number267125858f_real @ plus_plus_real ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ number267125858f_real @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(368,axiom,
! [A: real] :
( ( A @ ( pls @ bit1 @ number267125858f_real @ times_times_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_mult__numeral__1) ).
thf(2093,plain,
! [A: real] :
( ( A @ ( pls @ bit1 @ number267125858f_real @ times_times_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(278,axiom,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_semiring__norm_I112_J) ).
thf(1783,plain,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(342,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( A @ number_number_of_int @ times_times_int ) @ ( B @ ( A @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_right__distrib__number__of) ).
thf(2011,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( A @ number_number_of_int @ times_times_int ) @ ( B @ ( A @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(619,axiom,
! [A: int] :
( ( A @ bit0 @ number_number_of_int )
= ( A @ number_number_of_int @ ( A @ number_number_of_int @ ( zero_zero_int @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_number__of__Bit0) ).
thf(3097,plain,
! [A: int] :
( ( A @ bit0 @ number_number_of_int )
= ( A @ number_number_of_int @ ( A @ number_number_of_int @ ( zero_zero_int @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(661,axiom,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_one__is__num__one) ).
thf(3265,plain,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(64,axiom,
! [A: real] :
( ( A @ ( one_one_real @ times_times_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(925,plain,
! [A: real] :
( ( A @ ( one_one_real @ times_times_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(336,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
<=> ( A != zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_zero__less__power2) ).
thf(1984,plain,
! [A: int] :
( ( ( A != zero_zero_int )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( A != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1985,plain,
( ! [A: int] :
( ( A != zero_zero_int )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( A != zero_zero_int ) ) ),
inference(miniscope,[status(thm)],[1984]) ).
thf(1986,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
| ( B = zero_zero_int ) )
& ( ( A != zero_zero_int )
| ~ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) ) ),
inference(cnf,[status(esa)],[1985]) ).
thf(1987,plain,
! [A: int] :
( ( A != zero_zero_int )
| ~ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) ),
inference(cnfConj,[status(thm)],[1986]) ).
thf(1989,plain,
! [A: int] :
( ~ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
| ( A != zero_zero_int ) ),
inference(lifteq,[status(thm)],[1987]) ).
thf(1990,plain,
~ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ),
inference(simp,[status(thm)],[1989]) ).
thf(5862,plain,
~ ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ),
inference(rewrite,[status(thm)],[1990,3057]) ).
thf(420,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_rel__simps_I17_J) ).
thf(2296,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(495,axiom,
! [A: int] :
( ( one_one_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( pls @ bit1 @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_less__special_I4_J) ).
thf(2621,plain,
! [A: int] :
( ( ( pls @ bit1 @ ( A @ ord_less_int ) )
=> ( one_one_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( one_one_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( pls @ bit1 @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(537,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( B @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( D @ plus_plus_int ) @ ( A @ ( C @ plus_plus_int ) @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_zcong__zadd) ).
thf(2790,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( B @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( D @ plus_plus_int ) @ ( A @ ( C @ plus_plus_int ) @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(505,axiom,
! [A: real,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) )
= ( B @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2660,plain,
! [A: real,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) )
= ( B @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(710,plain,
( ! [A: real,B: real] :
( ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_real ) ) )
& ! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
=> ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) ) ) ),
inference(miniscope,[status(thm)],[709]) ).
thf(711,plain,
! [D: real,C: real,B: real,A: real] :
( ( ( D @ ( C @ ord_less_eq_real ) )
| ~ ( zero_zero_real @ ( D @ ( C @ minus_minus_real ) @ ord_less_eq_real ) ) )
& ( ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) )
| ~ ( B @ ( A @ ord_less_eq_real ) ) ) ),
inference(cnf,[status(esa)],[710]) ).
thf(713,plain,
! [B: real,A: real] :
( ( B @ ( A @ ord_less_eq_real ) )
| ~ ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) ) ),
inference(cnfConj,[status(thm)],[711]) ).
thf(714,plain,
! [B: real,A: real] :
( ( B @ ( A @ ord_less_eq_real ) )
| ~ ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) ) ),
inference(simp,[status(thm)],[713]) ).
thf(302,axiom,
! [A: nat] :
( ( A @ ( A @ times_times_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(1868,plain,
! [A: nat] :
( ( A @ ( A @ times_times_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(357,axiom,
( ( pls @ number_number_of_int )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_number__of__Pls) ).
thf(2061,plain,
( ( pls @ number_number_of_int )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1887,plain,
( ! [A: real] :
( ( A = zero_zero_real )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real ) )
& ! [A: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(miniscope,[status(thm)],[1886]) ).
thf(1888,plain,
! [B: real,A: real] :
( ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) )
= zero_zero_real )
| ( B != zero_zero_real ) )
& ( ( A = zero_zero_real )
| ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
!= zero_zero_real ) ) ),
inference(cnf,[status(esa)],[1887]) ).
thf(1890,plain,
! [A: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real )
| ( A != zero_zero_real ) ),
inference(cnfConj,[status(thm)],[1888]) ).
thf(1892,plain,
! [A: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= zero_zero_real )
| ( A != zero_zero_real ) ),
inference(lifteq,[status(thm)],[1890]) ).
thf(1893,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ),
inference(simp,[status(thm)],[1892]) ).
thf(5281,plain,
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ),
inference(rewrite,[status(thm)],[1893,3057]) ).
thf(265,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_add__Bit0__Bit1) ).
thf(1730,plain,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(5471,plain,
! [B: int,A: int] :
( ( ( one_one_int @ ( zero_zero_int @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,757]) ).
thf(5472,plain,
! [B: int,A: int] :
( ( ( one_one_int @ ( zero_zero_int @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5471]) ).
thf(5473,plain,
zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_int ),
inference(pattern_uni,[status(thm)],[5472:[bind(A,$thf( zero_zero_int )),bind(B,$thf( one_one_int ))]]) ).
thf(5572,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5473,757]) ).
thf(5573,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5572]) ).
thf(5574,plain,
zero_zero_int @ ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ),
inference(pattern_uni,[status(thm)],[5573:[bind(A,$thf( one_one_int @ ( zero_zero_int @ minus_minus_int ) )),bind(B,$thf( zero_zero_int ))]]) ).
thf(746,plain,
! [B: int,A: int] :
( ( A != B )
| ~ ( B @ ( A @ ord_less_int ) ) ),
inference(cnfConj,[status(thm)],[744]) ).
thf(748,plain,
! [B: int,A: int] :
( ~ ( B @ ( A @ ord_less_int ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[746]) ).
thf(749,plain,
! [A: int] :
~ ( A @ ( A @ ord_less_int ) ),
inference(simp,[status(thm)],[748]) ).
thf(6184,plain,
! [A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5574,749]) ).
thf(6185,plain,
! [A: int] :
( ( zero_zero_int @ ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) ),
inference(simp,[status(thm)],[6184]) ).
thf(6191,plain,
! [A: int] :
( ( zero_zero_int != A )
| ( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) )
!= A ) ),
inference(simp,[status(thm)],[6185]) ).
thf(6200,plain,
( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) )
!= zero_zero_int ),
inference(simp,[status(thm)],[6191]) ).
thf(488,axiom,
! [A: real] :
( ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_mult__2) ).
thf(2589,plain,
! [A: real] :
( ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(33,axiom,
! [A: nat] :
( ( A @ ( A @ plus_plus_nat ) )
= ( A @ ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(825,plain,
! [A: nat] :
( ( A @ ( A @ plus_plus_nat ) )
= ( A @ ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(95,axiom,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( B @ times_times_real ) @ ( one_one_real @ ord_less_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_power__gt1__lemma) ).
thf(1042,plain,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( B @ times_times_real ) @ ( one_one_real @ ord_less_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(150,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) )
= ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1255,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) )
= ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ~ ( A @ ( zero_zero_int @ ( B @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_zcong__not__zero) ).
thf(820,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ~ ( A @ ( zero_zero_int @ ( B @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(589,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rel__simps_I31_J) ).
thf(2969,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(578,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Bit0__def) ).
thf(2937,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(784,plain,
! [B: real,A: real] :
( ( B @ ( A @ ord_less_eq_real ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[781]) ).
thf(787,plain,
! [B: real,A: real] :
( ( B @ ( A @ ord_less_eq_real ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[784]) ).
thf(788,plain,
! [A: real] : ( A @ ( A @ ord_less_eq_real ) ),
inference(simp,[status(thm)],[787]) ).
thf(347,axiom,
! [A: int,B: int] :
( ( A
= ( B @ ( A @ plus_plus_int ) ) )
<=> ( B = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_add__0__iff) ).
thf(2032,plain,
! [A: int,B: int] :
( ( ( B = zero_zero_int )
=> ( A
= ( B @ ( A @ plus_plus_int ) ) ) )
& ( ( A
= ( B @ ( A @ plus_plus_int ) ) )
=> ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(470,axiom,
! [A: real] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_zero__le__power2) ).
thf(2528,plain,
! [A: real] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(311,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ number_number_of_nat @ power_power_nat ) )
= ( A @ number_number_of_nat @ ( A @ number_number_of_nat @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of) ).
thf(1900,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ number_number_of_nat @ power_power_nat ) )
= ( A @ number_number_of_nat @ ( A @ number_number_of_nat @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(58,axiom,
! [A: real] :
( ( A @ ( zero_zero_real @ times_times_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(908,plain,
! [A: real] :
( ( A @ ( zero_zero_real @ times_times_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(909,plain,
! [A: real] :
( ( A @ ( zero_zero_real @ times_times_real ) )
= zero_zero_real ),
inference(cnf,[status(esa)],[908]) ).
thf(910,plain,
! [A: real] :
( ( A @ ( zero_zero_real @ times_times_real ) )
= zero_zero_real ),
inference(lifteq,[status(thm)],[909]) ).
thf(92,axiom,
! [A: int,B: int] :
( ( ( A @ number267125858f_real )
= ( B @ number267125858f_real ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_eq__number__of) ).
thf(1021,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( ( A @ number267125858f_real )
= ( B @ number267125858f_real ) ) )
& ( ( ( A @ number267125858f_real )
= ( B @ number267125858f_real ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ord_less_eq_nat ) )
=> ( ( A != B )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_order__le__neq__implies__less) ).
thf(776,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ord_less_eq_nat ) )
=> ( ( A != B )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(777,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ ord_less_nat ) )
| ( A = B )
| ~ ( B @ ( A @ ord_less_eq_nat ) ) ),
inference(cnf,[status(esa)],[776]) ).
thf(778,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ ord_less_nat ) )
| ~ ( B @ ( A @ ord_less_eq_nat ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[777]) ).
thf(174,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_real__mult__assoc) ).
thf(1355,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(413,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_semiring__add__number__of) ).
thf(2277,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(44,axiom,
! [A: int,B: int] :
( ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_le__number__of) ).
thf(862,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_eq_real ) ) )
& ( ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(5577,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5473,745]) ).
thf(5578,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[5577]) ).
thf(5579,plain,
zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_eq_int ),
inference(pattern_uni,[status(thm)],[5578:[bind(A,$thf( one_one_int @ ( zero_zero_int @ minus_minus_int ) )),bind(B,$thf( zero_zero_int ))]]) ).
thf(228,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( one_one_real @ ord_less_eq_real ) )
=> ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ ord_less_eq_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_power__increasing) ).
thf(1570,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( one_one_real @ ord_less_eq_real ) )
=> ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ ord_less_eq_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(133,axiom,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_real ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_real ) @ ( one_one_real @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_one__less__power) ).
thf(1174,plain,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_real ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_real ) @ ( one_one_real @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(251,axiom,
( one_one_nat
= ( pls @ bit1 @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(1676,plain,
( one_one_nat
= ( pls @ bit1 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(381,axiom,
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ legendre ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(2133,plain,
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ legendre ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(445,axiom,
! [A: int,B: int] :
( ( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) )
= zero_zero_int )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_sum__squares__eq__zero__iff) ).
thf(2414,plain,
! [A: int,B: int] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) )
= zero_zero_int ) )
& ( ( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) )
= zero_zero_int )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(657,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_less__eq__int__code_I15_J) ).
thf(3250,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(10,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(729,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(584,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_power__le__imp__le__exp) ).
thf(2958,plain,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(456,axiom,
! [A: int] :
( ( pls @ number_number_of_int @ ( A @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_add__numeral__0__right) ).
thf(2464,plain,
! [A: int] :
( ( pls @ number_number_of_int @ ( A @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(318,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number267125858f_real @ ( B @ number267125858f_real @ plus_plus_real ) )
= ( A @ ( B @ plus_plus_int ) @ number267125858f_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_semiring__add__number__of) ).
thf(1920,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number267125858f_real @ ( B @ number267125858f_real @ plus_plus_real ) )
= ( A @ ( B @ plus_plus_int ) @ number267125858f_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(617,axiom,
t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ twoSqu512355103sum2sq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(3090,plain,
t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ twoSqu512355103sum2sq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(135,axiom,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_real ) )
<=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_power__strict__increasing__iff) ).
thf(1178,plain,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( ( B @ ( A @ ord_less_nat ) )
=> ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_real ) ) )
& ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_real ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(35,axiom,
! [A: real] :
( ( zero_zero_real @ ( A @ ( A @ plus_plus_real ) @ ord_less_real ) )
<=> ( zero_zero_real @ ( A @ ord_less_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_even__less__0__iff) ).
thf(830,plain,
! [A: real] :
( ( ( zero_zero_real @ ( A @ ord_less_real ) )
=> ( zero_zero_real @ ( A @ ( A @ plus_plus_real ) @ ord_less_real ) ) )
& ( ( zero_zero_real @ ( A @ ( A @ plus_plus_real ) @ ord_less_real ) )
=> ( zero_zero_real @ ( A @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(130,axiom,
! [A: nat,B: real,C: nat,D: real] :
( ( D @ ( C @ ( B @ power_power_real ) @ dvd_dvd_real ) )
=> ( ( C @ ( A @ ord_less_eq_nat ) )
=> ( D @ ( A @ ( B @ power_power_real ) @ dvd_dvd_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_power__le__dvd) ).
thf(1159,plain,
! [A: nat,B: real,C: nat,D: real] :
( ( D @ ( C @ ( B @ power_power_real ) @ dvd_dvd_real ) )
=> ( ( C @ ( A @ ord_less_eq_nat ) )
=> ( D @ ( A @ ( B @ power_power_real ) @ dvd_dvd_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(280,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1787,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(428,axiom,
! [A: int,B: int] :
( ( ( A @ bit1 )
= ( B @ bit1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_rel__simps_I51_J) ).
thf(2327,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( ( A @ bit1 )
= ( B @ bit1 ) ) )
& ( ( ( A @ bit1 )
= ( B @ bit1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(374,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_zero__power2) ).
thf(2112,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(78,axiom,
! [A: int,B: int] :
( ( zero_zero_int @ ( B @ ( A @ zcong ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_IntPrimes_Ozcong__zero) ).
thf(974,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( zero_zero_int @ ( B @ ( A @ zcong ) ) ) )
& ( ( zero_zero_int @ ( B @ ( A @ zcong ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( ( A @ ( one_one_nat @ ord_less_nat ) )
=> ( C @ ( B @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_power__dvd__imp__le) ).
thf(852,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( ( A @ ( one_one_nat @ ord_less_nat ) )
=> ( C @ ( B @ ord_less_eq_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(506,axiom,
! [A: int] :
( ( A @ ( pls @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_add__Pls) ).
thf(2663,plain,
! [A: int] :
( ( A @ ( pls @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(223,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( B @ ( C @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ ord_less_eq_real ) )
<=> ( B @ ( A @ ord_less_eq_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_real__mult__le__cancel__iff2) ).
thf(1555,plain,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( ( B @ ( A @ ord_less_eq_real ) )
=> ( B @ ( C @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ ord_less_eq_real ) ) )
& ( ( B @ ( C @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(673,axiom,
~ ( pls @ ( pls @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rel__simps_I2_J) ).
thf(3314,plain,
~ ( pls @ ( pls @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(560,axiom,
! [A: int] :
( ( A @ bit1 @ number267125858f_real )
= ( A @ number267125858f_real @ ( A @ number267125858f_real @ ( one_one_real @ plus_plus_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_number__of__Bit1) ).
thf(2872,plain,
! [A: int] :
( ( A @ bit1 @ number267125858f_real )
= ( A @ number267125858f_real @ ( A @ number267125858f_real @ ( one_one_real @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(327,axiom,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_power2__le__imp__le) ).
thf(1951,plain,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ ord_less_eq_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(607,axiom,
! [A: int] :
( ( one_one_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( pls @ bit1 @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_le__special_I4_J) ).
thf(3050,plain,
! [A: int] :
( ( ( pls @ bit1 @ ( A @ ord_less_eq_int ) )
=> ( one_one_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( one_one_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( pls @ bit1 @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(476,axiom,
! [A: int] :
( ( A @ bit1 @ ( min @ minus_minus_int ) )
= ( A @ ( min @ minus_minus_int ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_diff__bin__simps_I6_J) ).
thf(2547,plain,
! [A: int] :
( ( A @ bit1 @ ( min @ minus_minus_int ) )
= ( A @ ( min @ minus_minus_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(424,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ~ ( A @ number_number_of_int @ ( B @ number_number_of_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(2313,plain,
! [A: int,B: int] :
( ( ~ ( A @ number_number_of_int @ ( B @ number_number_of_int @ ord_less_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ~ ( A @ number_number_of_int @ ( B @ number_number_of_int @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(4102,plain,
! [B: int,A: int] :
( ( ( t @ ( one_one_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[2925,741]) ).
thf(4103,plain,
! [B: int,A: int] :
( ( ( t @ ( one_one_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ( A = B ) ),
inference(simp,[status(thm)],[4102]) ).
thf(4104,plain,
( ( t @ ( one_one_int @ ord_less_int ) )
| ( t = one_one_int ) ),
inference(pattern_uni,[status(thm)],[4103:[bind(A,$thf( one_one_int )),bind(B,$thf( t ))]]) ).
thf(241,axiom,
! [A: int,B: int] :
( ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add1__zle__eq) ).
thf(1634,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) )
& ( ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(402,axiom,
! [A: int] :
( ( A @ ( zero_zero_int @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_zadd__0) ).
thf(2228,plain,
! [A: int] :
( ( A @ ( zero_zero_int @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1957,plain,
~ ? [A: int] :
( pls
= ( A @ bit1 ) ),
inference(miniscope,[status(thm)],[1956]) ).
thf(1958,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(cnf,[status(esa)],[1957]) ).
thf(1959,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(lifteq,[status(thm)],[1958]) ).
thf(3595,plain,
! [A: int] :
( ( A @ bit1 )
!= zero_zero_int ),
inference(rewrite,[status(thm)],[1959,3057]) ).
thf(532,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ dvd_dvd_nat ) )
=> ( ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ord_less_eq_nat ) )
| ( B = A )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_divides__cases) ).
thf(2769,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ dvd_dvd_nat ) )
=> ( ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ord_less_eq_nat ) )
| ( B = A )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(183,axiom,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( D @ ( B @ ( A @ times_times_real ) @ times_times_real ) @ ( C @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1402,plain,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( D @ ( B @ ( A @ times_times_real ) @ times_times_real ) @ ( C @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(371,axiom,
! [A: real] :
( ( pls @ number267125858f_real @ ( A @ plus_plus_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_add__numeral__0__right) ).
thf(2100,plain,
! [A: real] :
( ( pls @ number267125858f_real @ ( A @ plus_plus_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(287,axiom,
! [A: int] :
( ( one_one_nat @ ( A @ power_power_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_power__one__right) ).
thf(1804,plain,
! [A: int] :
( ( one_one_nat @ ( A @ power_power_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A != B )
& ( C != D ) )
<=> ( ( B @ ( D @ times_times_nat ) @ ( A @ ( C @ times_times_nat ) @ plus_plus_nat ) )
!= ( A @ ( D @ times_times_nat ) @ ( B @ ( C @ times_times_nat ) @ plus_plus_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_crossproduct__noteq) ).
thf(1121,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( B @ ( D @ times_times_nat ) @ ( A @ ( C @ times_times_nat ) @ plus_plus_nat ) )
!= ( A @ ( D @ times_times_nat ) @ ( B @ ( C @ times_times_nat ) @ plus_plus_nat ) ) )
=> ( ( A != B )
& ( C != D ) ) )
& ( ( ( A != B )
& ( C != D ) )
=> ( ( B @ ( D @ times_times_nat ) @ ( A @ ( C @ times_times_nat ) @ plus_plus_nat ) )
!= ( A @ ( D @ times_times_nat ) @ ( B @ ( C @ times_times_nat ) @ plus_plus_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(692,axiom,
( ( pls @ bit1 @ number267125858f_real )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_numeral__1__eq__1) ).
thf(3381,plain,
( ( pls @ bit1 @ number267125858f_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( B @ times_times_nat ) @ ( A @ ( B @ power_power_nat ) @ ord_less_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_power__less__power__Suc) ).
thf(1587,plain,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( B @ times_times_nat ) @ ( A @ ( B @ power_power_nat ) @ ord_less_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(220,axiom,
! [A: real,B: nat,C: real] :
( ( ( B @ ( A @ power_power_real ) )
= ( B @ ( C @ power_power_real ) ) )
=> ( ( A @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( C @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_power__eq__imp__eq__base) ).
thf(1540,plain,
! [A: real,B: nat,C: real] :
( ( ( B @ ( A @ power_power_real ) )
= ( B @ ( C @ power_power_real ) ) )
=> ( ( A @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( C @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(125,axiom,
! [A: real,B: real,C: int] :
( ( C @ number267125858f_real @ ( B @ ( A @ plus_plus_real ) @ times_times_real ) )
= ( C @ number267125858f_real @ ( B @ times_times_real ) @ ( C @ number267125858f_real @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_left__distrib__number__of) ).
thf(1138,plain,
! [A: real,B: real,C: int] :
( ( C @ number267125858f_real @ ( B @ ( A @ plus_plus_real ) @ times_times_real ) )
= ( C @ number267125858f_real @ ( B @ times_times_real ) @ ( C @ number267125858f_real @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(625,axiom,
! [A: int,B: int] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_power2__eq__imp__eq) ).
thf(3119,plain,
! [A: int,B: int] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(612,axiom,
! [A: int] :
( ( one_one_int @ ( A @ times_times_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3078,plain,
! [A: int] :
( ( one_one_int @ ( A @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(653,axiom,
! [A: int,B: int,C: int] :
( ( B @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( B @ ( C @ ( A @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3237,plain,
! [A: int,B: int,C: int] :
( ( B @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( B @ ( C @ ( A @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(645,axiom,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ minus_minus_nat ) )
= ( B @ ( A @ minus_minus_nat ) @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_diff__square) ).
thf(3205,plain,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ minus_minus_nat ) )
= ( B @ ( A @ minus_minus_nat ) @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ ord_less_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_power__strict__mono) ).
thf(989,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ ord_less_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(42,axiom,
! [A: int] : ( A @ ( A @ ord_less_eq_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zle__refl) ).
thf(857,plain,
! [A: int] : ( A @ ( A @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(176,axiom,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( ( A @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ) )
& ( ( A = zero_zero_nat )
=> ( ( A @ ( zero_zero_real @ power_power_real ) )
= one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_power__0__left) ).
thf(1360,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( ( A @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ) )
& ( ( A = zero_zero_nat )
=> ( ( A @ ( zero_zero_real @ power_power_real ) )
= one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(172,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) )
= ( C @ ( A @ times_times_nat ) @ ( B @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1350,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) )
= ( C @ ( A @ times_times_nat ) @ ( B @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(323,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_less__int__code_I15_J) ).
thf(1936,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(360,axiom,
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( s @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( s @ ord_less_int ) )
& ( s @ ( zero_zero_int @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_s0p) ).
thf(2069,plain,
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( s @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( s @ ord_less_int ) )
& ( s @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(2070,plain,
( ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( s @ ( s1 @ zcong ) ) )
& ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( s @ ord_less_int ) )
& ( s @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(cnf,[status(esa)],[2069]) ).
thf(2071,plain,
s @ ( zero_zero_int @ ord_less_eq_int ),
inference(cnfConj,[status(thm)],[2070]) ).
thf(3464,plain,
( ( ( s @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2071,3451]) ).
thf(3465,plain,
( ( s @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[3464]) ).
thf(3466,plain,
( ( s != min )
| ( zero_zero_int != zero_zero_int ) ),
inference(simp,[status(thm)],[3465]) ).
thf(3467,plain,
s != min,
inference(simp,[status(thm)],[3466]) ).
thf(155,axiom,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( D @ ( C @ times_times_real ) @ ( B @ times_times_real ) @ ( A @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1270,plain,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( D @ ( C @ times_times_real ) @ ( B @ times_times_real ) @ ( A @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(626,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( min @ number267125858f_real @ power_power_real ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_power__m1__even) ).
thf(3122,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( min @ number267125858f_real @ power_power_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(283,axiom,
( ( one_one_int @ ( s @ product_Pair_int_int ) @ twoSqu2107342101sum2sq )
= ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
thf(1794,plain,
( ( one_one_int @ ( s @ product_Pair_int_int ) @ twoSqu2107342101sum2sq )
= ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(328,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_zadd__0__right) ).
thf(1953,plain,
! [A: int] :
( ( zero_zero_int @ ( A @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(513,axiom,
! [A: real,B: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) )
= zero_zero_real )
<=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_realpow__two__sum__zero__iff) ).
thf(2685,plain,
! [A: real,B: real] :
( ( ( ( B = zero_zero_real )
& ( A = zero_zero_real ) )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) )
= zero_zero_real ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) )
= zero_zero_real )
=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(106,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
<=> ( A @ ( B @ dvd_dvd_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_zcong__eq__zdvd__prop) ).
thf(1082,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ dvd_dvd_int ) )
=> ( B @ ( zero_zero_int @ ( A @ zcong ) ) ) )
& ( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ( A @ ( B @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(631,axiom,
! [A: int,B: int] :
( ( ( B @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
<=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_power__eq__0__iff__number__of) ).
thf(3143,plain,
! [A: int,B: int] :
( ( ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_int ) )
=> ( ( B @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( B @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(324,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ ( A @ minus_minus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( A @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) @ minus_minus_int ) @ plus_plus_int ) @ minus_minus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_zdiff__power3) ).
thf(1942,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ ( A @ minus_minus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( A @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) @ minus_minus_int ) @ plus_plus_int ) @ minus_minus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(594,axiom,
( ( one_one_real @ ( one_one_real @ plus_plus_real ) )
= ( pls @ bit1 @ bit0 @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_one__add__one__is__two) ).
thf(3000,plain,
( ( one_one_real @ ( one_one_real @ plus_plus_real ) )
= ( pls @ bit1 @ bit0 @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(200,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( A != B )
& ( C = D ) )
=> ( ( A @ ( E @ times_times_nat ) @ ( C @ plus_plus_nat ) )
!= ( B @ ( E @ times_times_nat ) @ ( D @ plus_plus_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_add__scale__eq__noteq) ).
thf(1461,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E != zero_zero_nat )
=> ( ( ( A != B )
& ( C = D ) )
=> ( ( A @ ( E @ times_times_nat ) @ ( C @ plus_plus_nat ) )
!= ( B @ ( E @ times_times_nat ) @ ( D @ plus_plus_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(37,axiom,
! [A: real,B: nat] :
( ( ( A = one_one_real )
| ( B @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_real ) @ ( A @ dvd_dvd_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_dvd__power) ).
thf(839,plain,
! [A: real,B: nat] :
( ( ( A = one_one_real )
| ( B @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_real ) @ ( A @ dvd_dvd_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(840,plain,
! [B: nat,A: real] :
( ( ( B @ ( A @ power_power_real ) @ ( A @ dvd_dvd_real ) )
| ( A != one_one_real ) )
& ( ( B @ ( A @ power_power_real ) @ ( A @ dvd_dvd_real ) )
| ~ ( B @ ( zero_zero_nat @ ord_less_nat ) ) ) ),
inference(cnf,[status(esa)],[839]) ).
thf(842,plain,
! [B: nat,A: real] :
( ( B @ ( A @ power_power_real ) @ ( A @ dvd_dvd_real ) )
| ( A != one_one_real ) ),
inference(cnfConj,[status(thm)],[840]) ).
thf(843,plain,
! [B: nat,A: real] :
( ( B @ ( A @ power_power_real ) @ ( A @ dvd_dvd_real ) )
| ( A != one_one_real ) ),
inference(lifteq,[status(thm)],[842]) ).
thf(844,plain,
! [A: nat] : ( A @ ( one_one_real @ power_power_real ) @ ( one_one_real @ dvd_dvd_real ) ),
inference(simp,[status(thm)],[843]) ).
thf(160,axiom,
! [A: nat] :
( ( A @ ( one_one_real @ power_power_real ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_power__one) ).
thf(1299,plain,
! [A: nat] :
( ( A @ ( one_one_real @ power_power_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1300,plain,
! [A: nat] :
( ( A @ ( one_one_real @ power_power_real ) )
= one_one_real ),
inference(cnf,[status(esa)],[1299]) ).
thf(1301,plain,
! [A: nat] :
( ( A @ ( one_one_real @ power_power_real ) )
= one_one_real ),
inference(lifteq,[status(thm)],[1300]) ).
thf(6642,plain,
one_one_real @ ( one_one_real @ dvd_dvd_real ),
inference(rewrite,[status(thm)],[844,1301]) ).
thf(188,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( one_one_nat @ ( A @ ord_less_nat ) )
=> ( B @ ( A @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ ord_less_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_power__strict__decreasing) ).
thf(1424,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( one_one_nat @ ( A @ ord_less_nat ) )
=> ( B @ ( A @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ ord_less_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(363,axiom,
( zero_zero_nat
= ( pls @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_semiring__norm_I113_J) ).
thf(2080,plain,
( zero_zero_nat
= ( pls @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(493,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ bit0 @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_bin__less__0__simps_I3_J) ).
thf(2613,plain,
! [A: int] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ bit0 @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(289,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( A @ ( C @ plus_plus_int ) @ ( A @ ( B @ plus_plus_int ) @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_zcong__shift) ).
thf(1810,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( A @ ( C @ plus_plus_int ) @ ( A @ ( B @ plus_plus_int ) @ zcong ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(642,axiom,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ord_less_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_power2__less__imp__less) ).
thf(3194,plain,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ord_less_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(196,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ plus_plus_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1446,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ plus_plus_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(507,axiom,
! [A: int,B: int,C: int] :
( ~ ( C @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( ( C @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ zcong ) ) )
=> ~ ( A @ ( C @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_Euler_Oaux____1) ).
thf(2666,plain,
! [A: int,B: int,C: int] :
( ~ ( C @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( ( C @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ zcong ) ) )
=> ~ ( A @ ( C @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(669,axiom,
! [A: int] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_power__0__left__number__of) ).
thf(3294,plain,
! [A: int] :
( ( ( ( A @ number_number_of_nat )
!= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( ( A @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(4,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_real ) )
= ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_power__add) ).
thf(706,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_real ) )
= ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(672,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( A @ times_times_int ) )
= ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_cube__square) ).
thf(3311,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( A @ times_times_int ) )
= ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(562,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_odd__less__0) ).
thf(2877,plain,
! [A: int] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(574,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_rel__simps_I37_J) ).
thf(2926,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(2927,plain,
pls != min,
inference(polarity_switch,[status(thm)],[2926]) ).
thf(2928,plain,
pls != min,
inference(lifteq,[status(thm)],[2927]) ).
thf(3407,plain,
min != zero_zero_int,
inference(rewrite,[status(thm)],[2928,3057]) ).
thf(15,axiom,
! [A: int,B: int] :
( ( B @ ( A @ dvd_dvd_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_zdvd__imp__le) ).
thf(752,plain,
! [A: int,B: int] :
( ( B @ ( A @ dvd_dvd_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(753,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_eq_int ) )
| ~ ( B @ ( zero_zero_int @ ord_less_int ) )
| ~ ( B @ ( A @ dvd_dvd_int ) ) ),
inference(cnf,[status(esa)],[752]) ).
thf(548,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ times_times_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2830,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ times_times_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(136,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_eq_int ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(1182,plain,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_eq_int ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( D @ ( C @ times_times_nat ) @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1016,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( D @ ( C @ times_times_nat ) @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(365,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_zcong__scalar2) ).
thf(2085,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ zcong ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(238,axiom,
one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ dvd_dvd_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(1612,plain,
one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ dvd_dvd_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(591,axiom,
! [A: int] :
( ( A @ zprime )
<=> ( ! [B: int] :
( ( ( A @ ( B @ dvd_dvd_int ) )
& ( B @ ( zero_zero_int @ ord_less_eq_int ) ) )
=> ( ( B = A )
| ( B = one_one_int ) ) )
& ( A @ ( one_one_int @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_zprime__def) ).
thf(2978,plain,
! [A: int] :
( ( ( ! [B: int] :
( ( ( A @ ( B @ dvd_dvd_int ) )
& ( B @ ( zero_zero_int @ ord_less_eq_int ) ) )
=> ( ( B = A )
| ( B = one_one_int ) ) )
& ( A @ ( one_one_int @ ord_less_int ) ) )
=> ( A @ zprime ) )
& ( ( A @ zprime )
=> ( ! [B: int] :
( ( ( A @ ( B @ dvd_dvd_int ) )
& ( B @ ( zero_zero_int @ ord_less_eq_int ) ) )
=> ( ( B = A )
| ( B = one_one_int ) ) )
& ( A @ ( one_one_int @ ord_less_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(459,axiom,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_semiring__one__add__one__is__two) ).
thf(2472,plain,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(655,axiom,
( ( pls @ bit1 @ number_number_of_int )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_numeral__1__eq__1) ).
thf(3242,plain,
( ( pls @ bit1 @ number_number_of_int )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(85,axiom,
! [A: real,B: real] :
( ( B @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) )
= ( B @ ( one_one_real @ ( A @ plus_plus_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(997,plain,
! [A: real,B: real] :
( ( B @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) )
= ( B @ ( one_one_real @ ( A @ plus_plus_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(473,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_int ) )
<=> ( A @ ( pls @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_less__special_I1_J) ).
thf(2536,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_int ) )
=> ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( pls @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(12,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( B @ ( C @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(736,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( B @ ( C @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(737,plain,
! [C: real,B: real,A: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( B @ ( C @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(cnf,[status(esa)],[736]) ).
thf(738,plain,
! [C: real,B: real,A: real] :
( ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( B @ ( C @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(lifteq,[status(thm)],[737]) ).
thf(551,axiom,
! [A: int,B: int] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_sum__power2__eq__zero__iff) ).
thf(2836,plain,
! [A: int,B: int] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(464,axiom,
! [A: int,B: nat] :
( ( A @ ( B @ ( A @ power_power_int ) @ times_times_int ) )
= ( B @ ( A @ power_power_int ) @ ( A @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_power__commutes) ).
thf(2487,plain,
! [A: int,B: nat] :
( ( A @ ( B @ ( A @ power_power_int ) @ times_times_int ) )
= ( B @ ( A @ power_power_int ) @ ( A @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(684,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(3354,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(248,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_quartic__square__square) ).
thf(1668,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(485,axiom,
! [A: int,B: int] :
( ( B @ ( A @ bit0 @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_mult__Bit0) ).
thf(2581,plain,
! [A: int,B: int] :
( ( B @ ( A @ bit0 @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(480,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_power2__less__imp__less) ).
thf(2566,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(544,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_nat__mult__2) ).
thf(2813,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(353,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_zmult__zless__mono2) ).
thf(2052,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(146,axiom,
! [A: real] :
( ~ ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_not__real__square__gt__zero) ).
thf(1229,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ~ ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) ) )
& ( ~ ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1230,plain,
( ! [A: real] :
( ( A = zero_zero_real )
=> ~ ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) ) )
& ! [A: real] :
( ~ ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) )
=> ( A = zero_zero_real ) ) ),
inference(miniscope,[status(thm)],[1229]) ).
thf(1231,plain,
! [B: real,A: real] :
( ( ~ ( B @ ( B @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) )
| ( B != zero_zero_real ) )
& ( ( A = zero_zero_real )
| ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) ) ) ),
inference(cnf,[status(esa)],[1230]) ).
thf(1233,plain,
! [A: real] :
( ~ ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) )
| ( A != zero_zero_real ) ),
inference(cnfConj,[status(thm)],[1231]) ).
thf(1235,plain,
! [A: real] :
( ~ ( A @ ( A @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) )
| ( A != zero_zero_real ) ),
inference(lifteq,[status(thm)],[1233]) ).
thf(1236,plain,
~ ( zero_zero_real @ ( zero_zero_real @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) ),
inference(simp,[status(thm)],[1235]) ).
thf(21,axiom,
! [A: real] :
( ( zero_zero_real @ ( A @ times_times_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(771,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ times_times_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(772,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ times_times_real ) )
= zero_zero_real ),
inference(cnf,[status(esa)],[771]) ).
thf(773,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ times_times_real ) )
= zero_zero_real ),
inference(lifteq,[status(thm)],[772]) ).
thf(3920,plain,
~ ( zero_zero_real @ ( zero_zero_real @ ord_less_real ) ),
inference(rewrite,[status(thm)],[1236,773]) ).
thf(166,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_real__zero__not__eq__one) ).
thf(1324,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(416,axiom,
! [A: int] :
( ( A @ number267125858f_real @ ( one_one_real @ ord_less_eq_real ) )
<=> ( A @ ( pls @ bit1 @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__special_I2_J) ).
thf(2285,plain,
! [A: int] :
( ( ( A @ ( pls @ bit1 @ ord_less_eq_int ) )
=> ( A @ number267125858f_real @ ( one_one_real @ ord_less_eq_real ) ) )
& ( ( A @ number267125858f_real @ ( one_one_real @ ord_less_eq_real ) )
=> ( A @ ( pls @ bit1 @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(204,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( C @ times_times_nat ) @ ( A @ ( B @ times_times_nat ) @ dvd_dvd_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_divides__mul__r) ).
thf(1478,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( C @ times_times_nat ) @ ( A @ ( B @ times_times_nat ) @ dvd_dvd_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(468,axiom,
! [A: int] :
( ( one_one_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
<=> ( pls @ bit1 @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_le__special_I4_J) ).
thf(2519,plain,
! [A: int] :
( ( ( pls @ bit1 @ ( A @ ord_less_eq_int ) )
=> ( one_one_real @ ( A @ number267125858f_real @ ord_less_eq_real ) ) )
& ( ( one_one_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
=> ( pls @ bit1 @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(80,axiom,
! [A: nat,B: real] :
( ( B @ ( zero_zero_real @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( zero_zero_real @ ord_less_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_zero__less__power) ).
thf(984,plain,
! [A: nat,B: real] :
( ( B @ ( zero_zero_real @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( zero_zero_real @ ord_less_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ dvd_dvd_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_divides__exp) ).
thf(911,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ dvd_dvd_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(334,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1979,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(596,axiom,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_number__of__is__id) ).
thf(3005,plain,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(384,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2140,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(600,axiom,
! [A: int,B: nat] :
( ( ( A = one_one_int )
| ( B @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_int ) @ ( A @ dvd_dvd_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_dvd__power) ).
thf(3023,plain,
! [A: int,B: nat] :
( ( ( A = one_one_int )
| ( B @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_int ) @ ( A @ dvd_dvd_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(3024,plain,
! [B: nat,A: int] :
( ( ( B @ ( A @ power_power_int ) @ ( A @ dvd_dvd_int ) )
| ( A != one_one_int ) )
& ( ( B @ ( A @ power_power_int ) @ ( A @ dvd_dvd_int ) )
| ~ ( B @ ( zero_zero_nat @ ord_less_nat ) ) ) ),
inference(cnf,[status(esa)],[3023]) ).
thf(3026,plain,
! [B: nat,A: int] :
( ( B @ ( A @ power_power_int ) @ ( A @ dvd_dvd_int ) )
| ( A != one_one_int ) ),
inference(cnfConj,[status(thm)],[3024]) ).
thf(3027,plain,
! [B: nat,A: int] :
( ( B @ ( A @ power_power_int ) @ ( A @ dvd_dvd_int ) )
| ( A != one_one_int ) ),
inference(lifteq,[status(thm)],[3026]) ).
thf(3028,plain,
! [A: nat] : ( A @ ( one_one_int @ power_power_int ) @ ( one_one_int @ dvd_dvd_int ) ),
inference(simp,[status(thm)],[3027]) ).
thf(6988,plain,
one_one_int @ ( one_one_int @ dvd_dvd_int ),
inference(rewrite,[status(thm)],[3028,2010]) ).
thf(614,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_int @ power_power_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(3083,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_int @ power_power_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(636,axiom,
! [A: int,B: int] :
( ( ( A @ number_number_of_int )
= B )
<=> ( B
= ( A @ number_number_of_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_number__of__reorient) ).
thf(3162,plain,
! [A: int,B: int] :
( ( ( B
= ( A @ number_number_of_int ) )
=> ( ( A @ number_number_of_int )
= B ) )
& ( ( ( A @ number_number_of_int )
= B )
=> ( B
= ( A @ number_number_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_eq_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( one_one_nat @ ord_less_eq_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_one__le__power) ).
thf(1333,plain,
! [A: nat,B: nat] :
( ( B @ ( one_one_nat @ ord_less_eq_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( one_one_nat @ ord_less_eq_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(536,axiom,
! [A: nat,B: nat,C: int,D: int] :
( ( D @ ( C @ dvd_dvd_int ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( D @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_dvd__power__le) ).
thf(2788,plain,
! [A: nat,B: nat,C: int,D: int] :
( ( D @ ( C @ dvd_dvd_int ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( D @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(142,axiom,
! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
=> ( ( A != B )
=> ( B @ ( A @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_order__le__neq__implies__less) ).
thf(1202,plain,
! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
=> ( ( A != B )
=> ( B @ ( A @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(563,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_times__numeral__code_I5_J) ).
thf(2883,plain,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(676,axiom,
! [A: int] :
( ( A @ number267125858f_real @ ( zero_zero_real @ ord_less_real ) )
<=> ( A @ ( pls @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_less__special_I1_J) ).
thf(3321,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_int ) )
=> ( A @ number267125858f_real @ ( zero_zero_real @ ord_less_real ) ) )
& ( ( A @ number267125858f_real @ ( zero_zero_real @ ord_less_real ) )
=> ( A @ ( pls @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(104,axiom,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_power__0__left) ).
thf(1071,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(138,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) )
= ( C @ ( A @ times_times_real ) @ ( B @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1187,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) )
= ( C @ ( A @ times_times_real ) @ ( B @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(569,axiom,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) )
= ( A @ ( B @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_zmult__commute) ).
thf(2909,plain,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) )
= ( A @ ( B @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(349,axiom,
! [A: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_power2__less__0) ).
thf(2043,plain,
! [A: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(665,axiom,
! [A: int] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_zero__eq__power2) ).
thf(3279,plain,
! [A: int] :
( ( ( A = zero_zero_int )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( one_one_nat @ ( A @ plus_plus_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(765,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( one_one_nat @ ( A @ plus_plus_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(298,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
<=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_sum__power2__gt__zero__iff) ).
thf(1846,plain,
! [A: int,B: int] :
( ( ( ( B != zero_zero_int )
| ( A != zero_zero_int ) )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(444,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__special_I3_J) ).
thf(2408,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(641,axiom,
! [A: int,B: int] :
( ( A @ bit1 )
!= ( B @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_rel__simps_I50_J) ).
thf(3190,plain,
! [A: int,B: int] :
( ( A @ bit1 )
!= ( B @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(501,axiom,
! [A: nat] : ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ power_power_real ) @ ( one_one_real @ ord_less_eq_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_two__realpow__ge__one) ).
thf(2645,plain,
! [A: nat] : ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ power_power_real ) @ ( one_one_real @ ord_less_eq_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(395,axiom,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) @ number267125858f_real )
= ( B @ number267125858f_real @ ( A @ number267125858f_real @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_number__of__mult) ).
thf(2189,plain,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) @ number267125858f_real )
= ( B @ number267125858f_real @ ( A @ number267125858f_real @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(377,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_less__eq__int__code_I14_J) ).
thf(2121,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( B @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( ( C @ ( A @ ord_less_eq_nat ) )
=> ( D @ ( A @ ( B @ power_power_nat ) @ dvd_dvd_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_power__le__dvd) ).
thf(1135,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( B @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( ( C @ ( A @ ord_less_eq_nat ) )
=> ( D @ ( A @ ( B @ power_power_nat ) @ dvd_dvd_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(392,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_rel__simps_I38_J) ).
thf(2176,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(418,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s1 @ power_power_int ) @ zcong ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_s1) ).
thf(2292,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s1 @ power_power_int ) @ zcong ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(113,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ minus_minus_int ) @ ( A @ dvd_dvd_int ) )
=> ( ( C @ ( A @ dvd_dvd_int ) )
=> ( B @ ( A @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_zdvd__zdiffD) ).
thf(1103,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ minus_minus_int ) @ ( A @ dvd_dvd_int ) )
=> ( ( C @ ( A @ dvd_dvd_int ) )
=> ( B @ ( A @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(604,axiom,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( B @ times_times_int ) @ ( A @ ( B @ power_power_int ) @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_power__less__power__Suc) ).
thf(3042,plain,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( B @ times_times_int ) @ ( A @ ( B @ power_power_int ) @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1273,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) )
= ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(660,axiom,
! [A: int] :
( ( one_one_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__special_I3_J) ).
thf(3262,plain,
! [A: int] :
( ( one_one_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(634,axiom,
! [A: real,B: nat] : ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_zero__le__even__power_H) ).
thf(3158,plain,
! [A: real,B: nat] : ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(158,axiom,
! [A: real,B: real] :
( ( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) )
= zero_zero_real )
<=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_real__two__squares__add__zero__iff) ).
thf(1278,plain,
! [A: real,B: real] :
( ( ( ( B = zero_zero_real )
& ( A = zero_zero_real ) )
=> ( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) )
= zero_zero_real )
=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(314,axiom,
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
= ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_t) ).
thf(1906,plain,
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
= ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(408,axiom,
! [A: int] :
( ( A @ bit1 @ ( min @ ord_less_eq_int ) )
<=> ( A @ ( min @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_rel__simps_I26_J) ).
thf(2253,plain,
! [A: int] :
( ( ( A @ ( min @ ord_less_eq_int ) )
=> ( A @ bit1 @ ( min @ ord_less_eq_int ) ) )
& ( ( A @ bit1 @ ( min @ ord_less_eq_int ) )
=> ( A @ ( min @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(482,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( A @ ( C @ times_times_int ) @ ( A @ ( B @ times_times_int ) @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_zcong__scalar) ).
thf(2570,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( A @ ( C @ times_times_int ) @ ( A @ ( B @ times_times_int ) @ zcong ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(580,axiom,
! [A: int,B: int] :
( ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_zle__diff1__eq) ).
thf(2941,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ ord_less_eq_int ) ) )
& ( ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(667,axiom,
( zero_zero_real
= ( pls @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_semiring__norm_I112_J) ).
thf(3289,plain,
( zero_zero_real
= ( pls @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(3523,plain,
zero_zero_int @ ( min @ ord_less_eq_int ),
inference(rewrite,[status(thm)],[2291,3057]) ).
thf(88,axiom,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( ( A @ ( C @ power_power_real ) )
= ( B @ ( C @ power_power_real ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_power__inject__exp) ).
thf(1007,plain,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( ( A = B )
=> ( ( A @ ( C @ power_power_real ) )
= ( B @ ( C @ power_power_real ) ) ) )
& ( ( ( A @ ( C @ power_power_real ) )
= ( B @ ( C @ power_power_real ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ power_power_nat ) )
= one_one_nat )
<=> ( ( B = zero_zero_nat )
| ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_exp__eq__1) ).
thf(1389,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = one_one_nat ) )
=> ( ( B @ ( A @ power_power_nat ) )
= one_one_nat ) )
& ( ( ( B @ ( A @ power_power_nat ) )
= one_one_nat )
=> ( ( B = zero_zero_nat )
| ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(654,axiom,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_semiring__one__add__one__is__two) ).
thf(3240,plain,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(2081,plain,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[2080]) ).
thf(3472,plain,
( ( zero_zero_int @ number_number_of_nat )
= zero_zero_nat ),
inference(rewrite,[status(thm)],[2081,3057]) ).
thf(270,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ ( A @ plus_plus_int ) @ ord_less_int ) )
<=> ( zero_zero_int @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_even__less__0__iff) ).
thf(1752,plain,
! [A: int] :
( ( ( zero_zero_int @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ( A @ plus_plus_int ) @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ ( A @ plus_plus_int ) @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(218,axiom,
! [A: real,B: real] :
( ( A @ ( B @ times_times_real ) @ ( A @ plus_plus_real ) )
= ( A @ ( one_one_real @ ( B @ plus_plus_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1535,plain,
! [A: real,B: real] :
( ( A @ ( B @ times_times_real ) @ ( A @ plus_plus_real ) )
= ( A @ ( one_one_real @ ( B @ plus_plus_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(257,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ number267125858f_real @ power_power_real ) )
= ( A @ number267125858f_real @ ( A @ number267125858f_real @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_power2__eq__square__number__of) ).
thf(1701,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ number267125858f_real @ power_power_real ) )
= ( A @ number267125858f_real @ ( A @ number267125858f_real @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(547,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) )
= ( A @ ( A @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_power2__eq__square) ).
thf(2827,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) )
= ( A @ ( A @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(652,axiom,
! [A: int] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) )
= ( A @ ( A @ ( A @ times_times_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_power3__eq__cube) ).
thf(3234,plain,
! [A: int] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_int ) )
= ( A @ ( A @ ( A @ times_times_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(351,axiom,
pls @ ( min @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_rel__simps_I6_J) ).
thf(2048,plain,
pls @ ( min @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( D @ ( C @ ( B @ times_times_nat ) @ plus_plus_nat ) ) )
=> ( ( D @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( C @ ( D @ ord_less_nat ) )
=> ~ ( A @ ( C @ dvd_dvd_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_divides__div__not) ).
thf(732,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( D @ ( C @ ( B @ times_times_nat ) @ plus_plus_nat ) ) )
=> ( ( D @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( C @ ( D @ ord_less_nat ) )
=> ~ ( A @ ( C @ dvd_dvd_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(307,axiom,
! [A: int] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ ord_less_int ) )
=> ~ ( A @ ( min @ number_number_of_int @ ( one_one_int @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_one__not__neg__one__mod__m) ).
thf(1884,plain,
! [A: int] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ ord_less_int ) )
=> ~ ( A @ ( min @ number_number_of_int @ ( one_one_int @ zcong ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(469,axiom,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_real ) @ power_power_real ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) @ times_times_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_real__sum__squared__expand) ).
thf(2525,plain,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_real ) @ power_power_real ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) @ times_times_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(504,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( D @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2657,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( D @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(553,axiom,
! [A: int,B: int] :
( ( B @ ( one_one_int @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ times_times_int ) @ zcong ) ) )
<=> ( B @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_inv__not__p__minus__1__aux) ).
thf(2849,plain,
! [A: int,B: int] :
( ( ( B @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ zcong ) ) )
=> ( B @ ( one_one_int @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ times_times_int ) @ zcong ) ) ) )
& ( ( B @ ( one_one_int @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ times_times_int ) @ zcong ) ) )
=> ( B @ ( one_one_int @ ( B @ minus_minus_int ) @ ( A @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(245,axiom,
! [A: real,B: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_real ) )
<=> ( ( B != zero_zero_real )
| ( A != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_sum__power2__gt__zero__iff) ).
thf(1652,plain,
! [A: real,B: real] :
( ( ( ( B != zero_zero_real )
| ( A != zero_zero_real ) )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_real ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_real ) )
=> ( ( B != zero_zero_real )
| ( A != zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(613,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_int ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_power__less__imp__less__exp) ).
thf(3081,plain,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_int ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(510,axiom,
! [A: int] :
( ( one_one_real @ ( A @ number267125858f_real @ ord_less_real ) )
<=> ( pls @ bit1 @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_less__special_I4_J) ).
thf(2674,plain,
! [A: int] :
( ( ( pls @ bit1 @ ( A @ ord_less_int ) )
=> ( one_one_real @ ( A @ number267125858f_real @ ord_less_real ) ) )
& ( ( one_one_real @ ( A @ number267125858f_real @ ord_less_real ) )
=> ( pls @ bit1 @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(481,axiom,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_semiring__numeral__0__eq__0) ).
thf(2568,plain,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(215,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ power_power_nat ) )
= ( C @ ( B @ ( A @ power_power_nat ) @ power_power_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_power__mult) ).
thf(1520,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ power_power_nat ) )
= ( C @ ( B @ ( A @ power_power_nat ) @ power_power_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(699,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( one_one_int @ ord_less_eq_int ) )
=> ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_power__increasing) ).
thf(3404,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( one_one_int @ ord_less_eq_int ) )
=> ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(514,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ dvd_dvd_int ) )
=> ( ( C @ ( B @ plus_plus_int ) @ ( D @ dvd_dvd_int ) )
<=> ( C @ ( E @ ( A @ times_times_int ) @ ( B @ plus_plus_int ) @ plus_plus_int ) @ ( D @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_zdvd__period) ).
thf(2695,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ dvd_dvd_int ) )
=> ( ( ( C @ ( E @ ( A @ times_times_int ) @ ( B @ plus_plus_int ) @ plus_plus_int ) @ ( D @ dvd_dvd_int ) )
=> ( C @ ( B @ plus_plus_int ) @ ( D @ dvd_dvd_int ) ) )
& ( ( C @ ( B @ plus_plus_int ) @ ( D @ dvd_dvd_int ) )
=> ( C @ ( E @ ( A @ times_times_int ) @ ( B @ plus_plus_int ) @ plus_plus_int ) @ ( D @ dvd_dvd_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(145,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ times_times_nat ) @ ( A @ plus_plus_nat ) )
= ( A @ ( one_one_nat @ ( B @ plus_plus_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1226,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ times_times_nat ) @ ( A @ plus_plus_nat ) )
= ( A @ ( one_one_nat @ ( B @ plus_plus_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(208,axiom,
! [A: real] :
( ( one_one_nat @ ( A @ power_power_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_power__one__right) ).
thf(1488,plain,
! [A: real] :
( ( one_one_nat @ ( A @ power_power_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(419,axiom,
( ( pls @ number_number_of_int )
!= ( min @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_eq__number__of__Pls__Min) ).
thf(2293,plain,
( ( pls @ number_number_of_int )
!= ( min @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1672,plain,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
inference(lifteq,[status(thm)],[1671]) ).
thf(3651,plain,
( ( zero_zero_int @ bit1 @ number_number_of_nat )
= one_one_nat ),
inference(rewrite,[status(thm)],[1672,3057]) ).
thf(646,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_zadd__zmult__distrib) ).
thf(3208,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1106,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
inference(cnf,[status(esa)],[1105]) ).
thf(1107,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
inference(lifteq,[status(thm)],[1106]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
<=> ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_nat__zero__less__power__iff) ).
thf(868,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ) )
& ( ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ord_less_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(869,plain,
( ! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ord_less_nat ) ) )
=> ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ) )
& ! [A: nat,B: nat] :
( ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ord_less_nat ) ) ) ) ),
inference(miniscope,[status(thm)],[868]) ).
thf(870,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( D @ ( C @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
| ( D != zero_zero_nat ) )
& ( ( D @ ( C @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
| ~ ( C @ ( zero_zero_nat @ ord_less_nat ) ) )
& ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ord_less_nat ) )
| ~ ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ) ) ),
inference(cnf,[status(esa)],[869]) ).
thf(873,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
| ( B != zero_zero_nat ) ),
inference(cnfConj,[status(thm)],[870]) ).
thf(876,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) )
| ( B != zero_zero_nat ) ),
inference(lifteq,[status(thm)],[873]) ).
thf(877,plain,
! [A: nat] : ( zero_zero_nat @ ( A @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ),
inference(simp,[status(thm)],[876]) ).
thf(6649,plain,
one_one_nat @ ( zero_zero_nat @ ord_less_nat ),
inference(rewrite,[status(thm)],[877,1269]) ).
thf(528,axiom,
! [A: int,B: int] : ( one_one_int @ ( B @ ( A @ zcong ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_zcong__1) ).
thf(2753,plain,
! [A: int,B: int] : ( one_one_int @ ( B @ ( A @ zcong ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(2113,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
inference(lifteq,[status(thm)],[2112]) ).
thf(5703,plain,
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
inference(rewrite,[status(thm)],[2113,3057]) ).
thf(108,axiom,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( D @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1090,plain,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( D @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(670,axiom,
! [A: int,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ power_power_int ) @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_power__even__eq) ).
thf(3302,plain,
! [A: int,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ power_power_int ) @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(425,axiom,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_nat ) @ power_power_nat ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ times_times_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ plus_plus_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__sum) ).
thf(2319,plain,
! [A: nat,B: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_nat ) @ power_power_nat ) )
= ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ times_times_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_nat ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_nat ) @ plus_plus_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(595,axiom,
! [A: int] :
( ( A @ zprime )
=> ( ( A
!= ( pls @ bit1 @ bit0 @ number_number_of_int ) )
=> ( ( A
!= ( pls @ bit1 @ bit1 @ number_number_of_int ) )
=> ( A @ ( pls @ bit1 @ bit0 @ bit1 @ number_number_of_int @ ord_less_eq_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_prime__g__5) ).
thf(3002,plain,
! [A: int] :
( ( A @ zprime )
=> ( ( A
!= ( pls @ bit1 @ bit0 @ number_number_of_int ) )
=> ( ( A
!= ( pls @ bit1 @ bit1 @ number_number_of_int ) )
=> ( A @ ( pls @ bit1 @ bit0 @ bit1 @ number_number_of_int @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(266,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ( zero_zero_real @ ord_less_real ) )
<=> ( A != zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_zero__less__power2) ).
thf(1733,plain,
! [A: real] :
( ( ( A != zero_zero_real )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ( zero_zero_real @ ord_less_real ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ( zero_zero_real @ ord_less_real ) )
=> ( A != zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(679,axiom,
one_one_int @ ( zero_zero_int @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(3331,plain,
one_one_int @ ( zero_zero_int @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(3591,plain,
( ( ( min @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( one_one_int @ ( zero_zero_int @ ord_less_eq_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3331,3451]) ).
thf(3592,plain,
( ( min @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( one_one_int @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[3591]) ).
thf(3593,plain,
( ( min != one_one_int )
| ( zero_zero_int != zero_zero_int ) ),
inference(simp,[status(thm)],[3592]) ).
thf(3594,plain,
min != one_one_int,
inference(simp,[status(thm)],[3593]) ).
thf(338,axiom,
( ( one_one_real @ ( one_one_real @ plus_plus_real ) )
= ( pls @ bit1 @ bit0 @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_semiring__one__add__one__is__two) ).
thf(1997,plain,
( ( one_one_real @ ( one_one_real @ plus_plus_real ) )
= ( pls @ bit1 @ bit0 @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(310,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ minus_minus_int ) )
= ( B @ ( A @ minus_minus_int ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_diff__bin__simps_I10_J) ).
thf(1897,plain,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ minus_minus_int ) )
= ( B @ ( A @ minus_minus_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_real ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__number__of) ).
thf(919,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_real ) ) )
& ( ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_real ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(151,axiom,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(1258,plain,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(3,axiom,
! [A: nat,B: real,C: real] :
( ( C @ ( B @ dvd_dvd_real ) )
=> ( A @ ( C @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ dvd_dvd_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_dvd__power__same) ).
thf(704,plain,
! [A: nat,B: real,C: real] :
( ( C @ ( B @ dvd_dvd_real ) )
=> ( A @ ( C @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ dvd_dvd_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(618,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ord_less_eq_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_rel__simps_I21_J) ).
thf(3091,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ bit0 @ ( pls @ ord_less_eq_int ) ) )
& ( ( A @ bit0 @ ( pls @ ord_less_eq_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(460,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s1 @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ zcong ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(2474,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s1 @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ zcong ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( ( A @ ( C @ power_power_nat ) )
= ( B @ ( C @ power_power_nat ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_power__inject__exp) ).
thf(947,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( ( A = B )
=> ( ( A @ ( C @ power_power_nat ) )
= ( B @ ( C @ power_power_nat ) ) ) )
& ( ( ( A @ ( C @ power_power_nat ) )
= ( B @ ( C @ power_power_nat ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(18,axiom,
! [A: nat,B: real] :
( ( B @ ( zero_zero_real @ ord_less_real ) )
=> ( ( one_one_real @ ( B @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ ( B @ times_times_real ) @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_power__Suc__less) ).
thf(763,plain,
! [A: nat,B: real] :
( ( B @ ( zero_zero_real @ ord_less_real ) )
=> ( ( one_one_real @ ( B @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ ( B @ times_times_real ) @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(764,plain,
! [B: real,A: nat] :
( ( A @ ( B @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ ( B @ times_times_real ) @ ord_less_real ) )
| ~ ( one_one_real @ ( B @ ord_less_real ) )
| ~ ( B @ ( zero_zero_real @ ord_less_real ) ) ),
inference(cnf,[status(esa)],[763]) ).
thf(55,axiom,
! [A: real,B: nat] :
( ( A @ ( B @ ( A @ power_power_real ) @ times_times_real ) )
= ( B @ ( A @ power_power_real ) @ ( A @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_power__commutes) ).
thf(900,plain,
! [A: real,B: nat] :
( ( A @ ( B @ ( A @ power_power_real ) @ times_times_real ) )
= ( B @ ( A @ power_power_real ) @ ( A @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(185,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ power_power_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1408,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ power_power_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(606,axiom,
! [A: int] :
( ( A @ ( pls @ times_times_int ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_mult__Pls) ).
thf(3047,plain,
! [A: int] :
( ( A @ ( pls @ times_times_int ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(3048,plain,
! [A: int] :
( ( A @ ( pls @ times_times_int ) )
= pls ),
inference(cnf,[status(esa)],[3047]) ).
thf(3049,plain,
! [A: int] :
( ( A @ ( pls @ times_times_int ) )
= pls ),
inference(lifteq,[status(thm)],[3048]) ).
thf(5244,plain,
! [A: int] :
( ( A @ ( zero_zero_int @ times_times_int ) )
= zero_zero_int ),
inference(rewrite,[status(thm)],[3049,3057]) ).
thf(309,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_semiring__mult__number__of) ).
thf(1894,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_nat ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_power__less__imp__less__exp) ).
thf(1117,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_nat ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(230,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat )
<=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_power__eq__0__iff) ).
thf(1574,plain,
! [A: nat,B: nat] :
( ( ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(666,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( D @ ( one_one_int @ ( C @ ( B @ power_power_int ) @ zcong ) ) )
=> ( D @ ( one_one_int @ ( A @ ( C @ times_times_nat ) @ ( B @ power_power_int ) @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_zcong__zpower__zmult) ).
thf(3287,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( D @ ( one_one_int @ ( C @ ( B @ power_power_int ) @ zcong ) ) )
=> ( D @ ( one_one_int @ ( A @ ( C @ times_times_nat ) @ ( B @ power_power_int ) @ zcong ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(663,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) )
= ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3270,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) )
= ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(235,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number267125858f_real @ ( A @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_semiring__mult__2__right) ).
thf(1603,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number267125858f_real @ ( A @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(621,axiom,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ~ ( C @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( ~ ( C @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ~ ( C @ ( zero_zero_int @ ( A @ ( B @ times_times_int ) @ zcong ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_zcong__zmult__prop3) ).
thf(3106,plain,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ~ ( C @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( ~ ( C @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ~ ( C @ ( zero_zero_int @ ( A @ ( B @ times_times_int ) @ zcong ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(541,axiom,
! [A: int,B: nat] : ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_zero__le__even__power_H) ).
thf(2802,plain,
! [A: int,B: nat] : ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(610,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ ord_less_eq_int ) )
<=> ( A @ ( pls @ bit1 @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__special_I2_J) ).
thf(3066,plain,
! [A: int] :
( ( ( A @ ( pls @ bit1 @ ord_less_eq_int ) )
=> ( A @ number_number_of_int @ ( one_one_int @ ord_less_eq_int ) ) )
& ( ( A @ number_number_of_int @ ( one_one_int @ ord_less_eq_int ) )
=> ( A @ ( pls @ bit1 @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(179,axiom,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( A @ ( B @ power_power_real ) )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_field__power__not__zero) ).
thf(1376,plain,
! [A: nat,B: real] :
( ( B != zero_zero_real )
=> ( ( A @ ( B @ power_power_real ) )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(500,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_plus__numeral__code_I9_J) ).
thf(2642,plain,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(633,axiom,
! [A: real,B: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) ) )
=> ( ( A @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_power2__eq__imp__eq) ).
thf(3155,plain,
! [A: real,B: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) ) )
=> ( ( A @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(3779,plain,
zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ),
inference(rewrite,[status(thm)],[1664,3057]) ).
thf(2795,plain,
~ ( min @ ( pls @ ord_less_int ) ),
inference(polarity_switch,[status(thm)],[2794]) ).
thf(3419,plain,
~ ( min @ ( zero_zero_int @ ord_less_int ) ),
inference(rewrite,[status(thm)],[2795,3057]) ).
thf(233,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( A @ ( C @ times_times_real ) )
= ( B @ ( C @ times_times_real ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_real__mult__left__cancel) ).
thf(1589,plain,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( A = B )
=> ( ( A @ ( C @ times_times_real ) )
= ( B @ ( C @ times_times_real ) ) ) )
& ( ( ( A @ ( C @ times_times_real ) )
= ( B @ ( C @ times_times_real ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(322,axiom,
( ( t = one_one_int )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(1933,plain,
( ( t = one_one_int )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_zero__less__power) ).
thf(880,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( zero_zero_nat @ ord_less_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(286,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ number_number_of_int @ plus_plus_int ) @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ number_number_of_int @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_add__number__of__left) ).
thf(1801,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ number_number_of_int @ plus_plus_int ) @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ number_number_of_int @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(635,axiom,
! [A: real,B: real] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_sum__power2__ge__zero) ).
thf(3160,plain,
! [A: real,B: real] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(162,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ plus_plus_real ) )
= ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1307,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ plus_plus_real ) )
= ( C @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(890,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(105,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_real @ ord_less_real ) )
=> ( ( one_one_real @ ( A @ ord_less_real ) )
=> ( B @ ( A @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ ord_less_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_power__strict__decreasing) ).
thf(1080,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( zero_zero_real @ ord_less_real ) )
=> ( ( one_one_real @ ( A @ ord_less_real ) )
=> ( B @ ( A @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ ord_less_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(525,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ minus_minus_int ) )
= ( A @ ( min @ minus_minus_int ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_diff__bin__simps_I4_J) ).
thf(2742,plain,
! [A: int] :
( ( A @ bit1 @ ( pls @ minus_minus_int ) )
= ( A @ ( min @ minus_minus_int ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(629,axiom,
! [A: int] :
( ( A @ number267125858f_real @ ( zero_zero_real @ ord_less_eq_real ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_le__special_I1_J) ).
thf(3133,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ number267125858f_real @ ( zero_zero_real @ ord_less_eq_real ) ) )
& ( ( A @ number267125858f_real @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(4910,plain,
( ( t != t )
| ( one_one_int @ ( one_one_int @ ord_less_eq_int ) )
| ( t @ ( one_one_int @ ord_less_int ) ) ),
inference(paramod_ordered,[status(thm)],[4104,2925]) ).
thf(4911,plain,
( ( one_one_int @ ( one_one_int @ ord_less_eq_int ) )
| ( t @ ( one_one_int @ ord_less_int ) ) ),
inference(pattern_uni,[status(thm)],[4910:[]]) ).
thf(337,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_power__increasing__iff) ).
thf(1993,plain,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_eq_int ) ) )
& ( ( B @ ( C @ power_power_int ) @ ( A @ ( C @ power_power_int ) @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(530,axiom,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_mult__nat__number__of) ).
thf(2757,plain,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(295,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ dvd_dvd_int ) )
=> ( ( A != zero_zero_int )
=> ( C @ ( B @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_zdvd__mult__cancel) ).
thf(1838,plain,
! [A: int,B: int,C: int] :
( ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ dvd_dvd_int ) )
=> ( ( A != zero_zero_int )
=> ( C @ ( B @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(61,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( B @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( D @ minus_minus_int ) @ ( A @ ( C @ minus_minus_int ) @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_zcong__zdiff) ).
thf(915,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( B @ ( A @ zcong ) ) )
=> ( E @ ( B @ ( D @ minus_minus_int ) @ ( A @ ( C @ minus_minus_int ) @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(117,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_int ) )
| ( A = B )
| ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zless__linear) ).
thf(1112,plain,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_int ) )
| ( A = B )
| ( B @ ( A @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(171,axiom,
! [A: real,B: nat] :
( ( ( B @ ( A @ power_power_real ) )
= zero_zero_real )
<=> ( ( B != zero_zero_nat )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_power__eq__0__iff) ).
thf(1339,plain,
! [A: real,B: nat] :
( ( ( ( B != zero_zero_nat )
& ( A = zero_zero_real ) )
=> ( ( B @ ( A @ power_power_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( A @ power_power_real ) )
= zero_zero_real )
=> ( ( B != zero_zero_nat )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(491,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ord_less_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_rel__simps_I12_J) ).
thf(2605,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( pls @ ( A @ bit1 @ ord_less_int ) ) )
& ( ( pls @ ( A @ bit1 @ ord_less_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(535,axiom,
! [A: int] :
( ( A @ bit0 @ number267125858f_real )
= ( A @ number267125858f_real @ ( A @ number267125858f_real @ ( zero_zero_real @ plus_plus_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_number__of__Bit0) ).
thf(2785,plain,
! [A: int] :
( ( A @ bit0 @ number267125858f_real )
= ( A @ number267125858f_real @ ( A @ number267125858f_real @ ( zero_zero_real @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(53,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ times_times_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(895,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ times_times_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(474,axiom,
( ( pls @ number267125858f_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_number__of__Pls) ).
thf(2542,plain,
( ( pls @ number267125858f_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(502,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( ( A @ ( C @ power_power_int ) )
= ( B @ ( C @ power_power_int ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_power__inject__exp) ).
thf(2647,plain,
! [A: nat,B: nat,C: int] :
( ( C @ ( one_one_int @ ord_less_int ) )
=> ( ( ( A = B )
=> ( ( A @ ( C @ power_power_int ) )
= ( B @ ( C @ power_power_int ) ) ) )
& ( ( ( A @ ( C @ power_power_int ) )
= ( B @ ( C @ power_power_int ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(256,axiom,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_semiring__norm_I110_J) ).
thf(1699,plain,
( one_one_int
= ( pls @ bit1 @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(2138,plain,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int ) )
= one_one_int ),
inference(cnf,[status(esa)],[2137]) ).
thf(2139,plain,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int ) )
= one_one_int ),
inference(lifteq,[status(thm)],[2138]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( one_one_nat @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( A @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ ord_less_eq_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_power__decreasing) ).
thf(1176,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( ( one_one_nat @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( A @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ ord_less_eq_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(439,axiom,
! [A: int,B: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
<=> ( ( ( B
= ( min @ number_number_of_int ) )
& ( A
= ( min @ number_number_of_int ) ) )
| ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_zmult__eq__1__iff) ).
thf(2375,plain,
! [A: int,B: int] :
( ( ( ( ( B
= ( min @ number_number_of_int ) )
& ( A
= ( min @ number_number_of_int ) ) )
| ( ( B = one_one_int )
& ( A = one_one_int ) ) )
=> ( ( B @ ( A @ times_times_int ) )
= one_one_int ) )
& ( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
=> ( ( ( B
= ( min @ number_number_of_int ) )
& ( A
= ( min @ number_number_of_int ) ) )
| ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(2376,plain,
( ! [A: int,B: int] :
( ( ( ( B
= ( min @ number_number_of_int ) )
& ( A
= ( min @ number_number_of_int ) ) )
| ( ( B = one_one_int )
& ( A = one_one_int ) ) )
=> ( ( B @ ( A @ times_times_int ) )
= one_one_int ) )
& ! [A: int,B: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
=> ( ( ( B
= ( min @ number_number_of_int ) )
& ( A
= ( min @ number_number_of_int ) ) )
| ( ( B = one_one_int )
& ( A = one_one_int ) ) ) ) ),
inference(miniscope,[status(thm)],[2375]) ).
thf(2377,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( ( D @ ( C @ times_times_int ) )
= one_one_int )
| ( D
!= ( min @ number_number_of_int ) )
| ( C
!= ( min @ number_number_of_int ) ) )
& ( ( ( D @ ( C @ times_times_int ) )
= one_one_int )
| ( D != one_one_int )
| ( C != one_one_int ) )
& ( ( B
= ( min @ number_number_of_int ) )
| ( B = one_one_int )
| ( ( B @ ( A @ times_times_int ) )
!= one_one_int ) )
& ( ( A
= ( min @ number_number_of_int ) )
| ( B = one_one_int )
| ( ( B @ ( A @ times_times_int ) )
!= one_one_int ) )
& ( ( B
= ( min @ number_number_of_int ) )
| ( A = one_one_int )
| ( ( B @ ( A @ times_times_int ) )
!= one_one_int ) )
& ( ( A
= ( min @ number_number_of_int ) )
| ( A = one_one_int )
| ( ( B @ ( A @ times_times_int ) )
!= one_one_int ) ) ),
inference(cnf,[status(esa)],[2376]) ).
thf(2383,plain,
! [B: int,A: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
| ( B
!= ( min @ number_number_of_int ) )
| ( A
!= ( min @ number_number_of_int ) ) ),
inference(cnfConj,[status(thm)],[2377]) ).
thf(2389,plain,
! [B: int,A: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
| ( B
!= ( min @ number_number_of_int ) )
| ( A
!= ( min @ number_number_of_int ) ) ),
inference(lifteq,[status(thm)],[2383]) ).
thf(2390,plain,
( ( min @ number_number_of_int @ ( min @ number_number_of_int @ times_times_int ) )
= one_one_int ),
inference(simp,[status(thm)],[2389]) ).
thf(211,axiom,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ plus_plus_real ) @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( D @ ( B @ plus_plus_real ) @ ( C @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1496,plain,
! [A: real,B: real,C: real,D: real] :
( ( D @ ( C @ plus_plus_real ) @ ( B @ ( A @ plus_plus_real ) @ plus_plus_real ) )
= ( D @ ( B @ plus_plus_real ) @ ( C @ ( A @ plus_plus_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(388,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ord_less_eq_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_rel__simps_I22_J) ).
thf(2156,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ bit1 @ ( pls @ ord_less_eq_int ) ) )
& ( ( A @ bit1 @ ( pls @ ord_less_eq_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(296,axiom,
! [A: int] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( A @ ord_less_eq_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_power2__ge__self) ).
thf(1841,plain,
! [A: int] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( A @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(450,axiom,
! [A: int] :
( ( ( A @ bit1 )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_rel__simps_I47_J) ).
thf(2439,plain,
! [A: int] :
( ( ( A = min )
=> ( ( A @ bit1 )
= min ) )
& ( ( ( A @ bit1 )
= min )
=> ( A = min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(320,axiom,
! [A: int,B: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
=> ( ( A
= ( min @ number_number_of_int ) )
| ( A = one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_pos__zmult__eq__1__iff__lemma) ).
thf(1926,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
=> ( ( A
= ( min @ number_number_of_int ) )
| ( A = one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(586,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(2962,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(550,axiom,
pls @ bit1 @ bit0 @ number_number_of_int @ zprime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zprime__2) ).
thf(2835,plain,
pls @ bit1 @ bit0 @ number_number_of_int @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(531,axiom,
~ ! [A: int] :
~ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ zcong ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(2765,plain,
~ ! [A: int] :
~ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( min @ number_number_of_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ zcong ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(96,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( ( A @ ( C @ plus_plus_nat ) @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( B @ dvd_dvd_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_divides__add__revr) ).
thf(1044,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( ( A @ ( C @ plus_plus_nat ) @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( B @ dvd_dvd_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(477,axiom,
! [A: int,B: nat] :
( ( zero_zero_int @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) @ ord_less_eq_int ) )
=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_even__power__le__0__imp__0) ).
thf(2550,plain,
! [A: int,B: nat] :
( ( zero_zero_int @ ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) @ ord_less_eq_int ) )
=> ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(462,axiom,
! [A: int] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_semiring__mult__2) ).
thf(2481,plain,
! [A: int] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(727,plain,
! [B: int,A: int] :
( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
| ~ ( A @ ( B @ dvd_dvd_int ) ) ),
inference(cnfConj,[status(thm)],[725]) ).
thf(728,plain,
! [B: int,A: int] :
( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
| ~ ( A @ ( B @ dvd_dvd_int ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(7000,plain,
! [B: int,A: int] :
( ( ( one_one_int @ ( one_one_int @ dvd_dvd_int ) )
!= ( A @ ( B @ dvd_dvd_int ) ) )
| ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6988,728]) ).
thf(7001,plain,
! [B: int,A: int] :
( ( ( one_one_int @ ( one_one_int @ dvd_dvd_int ) )
!= ( A @ ( B @ dvd_dvd_int ) ) )
| ( B @ ( zero_zero_int @ ( A @ zcong ) ) ) ),
inference(simp,[status(thm)],[7000]) ).
thf(7002,plain,
one_one_int @ ( zero_zero_int @ ( one_one_int @ zcong ) ),
inference(pattern_uni,[status(thm)],[7001:[bind(A,$thf( one_one_int )),bind(B,$thf( one_one_int ))]]) ).
thf(576,axiom,
! [A: int] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_mult__2) ).
thf(2931,plain,
! [A: int] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(81,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_nat ) @ power_power_nat ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(986,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_nat ) @ power_power_nat ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(489,axiom,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( A @ ( B @ power_power_int ) )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_field__power__not__zero) ).
thf(2592,plain,
! [A: nat,B: int] :
( ( B != zero_zero_int )
=> ( ( A @ ( B @ power_power_int ) )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) )
= ( C @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1000,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ plus_plus_nat ) )
= ( C @ ( B @ ( A @ plus_plus_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(192,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ power_power_nat ) )
= ( C @ ( B @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1435,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ power_power_nat ) )
= ( C @ ( B @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(497,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( D @ ( B @ ( A @ times_times_int ) @ times_times_int ) @ ( C @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(2633,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( D @ ( B @ ( A @ times_times_int ) @ times_times_int ) @ ( C @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(346,axiom,
! [A: int,B: int] :
( ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_sum__power2__le__zero__iff) ).
thf(2022,plain,
! [A: int,B: int] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ord_less_eq_int ) ) )
& ( ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(2294,plain,
( ( pls @ number_number_of_int )
!= ( min @ number_number_of_int ) ),
inference(polarity_switch,[status(thm)],[2293]) ).
thf(2295,plain,
( ( pls @ number_number_of_int )
!= ( min @ number_number_of_int ) ),
inference(lifteq,[status(thm)],[2294]) ).
thf(3490,plain,
( ( min @ number_number_of_int )
!= ( zero_zero_int @ number_number_of_int ) ),
inference(rewrite,[status(thm)],[2295,3057]) ).
thf(225,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ plus_plus_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1562,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ plus_plus_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(2270,plain,
( ( pls @ number267125858f_real )
= zero_zero_real ),
inference(lifteq,[status(thm)],[2269]) ).
thf(3522,plain,
( ( zero_zero_int @ number267125858f_real )
= zero_zero_real ),
inference(rewrite,[status(thm)],[2270,3057]) ).
thf(94,axiom,
! [A: real,B: real] :
( ( A
= ( B @ ( A @ plus_plus_real ) ) )
<=> ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_add__0__iff) ).
thf(1034,plain,
! [A: real,B: real] :
( ( ( B = zero_zero_real )
=> ( A
= ( B @ ( A @ plus_plus_real ) ) ) )
& ( ( A
= ( B @ ( A @ plus_plus_real ) ) )
=> ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(583,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ ord_less_int ) )
<=> ( A @ ( pls @ bit1 @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_less__special_I2_J) ).
thf(2952,plain,
! [A: int] :
( ( ( A @ ( pls @ bit1 @ ord_less_int ) )
=> ( A @ number_number_of_int @ ( one_one_int @ ord_less_int ) ) )
& ( ( A @ number_number_of_int @ ( one_one_int @ ord_less_int ) )
=> ( A @ ( pls @ bit1 @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(369,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_zmult__assoc) ).
thf(2096,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(304,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ord_less_int ) )
<=> ( A @ ( pls @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_rel__simps_I4_J) ).
thf(1873,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_int ) )
=> ( A @ bit0 @ ( pls @ ord_less_int ) ) )
& ( ( A @ bit0 @ ( pls @ ord_less_int ) )
=> ( A @ ( pls @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(271,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( ( B
!= ( one_one_int @ ( A @ minus_minus_int ) ) )
=> ( one_one_int @ ( A @ minus_minus_int ) @ ( B @ ord_less_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_Euler_Oaux1) ).
thf(1758,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( ( B
!= ( one_one_int @ ( A @ minus_minus_int ) ) )
=> ( one_one_int @ ( A @ minus_minus_int ) @ ( B @ ord_less_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ power_power_nat ) )
= ( C @ ( B @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_power__mult__distrib) ).
thf(944,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ power_power_nat ) )
= ( C @ ( B @ power_power_nat ) @ ( C @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( A @ ( B @ times_times_nat ) )
= ( A @ ( one_one_nat @ ( B @ minus_minus_nat ) @ times_times_nat ) @ ( A @ plus_plus_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ times_times_nat ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_mult__eq__if) ).
thf(1509,plain,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( A @ ( B @ times_times_nat ) )
= ( A @ ( one_one_nat @ ( B @ minus_minus_nat ) @ times_times_nat ) @ ( A @ plus_plus_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ times_times_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ dvd_dvd_nat ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( D @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ dvd_dvd_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_dvd__power__le) ).
thf(939,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ dvd_dvd_nat ) )
=> ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( D @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ dvd_dvd_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_eq_int ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zle__antisym) ).
thf(836,plain,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_eq_int ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(98,axiom,
! [A: real] : ( A @ ( A @ ord_less_eq_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_real__le__refl) ).
thf(1049,plain,
! [A: real] : ( A @ ( A @ ord_less_eq_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(354,axiom,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_int ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_int ) @ ( one_one_int @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_one__less__power) ).
thf(2054,plain,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_int ) )
=> ( ( A @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( B @ power_power_int ) @ ( one_one_int @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(8,axiom,
! [A: real] :
( ( A @ ( one_one_real @ times_times_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_real__mult__1) ).
thf(720,plain,
! [A: real] :
( ( A @ ( one_one_real @ times_times_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(721,plain,
! [A: real] :
( ( A @ ( one_one_real @ times_times_real ) )
= A ),
inference(cnf,[status(esa)],[720]) ).
thf(722,plain,
! [A: real] :
( ( A @ ( one_one_real @ times_times_real ) )
= A ),
inference(lifteq,[status(thm)],[721]) ).
thf(326,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ number_number_of_int @ times_times_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( B @ ( A @ times_times_int ) @ number_number_of_int @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mult__number__of__left) ).
thf(1948,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ number_number_of_int @ times_times_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( B @ ( A @ times_times_int ) @ number_number_of_int @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(602,axiom,
! [A: int] :
( ( zero_zero_nat
= ( A @ number_number_of_nat ) )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_eq__0__number__of) ).
thf(3031,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( zero_zero_nat
= ( A @ number_number_of_nat ) ) )
& ( ( zero_zero_nat
= ( A @ number_number_of_nat ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(545,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( ( A @ ( B @ times_times_int ) )
= one_one_int )
<=> ( ( A = one_one_int )
& ( B = one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_pos__zmult__eq__1__iff) ).
thf(2816,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( ( ( A = one_one_int )
& ( B = one_one_int ) )
=> ( ( A @ ( B @ times_times_int ) )
= one_one_int ) )
& ( ( ( A @ ( B @ times_times_int ) )
= one_one_int )
=> ( ( A = one_one_int )
& ( B = one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(5529,plain,
! [A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5456,749]) ).
thf(5530,plain,
! [A: int] :
( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5529]) ).
thf(5531,plain,
! [A: int] :
( ( zero_zero_int != A )
| ( ( zero_zero_int @ ( min @ minus_minus_int ) )
!= A ) ),
inference(simp,[status(thm)],[5530]) ).
thf(5538,plain,
( ( zero_zero_int @ ( min @ minus_minus_int ) )
!= zero_zero_int ),
inference(simp,[status(thm)],[5531]) ).
thf(5582,plain,
! [A: int] :
( ( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5473,749]) ).
thf(5583,plain,
! [A: int] :
( ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5582]) ).
thf(5584,plain,
! [A: int] :
( ( zero_zero_int != A )
| ( ( one_one_int @ ( zero_zero_int @ minus_minus_int ) )
!= A ) ),
inference(simp,[status(thm)],[5583]) ).
thf(5587,plain,
( ( one_one_int @ ( zero_zero_int @ minus_minus_int ) )
!= zero_zero_int ),
inference(simp,[status(thm)],[5584]) ).
thf(202,axiom,
min @ ( min @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_rel__simps_I24_J) ).
thf(1467,plain,
min @ ( min @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(592,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_zadd__left__commute) ).
thf(2994,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(26,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ zcong ) ) )
<=> ( B @ ( A @ minus_minus_int ) @ ( C @ dvd_dvd_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_zcong__def) ).
thf(795,plain,
! [A: int,B: int,C: int] :
( ( ( B @ ( A @ minus_minus_int ) @ ( C @ dvd_dvd_int ) )
=> ( C @ ( B @ ( A @ zcong ) ) ) )
& ( ( C @ ( B @ ( A @ zcong ) ) )
=> ( B @ ( A @ minus_minus_int ) @ ( C @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(697,axiom,
! [A: int,B: int] :
( ( B @ ( A @ minus_minus_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ minus_minus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_number__of__diff) ).
thf(3395,plain,
! [A: int,B: int] :
( ( B @ ( A @ minus_minus_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ minus_minus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(412,axiom,
! [A: int,B: int] :
( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zle__add1__eq__le) ).
thf(2271,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) ) )
& ( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(127,axiom,
! [A: real] :
( ( ( A @ ( A @ plus_plus_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_double__eq__0__iff) ).
thf(1145,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( A @ plus_plus_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( A @ plus_plus_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(552,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_semiring__add__number__of) ).
thf(2846,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(467,axiom,
! [A: int] :
( ( A @ bit0 @ ( min @ ord_less_eq_int ) )
<=> ( A @ ( min @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_rel__simps_I25_J) ).
thf(2513,plain,
! [A: int] :
( ( ( A @ ( min @ ord_less_int ) )
=> ( A @ bit0 @ ( min @ ord_less_eq_int ) ) )
& ( ( A @ bit0 @ ( min @ ord_less_eq_int ) )
=> ( A @ ( min @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(285,axiom,
! [A: nat] :
( ( ( A @ ( min @ number_number_of_int @ power_power_int ) )
= ( min @ number_number_of_int ) )
| ( ( A @ ( min @ number_number_of_int @ power_power_int ) )
= one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_neg__one__power) ).
thf(1798,plain,
! [A: nat] :
( ( ( A @ ( min @ number_number_of_int @ power_power_int ) )
= ( min @ number_number_of_int ) )
| ( ( A @ ( min @ number_number_of_int @ power_power_int ) )
= one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(518,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ minus_minus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ minus_minus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_zdiff__zmult__distrib) ).
thf(2715,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ minus_minus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ minus_minus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(442,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) )
= ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_power__add) ).
thf(2397,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) )
= ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(4488,plain,
! [B: int,A: int] :
( ( ( s @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[2071,741]) ).
thf(4489,plain,
! [B: int,A: int] :
( ( ( s @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ( A = B ) ),
inference(simp,[status(thm)],[4488]) ).
thf(4490,plain,
( ( s @ ( zero_zero_int @ ord_less_int ) )
| ( s = zero_zero_int ) ),
inference(pattern_uni,[status(thm)],[4489:[bind(A,$thf( zero_zero_int )),bind(B,$thf( s ))]]) ).
thf(385,axiom,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_number__of__mult) ).
thf(2143,plain,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(243,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ minus_minus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ minus_minus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_zdiff__power2) ).
thf(1647,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ minus_minus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ minus_minus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(277,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1780,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(520,axiom,
! [A: int] :
( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_int @ ( A @ ord_less_int ) )
=> ( ( A = one_one_int )
| ( A = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_int__pos__lt__two__imp__zero__or__one) ).
thf(2720,plain,
! [A: int] :
( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_int @ ( A @ ord_less_int ) )
=> ( ( A = one_one_int )
| ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(712,plain,
! [B: real,A: real] :
( ( zero_zero_real @ ( B @ ( A @ minus_minus_real ) @ ord_less_eq_real ) )
| ~ ( B @ ( A @ ord_less_eq_real ) ) ),
inference(cnfConj,[status(thm)],[711]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_nat ) )
<=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_power__strict__increasing__iff) ).
thf(1003,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one_one_nat @ ord_less_nat ) )
=> ( ( ( B @ ( A @ ord_less_nat ) )
=> ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_nat ) ) )
& ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_nat ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(690,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_int ) @ power_power_int ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(3376,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_int ) @ power_power_int ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(6105,plain,
! [A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5521,749]) ).
thf(6106,plain,
! [A: int] :
( ( zero_zero_int @ ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( A @ ( A @ ord_less_int ) ) ),
inference(simp,[status(thm)],[6105]) ).
thf(6110,plain,
! [A: int] :
( ( zero_zero_int != A )
| ( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) )
!= A ) ),
inference(simp,[status(thm)],[6106]) ).
thf(6120,plain,
( ( zero_zero_int @ ( zero_zero_int @ ( min @ minus_minus_int ) @ minus_minus_int ) )
!= zero_zero_int ),
inference(simp,[status(thm)],[6110]) ).
thf(556,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ minus_minus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ minus_minus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_zdiff__zmult__distrib2) ).
thf(2863,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ minus_minus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ minus_minus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(705,plain,
! [C: real,B: real,A: nat] :
( ( A @ ( C @ power_power_real ) @ ( A @ ( B @ power_power_real ) @ dvd_dvd_real ) )
| ~ ( C @ ( B @ dvd_dvd_real ) ) ),
inference(cnf,[status(esa)],[704]) ).
thf(129,axiom,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( B @ ( C @ ( A @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( B @ ( A @ dvd_dvd_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_divides__exp2) ).
thf(1156,plain,
! [A: nat,B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( B @ ( C @ ( A @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( B @ ( A @ dvd_dvd_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(268,axiom,
! [A: int,B: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ord_less_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_not__sum__power2__lt__zero) ).
thf(1743,plain,
! [A: int,B: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(182,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ dvd_dvd_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_le__imp__power__dvd) ).
thf(1400,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ dvd_dvd_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(396,axiom,
! [A: int,B: nat] :
( ( ( A @ number_number_of_nat )
= B )
<=> ( B
= ( A @ number_number_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_number__of__reorient) ).
thf(2192,plain,
! [A: int,B: nat] :
( ( ( B
= ( A @ number_number_of_nat ) )
=> ( ( A @ number_number_of_nat )
= B ) )
& ( ( ( A @ number_number_of_nat )
= B )
=> ( B
= ( A @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_nat ) )
= ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_power__add) ).
thf(887,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_nat ) )
= ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(648,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( min @ number_number_of_int @ power_power_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_power__m1__even) ).
thf(3214,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( min @ number_number_of_int @ power_power_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(73,axiom,
zero_zero_int @ ( zero_zero_int @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(954,plain,
zero_zero_int @ ( zero_zero_int @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3454,plain,
( ( ( sk3 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1644,3451]) ).
thf(3455,plain,
( ( sk3 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[3454]) ).
thf(3459,plain,
( ( sk3 != min )
| ( zero_zero_int != zero_zero_int ) ),
inference(simp,[status(thm)],[3455]) ).
thf(3462,plain,
sk3 != min,
inference(simp,[status(thm)],[3459]) ).
thf(609,axiom,
! [A: int] :
( ( ( A @ number_number_of_nat )
= zero_zero_nat )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_eq__number__of__0) ).
thf(3058,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat )
= zero_zero_nat ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1651,plain,
( ( pls @ bit1 @ number_number_of_int )
= one_one_int ),
inference(lifteq,[status(thm)],[1650]) ).
thf(3642,plain,
( ( zero_zero_int @ bit1 @ number_number_of_int )
= one_one_int ),
inference(rewrite,[status(thm)],[1651,3057]) ).
thf(683,axiom,
! [A: int,B: int] :
( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
<=> ( ( A = B )
| ( B @ ( A @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_zless__add1__eq) ).
thf(3344,plain,
! [A: int,B: int] :
( ( ( ( A = B )
| ( B @ ( A @ ord_less_int ) ) )
=> ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) ) )
& ( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
=> ( ( A = B )
| ( B @ ( A @ ord_less_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(279,axiom,
! [A: nat,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_power__mono) ).
thf(1785,plain,
! [A: nat,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(429,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ minus_minus_int ) )
= ( B @ ( A @ minus_minus_int ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_diff__bin__simps_I7_J) ).
thf(2337,plain,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ minus_minus_int ) )
= ( B @ ( A @ minus_minus_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(426,axiom,
! [A: int,B: int] :
( ( B @ number267125858f_real @ ( A @ number267125858f_real @ times_times_real ) )
= ( B @ ( A @ times_times_int ) @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_arith__simps_I32_J) ).
thf(2322,plain,
! [A: int,B: int] :
( ( B @ number267125858f_real @ ( A @ number267125858f_real @ times_times_real ) )
= ( B @ ( A @ times_times_int ) @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(433,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= ( A @ ( A @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_power2__eq__square) ).
thf(2354,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= ( A @ ( A @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ times_times_nat ) )
= ( A @ ( B @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1053,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ times_times_nat ) )
= ( A @ ( B @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(212,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ dvd_dvd_nat ) )
<=> ( ( C @ ( A @ dvd_dvd_nat ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_nat__mult__dvd__cancel__disj_H) ).
thf(1499,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( A @ dvd_dvd_nat ) )
| ( B = zero_zero_nat ) )
=> ( B @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ dvd_dvd_nat ) ) )
& ( ( B @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ dvd_dvd_nat ) )
=> ( ( C @ ( A @ dvd_dvd_nat ) )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(281,axiom,
! [A: int,B: int] : ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_sum__squares__ge__zero) ).
thf(1790,plain,
! [A: int,B: int] : ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1729,plain,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_int ) ),
inference(lifteq,[status(thm)],[1728]) ).
thf(3940,plain,
( ( one_one_int @ ( one_one_int @ plus_plus_int ) )
= ( zero_zero_int @ bit1 @ bit0 @ number_number_of_int ) ),
inference(rewrite,[status(thm)],[1729,3057]) ).
thf(671,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_le__special_I1_J) ).
thf(3305,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) ) )
& ( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(191,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1432,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ times_times_real ) @ times_times_real ) )
= ( C @ ( B @ times_times_real ) @ ( A @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(623,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__mult__2__right) ).
thf(3114,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(664,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ord_less_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rel__simps_I5_J) ).
thf(3273,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ bit1 @ ( pls @ ord_less_int ) ) )
& ( ( A @ bit1 @ ( pls @ ord_less_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(400,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) )
= ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_zpower__zadd__distrib) ).
thf(2219,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) )
= ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(379,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_power2__le__imp__le) ).
thf(2128,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(219,axiom,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( B @ times_times_real ) @ ( A @ ( B @ power_power_real ) @ ord_less_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_power__less__power__Suc) ).
thf(1538,plain,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_real ) )
=> ( A @ ( B @ power_power_real ) @ ( B @ times_times_real ) @ ( A @ ( B @ power_power_real ) @ ord_less_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(516,axiom,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( ~ ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( B @ number_number_of_nat ) ) ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ number_number_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__nat__number__of) ).
thf(2701,plain,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( ~ ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( B @ number_number_of_nat ) ) ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(686,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ ( pls @ bit1 @ bit0 @ number_number_of_int @ ord_less_int ) )
=> ( ( C @ ( B @ ( min @ number_number_of_int @ power_power_int ) @ ( A @ ( min @ number_number_of_int @ power_power_int ) @ zcong ) ) )
=> ( ( A @ ( min @ number_number_of_int @ power_power_int ) )
= ( B @ ( min @ number_number_of_int @ power_power_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_neg__one__power__eq__mod__m) ).
thf(3359,plain,
! [A: nat,B: nat,C: int] :
( ( C @ ( pls @ bit1 @ bit0 @ number_number_of_int @ ord_less_int ) )
=> ( ( C @ ( B @ ( min @ number_number_of_int @ power_power_int ) @ ( A @ ( min @ number_number_of_int @ power_power_int ) @ zcong ) ) )
=> ( ( A @ ( min @ number_number_of_int @ power_power_int ) )
= ( B @ ( min @ number_number_of_int @ power_power_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(678,axiom,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(3329,plain,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(638,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3174,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(3485,plain,
( ( ( sk11 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2151,3451]) ).
thf(3486,plain,
( ( sk11 @ ( zero_zero_int @ ord_less_eq_int ) )
!= ( min @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[3485]) ).
thf(3487,plain,
( ( sk11 != min )
| ( zero_zero_int != zero_zero_int ) ),
inference(simp,[status(thm)],[3486]) ).
thf(3488,plain,
sk11 != min,
inference(simp,[status(thm)],[3487]) ).
thf(221,axiom,
! [A: real,B: real] :
~ ( zero_zero_real @ ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ord_less_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_not__sum__squares__lt__zero) ).
thf(1543,plain,
! [A: real,B: real] :
~ ( zero_zero_real @ ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ord_less_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(126,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( D = B )
=> ( ( E @ ( A @ ( B @ zcong ) ) )
=> ( E @ ( A @ ( C @ zcong ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_zcong__eq__trans) ).
thf(1141,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( D = B )
=> ( ( E @ ( A @ ( B @ zcong ) ) )
=> ( E @ ( A @ ( C @ zcong ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(685,axiom,
! [A: int,B: int] :
( ( B @ zprime )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_int ) )
=> ( ( B @ ( one_one_int @ ( A @ ( A @ times_times_int ) @ zcong ) ) )
=> ( ( A
= ( one_one_int @ ( B @ minus_minus_int ) ) )
| ( A = one_one_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_zcong__square__zless) ).
thf(3356,plain,
! [A: int,B: int] :
( ( B @ zprime )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_int ) )
=> ( ( B @ ( one_one_int @ ( A @ ( A @ times_times_int ) @ zcong ) ) )
=> ( ( A
= ( one_one_int @ ( B @ minus_minus_int ) ) )
| ( A = one_one_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(590,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_int @ ( A @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_mult__2__right) ).
thf(2975,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_int @ ( A @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(651,axiom,
! [A: real,B: real] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) )
= zero_zero_real )
<=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_sum__power2__eq__zero__iff) ).
thf(3224,plain,
! [A: real,B: real] :
( ( ( ( B = zero_zero_real )
& ( A = zero_zero_real ) )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) )
= zero_zero_real ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) )
= zero_zero_real )
=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(695,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( E @ ( C @ ( B @ times_times_int ) @ ( A @ zcong ) ) )
<=> ( E @ ( D @ ( B @ times_times_int ) @ ( A @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_zcong__zmult__prop2) ).
thf(3388,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( C @ zcong ) ) )
=> ( ( ( E @ ( D @ ( B @ times_times_int ) @ ( A @ zcong ) ) )
=> ( E @ ( C @ ( B @ times_times_int ) @ ( A @ zcong ) ) ) )
& ( ( E @ ( C @ ( B @ times_times_int ) @ ( A @ zcong ) ) )
=> ( E @ ( D @ ( B @ times_times_int ) @ ( A @ zcong ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(231,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( one_one_nat @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_power__increasing) ).
thf(1585,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( one_one_nat @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ ord_less_eq_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(624,axiom,
! [A: nat,B: int,C: nat,D: int] :
( ( D @ ( C @ ( B @ power_power_int ) @ dvd_dvd_int ) )
=> ( ( C @ ( A @ ord_less_eq_nat ) )
=> ( D @ ( A @ ( B @ power_power_int ) @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_power__le__dvd) ).
thf(3117,plain,
! [A: nat,B: int,C: nat,D: int] :
( ( D @ ( C @ ( B @ power_power_int ) @ dvd_dvd_int ) )
=> ( ( C @ ( A @ ord_less_eq_nat ) )
=> ( D @ ( A @ ( B @ power_power_int ) @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(522,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_rel__simps_I44_J) ).
thf(2728,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(543,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J) ).
thf(2807,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(43,axiom,
! [A: real,B: real] :
( ( B @ ( A @ times_times_real ) )
= ( A @ ( B @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(859,plain,
! [A: real,B: real] :
( ( B @ ( A @ times_times_real ) )
= ( A @ ( B @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(355,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_int @ ord_less_int ) )
=> ( ( B @ ( min @ number_number_of_int @ ( A @ zcong ) ) )
=> ~ ( B @ ( one_one_int @ ( A @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_zcong__neg__1__impl__ne__1) ).
thf(2056,plain,
! [A: int,B: int] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_int @ ord_less_int ) )
=> ( ( B @ ( min @ number_number_of_int @ ( A @ zcong ) ) )
=> ~ ( B @ ( one_one_int @ ( A @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(175,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ~ ( B @ ( A @ dvd_dvd_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_zdvd__not__zless) ).
thf(1358,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ~ ( B @ ( A @ dvd_dvd_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( one_one_nat @ ord_less_nat ) )
=> ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_power__strict__increasing) ).
thf(1353,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( one_one_nat @ ord_less_nat ) )
=> ( C @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(434,axiom,
! [A: int] :
( ( pls @ ( A @ minus_minus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_diff__bin__simps_I1_J) ).
thf(2357,plain,
! [A: int] :
( ( pls @ ( A @ minus_minus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(207,axiom,
! [A: real,B: real,C: nat] :
( ( C @ ( B @ ( A @ times_times_real ) @ power_power_real ) )
= ( C @ ( B @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_power__mult__distrib) ).
thf(1485,plain,
! [A: real,B: real,C: nat] :
( ( C @ ( B @ ( A @ times_times_real ) @ power_power_real ) )
= ( C @ ( B @ power_power_real ) @ ( C @ ( A @ power_power_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(332,axiom,
! [A: int,B: int,C: nat] :
( ( C @ ( B @ ( A @ times_times_int ) @ power_power_int ) )
= ( C @ ( B @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1972,plain,
! [A: int,B: int,C: nat] :
( ( C @ ( B @ ( A @ times_times_int ) @ power_power_int ) )
= ( C @ ( B @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(658,axiom,
! [A: real] :
~ ( zero_zero_real @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ord_less_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_power2__less__0) ).
thf(3256,plain,
! [A: real] :
~ ( zero_zero_real @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ord_less_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(566,axiom,
! [A: int] :
( ( A @ ( one_one_int @ ord_less_eq_int ) )
<=> ( A @ ( zero_zero_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_int__one__le__iff__zero__less) ).
thf(2892,plain,
! [A: int] :
( ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( one_one_int @ ord_less_eq_int ) ) )
& ( ( A @ ( one_one_int @ ord_less_eq_int ) )
=> ( A @ ( zero_zero_int @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(486,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_arith__simps_I32_J) ).
thf(2584,plain,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(698,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_rel__simps_I27_J) ).
thf(3398,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( pls @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( pls @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(148,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ times_times_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1240,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ times_times_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(991,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(561,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( one_one_int @ ( A @ ord_less_eq_int ) )
=> ( B @ ( A @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ ord_less_eq_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_power__decreasing) ).
thf(2875,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( one_one_int @ ( A @ ord_less_eq_int ) )
=> ( B @ ( A @ power_power_int ) @ ( C @ ( A @ power_power_int ) @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(38,axiom,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_eq_real ) )
<=> ( B @ ( A @ ord_less_eq_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_power__increasing__iff) ).
thf(845,plain,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( ( B @ ( A @ ord_less_eq_nat ) )
=> ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_eq_real ) ) )
& ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_eq_real ) )
=> ( B @ ( A @ ord_less_eq_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(187,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1421,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(630,axiom,
! [A: int] :
( ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_odd__nonzero) ).
thf(3139,plain,
! [A: int] :
( ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(432,axiom,
( ( min @ bit1 )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_Bit1__Min) ).
thf(2352,plain,
( ( min @ bit1 )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(199,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_nat ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_nat__power__less__imp__less) ).
thf(1459,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( B @ ( C @ power_power_nat ) @ ( A @ ( C @ power_power_nat ) @ ord_less_nat ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(331,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_less__special_I3_J) ).
thf(1966,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(66,axiom,
! [A: real] :
( ( A @ ( A @ plus_plus_real ) )
= ( A @ ( one_one_real @ ( one_one_real @ plus_plus_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(931,plain,
! [A: real] :
( ( A @ ( A @ plus_plus_real ) )
= ( A @ ( one_one_real @ ( one_one_real @ plus_plus_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(559,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_zero__power2) ).
thf(2870,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_real @ power_power_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(165,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) )
= ( C @ ( B @ times_times_nat ) @ ( C @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1321,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) )
= ( C @ ( B @ times_times_nat ) @ ( C @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1784,plain,
( ( pls @ number_number_of_int )
= zero_zero_int ),
inference(lifteq,[status(thm)],[1783]) ).
thf(3447,plain,
( ( zero_zero_int @ number_number_of_int )
= zero_zero_int ),
inference(rewrite,[status(thm)],[1784,3057]) ).
thf(399,axiom,
! [A: nat,B: int] :
( ( ( B @ number_number_of_nat @ ( A @ power_power_nat ) )
= zero_zero_nat )
<=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_power__eq__0__iff__number__of) ).
thf(2209,plain,
! [A: nat,B: int] :
( ( ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ number_number_of_nat @ ( A @ power_power_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ number_number_of_nat @ ( A @ power_power_nat ) )
= zero_zero_nat )
=> ( ( ( B @ number_number_of_nat )
!= zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(637,axiom,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) @ number267125858f_real )
= ( B @ number267125858f_real @ ( A @ number267125858f_real @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_number__of__add) ).
thf(3171,plain,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) @ number267125858f_real )
= ( B @ number267125858f_real @ ( A @ number267125858f_real @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(585,axiom,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_zero__is__num__zero) ).
thf(2960,plain,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(423,axiom,
! [A: int] :
( ( A @ ( A @ plus_plus_int ) )
= ( A @ ( one_one_int @ ( one_one_int @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2310,plain,
! [A: int] :
( ( A @ ( A @ plus_plus_int ) )
= ( A @ ( one_one_int @ ( one_one_int @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(56,axiom,
! [A: real,B: real] :
( ( B @ ( zero_zero_real @ ord_less_real ) )
=> ( ( A @ ( zero_zero_real @ ord_less_real ) )
=> ( A @ ( B @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_real__mult__order) ).
thf(903,plain,
! [A: real,B: real] :
( ( B @ ( zero_zero_real @ ord_less_real ) )
=> ( ( A @ ( zero_zero_real @ ord_less_real ) )
=> ( A @ ( B @ times_times_real ) @ ( zero_zero_real @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(492,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ ( D @ plus_plus_int ) @ ( A @ ( C @ plus_plus_int ) @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zadd__zless__mono) ).
thf(2611,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ ( D @ plus_plus_int ) @ ( A @ ( C @ plus_plus_int ) @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(427,axiom,
! [A: int,B: int] :
( ( B @ twoSqu512355103sum2sq )
=> ( ( A @ twoSqu512355103sum2sq )
=> ( A @ ( B @ times_times_int ) @ twoSqu512355103sum2sq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq) ).
thf(2325,plain,
! [A: int,B: int] :
( ( B @ twoSqu512355103sum2sq )
=> ( ( A @ twoSqu512355103sum2sq )
=> ( A @ ( B @ times_times_int ) @ twoSqu512355103sum2sq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(758,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_int ) )
| ~ ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ),
inference(cnfConj,[status(thm)],[756]) ).
thf(759,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_int ) )
| ~ ( zero_zero_int @ ( B @ ( A @ minus_minus_int ) @ ord_less_int ) ) ),
inference(simp,[status(thm)],[758]) ).
thf(593,axiom,
! [A: int] :
( ( one_one_int @ ( A @ times_times_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_zmult__1__right) ).
thf(2997,plain,
! [A: int] :
( ( one_one_int @ ( A @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(465,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( B @ ( C @ times_times_int ) @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) ) )
<=> ( ( B = D )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_crossproduct__eq) ).
thf(2490,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ( B = D )
| ( A = C ) )
=> ( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( B @ ( C @ times_times_int ) @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) ) ) )
& ( ( ( D @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) )
= ( B @ ( C @ times_times_int ) @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) ) )
=> ( ( B = D )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(394,axiom,
! [A: int] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_zero__le__power2) ).
thf(2187,plain,
! [A: int] : ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(301,axiom,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_zero__less__power) ).
thf(1866,plain,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(538,axiom,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( ~ ( C @ ( zero_zero_int @ ( A @ zcong ) ) )
& ~ ( C @ ( zero_zero_int @ ( B @ zcong ) ) ) )
=> ~ ( C @ ( zero_zero_int @ ( A @ ( B @ times_times_int ) @ zcong ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_zcong__zprime__prod__zero__contra) ).
thf(2792,plain,
! [A: int,B: int,C: int] :
( ( C @ zprime )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( ~ ( C @ ( zero_zero_int @ ( A @ zcong ) ) )
& ~ ( C @ ( zero_zero_int @ ( B @ zcong ) ) ) )
=> ~ ( C @ ( zero_zero_int @ ( A @ ( B @ times_times_int ) @ zcong ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(288,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number267125858f_real @ ( A @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_mult__2__right) ).
thf(1807,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number267125858f_real @ ( A @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(115,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
| ( A @ ( B @ ord_less_eq_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_Euler_Oaux2) ).
thf(1108,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
| ( A @ ( B @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(603,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_rel__simps_I40_J) ).
thf(3039,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(157,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ dvd_dvd_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_dvd__power__same) ).
thf(1276,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ dvd_dvd_nat ) )
=> ( A @ ( C @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ dvd_dvd_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1325,plain,
zero_zero_real != one_one_real,
inference(polarity_switch,[status(thm)],[1324]) ).
thf(1326,plain,
zero_zero_real != one_one_real,
inference(lifteq,[status(thm)],[1325]) ).
thf(391,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) @ ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( ( zero_zero_int @ ( E @ ord_less_eq_int ) )
=> ( ( E @ ( A @ ord_less_int ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ( B @ ( D @ ord_less_eq_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_unique__quotient__lemma__neg) ).
thf(2174,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( E @ ( D @ ( A @ times_times_int ) @ plus_plus_int ) @ ( C @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( ( zero_zero_int @ ( E @ ord_less_eq_int ) )
=> ( ( E @ ( A @ ord_less_int ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ( B @ ( D @ ord_less_eq_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(554,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_zcong__zpower) ).
thf(2855,plain,
! [A: nat,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( D @ ( A @ ( C @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ zcong ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(407,axiom,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( one_one_int @ ( B @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ ( B @ times_times_int ) @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_power__Suc__less) ).
thf(2251,plain,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( one_one_int @ ( B @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( A @ ( B @ power_power_int ) @ ( B @ times_times_int ) @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(478,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_nat ) )
<=> ( ( B @ ( A @ ord_less_int ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( pls @ ord_less_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_less__nat__number__of) ).
thf(2554,plain,
! [A: int,B: int] :
( ( ( ( B @ ( A @ ord_less_int ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( pls @ ord_less_int ) ) ) )
=> ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_nat ) ) )
& ( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_nat ) )
=> ( ( B @ ( A @ ord_less_int ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( pls @ ord_less_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(2425,plain,
( ! [A: int] :
( ( A = zero_zero_int )
=> ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int ) )
& ! [A: int] :
( ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int )
=> ( A = zero_zero_int ) ) ),
inference(miniscope,[status(thm)],[2424]) ).
thf(2426,plain,
! [B: int,A: int] :
( ( ( ( B @ ( B @ plus_plus_int ) )
= zero_zero_int )
| ( B != zero_zero_int ) )
& ( ( A = zero_zero_int )
| ( ( A @ ( A @ plus_plus_int ) )
!= zero_zero_int ) ) ),
inference(cnf,[status(esa)],[2425]) ).
thf(2428,plain,
! [A: int] :
( ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int )
| ( A != zero_zero_int ) ),
inference(cnfConj,[status(thm)],[2426]) ).
thf(2430,plain,
! [A: int] :
( ( ( A @ ( A @ plus_plus_int ) )
= zero_zero_int )
| ( A != zero_zero_int ) ),
inference(lifteq,[status(thm)],[2428]) ).
thf(2431,plain,
( ( zero_zero_int @ ( zero_zero_int @ plus_plus_int ) )
= zero_zero_int ),
inference(simp,[status(thm)],[2430]) ).
thf(293,axiom,
! [A: int] :
( ( A @ bit1 @ ( min @ ord_less_int ) )
<=> ( A @ ( min @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_rel__simps_I9_J) ).
thf(1822,plain,
! [A: int] :
( ( ( A @ ( min @ ord_less_int ) )
=> ( A @ bit1 @ ( min @ ord_less_int ) ) )
& ( ( A @ bit1 @ ( min @ ord_less_int ) )
=> ( A @ ( min @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(577,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C
= ( B @ ( C @ times_times_int ) @ ( A @ plus_plus_int ) ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ord_less_eq_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_self__quotient__aux1) ).
thf(2934,plain,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C
= ( B @ ( C @ times_times_int ) @ ( A @ plus_plus_int ) ) )
=> ( ( C @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(615,axiom,
! [A: real] :
( ( A @ ( A @ times_times_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(3085,plain,
! [A: real] :
( ( A @ ( A @ times_times_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(312,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_p0) ).
thf(1903,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(382,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ dvd_dvd_int ) )
=> ( ( B @ ( C @ times_times_int ) @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) )
=> ( B @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_zprime__power__zdvd__cancel__left) ).
thf(2135,plain,
! [A: nat,B: int,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ dvd_dvd_int ) )
=> ( ( B @ ( C @ times_times_int ) @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) )
=> ( B @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( B @ ( A @ power_power_nat ) )
= ( one_one_nat @ ( B @ minus_minus_nat ) @ ( A @ power_power_nat ) @ ( A @ times_times_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( B @ ( A @ power_power_nat ) )
= one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_power__eq__if) ).
thf(1523,plain,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( B @ ( A @ power_power_nat ) )
= ( one_one_nat @ ( B @ minus_minus_nat ) @ ( A @ power_power_nat ) @ ( A @ times_times_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( B @ ( A @ power_power_nat ) )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(380,axiom,
! [A: int,B: int,C: int] :
( ( C @ number_number_of_int @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ number_number_of_int @ ( B @ times_times_int ) @ ( C @ number_number_of_int @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_left__distrib__number__of) ).
thf(2130,plain,
! [A: int,B: int,C: int] :
( ( C @ number_number_of_int @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ number_number_of_int @ ( B @ times_times_int ) @ ( C @ number_number_of_int @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(688,axiom,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_zero__le__power) ).
thf(3368,plain,
! [A: nat,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( B @ power_power_int ) @ ( zero_zero_int @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(451,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( t @ ord_less_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(2447,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( t @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(209,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_real ) @ power_power_real ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1491,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ( A @ power_power_real ) @ power_power_real ) )
= ( C @ ( B @ times_times_nat ) @ ( A @ power_power_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(254,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ zcong ) ) )
<=> ? [D: int] :
( B
= ( D @ ( C @ times_times_int ) @ ( A @ plus_plus_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_zcong__iff__lin) ).
thf(1689,plain,
! [A: int,B: int,C: int] :
( ( ? [D: int] :
( B
= ( D @ ( C @ times_times_int ) @ ( A @ plus_plus_int ) ) )
=> ( C @ ( B @ ( A @ zcong ) ) ) )
& ( ( C @ ( B @ ( A @ zcong ) ) )
=> ? [D: int] :
( B
= ( D @ ( C @ times_times_int ) @ ( A @ plus_plus_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(461,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rel__simps_I33_J) ).
thf(2475,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(540,axiom,
! [A: int] :
( ( A @ number267125858f_real @ ( one_one_real @ ord_less_real ) )
<=> ( A @ ( pls @ bit1 @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__special_I2_J) ).
thf(2796,plain,
! [A: int] :
( ( ( A @ ( pls @ bit1 @ ord_less_int ) )
=> ( A @ number267125858f_real @ ( one_one_real @ ord_less_real ) ) )
& ( ( A @ number267125858f_real @ ( one_one_real @ ord_less_real ) )
=> ( A @ ( pls @ bit1 @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(276,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1777,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(194,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( ( B != zero_zero_nat )
=> ( C @ ( A @ dvd_dvd_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_divides__rev) ).
thf(1440,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ dvd_dvd_nat ) )
=> ( ( B != zero_zero_nat )
=> ( C @ ( A @ dvd_dvd_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(359,axiom,
! [A: int,B: nat,C: int] :
( ( ( B @ ( A @ power_power_int ) )
= ( B @ ( C @ power_power_int ) ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_power__eq__imp__eq__base) ).
thf(2066,plain,
! [A: int,B: nat,C: int] :
( ( ( B @ ( A @ power_power_int ) )
= ( B @ ( C @ power_power_int ) ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(389,axiom,
! [A: int] :
( ( min @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( min @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_rel__simps_I30_J) ).
thf(2162,plain,
! [A: int] :
( ( ( min @ ( A @ ord_less_eq_int ) )
=> ( min @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( min @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( min @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(511,axiom,
! [A: real,B: real] :
~ ( zero_zero_real @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ord_less_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_not__sum__power2__lt__zero) ).
thf(2680,plain,
! [A: real,B: real] :
~ ( zero_zero_real @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ord_less_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(524,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ minus_minus_int ) )
= ( A @ ( pls @ minus_minus_int ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_diff__bin__simps_I3_J) ).
thf(2739,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ minus_minus_int ) )
= ( A @ ( pls @ minus_minus_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(570,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rel__simps_I29_J) ).
thf(2912,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( pls @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( pls @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(6179,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5574,745]) ).
thf(6180,plain,
! [B: int,A: int] :
( ( ( zero_zero_int @ ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) @ ord_less_int ) )
!= ( B @ ( A @ ord_less_int ) ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
inference(simp,[status(thm)],[6179]) ).
thf(6181,plain,
zero_zero_int @ ( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) @ ord_less_eq_int ),
inference(pattern_uni,[status(thm)],[6180:[bind(A,$thf( zero_zero_int @ ( one_one_int @ ( zero_zero_int @ minus_minus_int ) @ minus_minus_int ) )),bind(B,$thf( zero_zero_int ))]]) ).
thf(662,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ( pls @ bit1 @ bit0 @ bit0 @ number267125858f_real @ times_times_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) @ power_power_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_four__x__squared) ).
thf(3267,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ ( pls @ bit1 @ bit0 @ bit0 @ number267125858f_real @ times_times_real ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) @ power_power_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(455,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Bit0__Pls) ).
thf(2462,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(259,axiom,
! [A: real,B: real] :
( ( zero_zero_real @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ord_less_eq_real ) )
<=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_sum__power2__le__zero__iff) ).
thf(1706,plain,
! [A: real,B: real] :
( ( ( ( B = zero_zero_real )
& ( A = zero_zero_real ) )
=> ( zero_zero_real @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ord_less_eq_real ) ) )
& ( ( zero_zero_real @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_real ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_real ) @ plus_plus_real ) @ ord_less_eq_real ) )
=> ( ( B = zero_zero_real )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(140,axiom,
! [A: int,B: int] :
( ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
<=> ~ ( A @ number267125858f_real @ ( B @ number267125858f_real @ ord_less_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_le__number__of__eq__not__less) ).
thf(1193,plain,
! [A: int,B: int] :
( ( ~ ( A @ number267125858f_real @ ( B @ number267125858f_real @ ord_less_real ) )
=> ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_eq_real ) ) )
& ( ( B @ number267125858f_real @ ( A @ number267125858f_real @ ord_less_eq_real ) )
=> ~ ( A @ number267125858f_real @ ( B @ number267125858f_real @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1998,plain,
( ( one_one_real @ ( one_one_real @ plus_plus_real ) )
= ( pls @ bit1 @ bit0 @ number267125858f_real ) ),
inference(lifteq,[status(thm)],[1997]) ).
thf(5336,plain,
( ( one_one_real @ ( one_one_real @ plus_plus_real ) )
= ( zero_zero_int @ bit1 @ bit0 @ number267125858f_real ) ),
inference(rewrite,[status(thm)],[1998,3057]) ).
thf(345,axiom,
( ( t @ ( one_one_int @ ord_less_int ) )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(2019,plain,
( ( t @ ( one_one_int @ ord_less_int ) )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(716,plain,
! [D: real,C: real,B: nat,A: nat] :
( ( B @ ( D @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ dvd_dvd_real ) )
| ~ ( B @ ( A @ ord_less_eq_nat ) )
| ~ ( D @ ( C @ dvd_dvd_real ) ) ),
inference(cnf,[status(esa)],[715]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( C @ times_times_nat ) @ ( D @ ( A @ times_times_nat ) @ plus_plus_nat ) ) )
<=> ( ( B = D )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_crossproduct__eq) ).
thf(1161,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( B = D )
| ( A = C ) )
=> ( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( C @ times_times_nat ) @ ( D @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ) )
& ( ( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( C @ times_times_nat ) @ ( D @ ( A @ times_times_nat ) @ plus_plus_nat ) ) )
=> ( ( B = D )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(275,axiom,
! [A: int] :
( ( A @ number267125858f_real @ ( one_one_real @ ( one_one_real @ plus_plus_real ) @ times_times_real ) )
= ( A @ bit0 @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_double__number__of__Bit0) ).
thf(1774,plain,
! [A: int] :
( ( A @ number267125858f_real @ ( one_one_real @ ( one_one_real @ plus_plus_real ) @ times_times_real ) )
= ( A @ bit0 @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(263,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( B @ ( C @ ( A @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1725,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( B @ ( C @ ( A @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(472,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_real @ power_power_real ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__power2) ).
thf(2534,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_real @ power_power_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(222,axiom,
! [A: int,B: real] :
( ( ( A @ number267125858f_real )
= B )
<=> ( B
= ( A @ number267125858f_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_number__of__reorient) ).
thf(1546,plain,
! [A: int,B: real] :
( ( ( B
= ( A @ number267125858f_real ) )
=> ( ( A @ number267125858f_real )
= B ) )
& ( ( ( A @ number267125858f_real )
= B )
=> ( B
= ( A @ number267125858f_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(620,axiom,
! [A: int] :
( ( A @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ) )
<=> ( A @ ( pls @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_less__0__number__of) ).
thf(3100,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_int ) )
=> ( A @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ) ) )
& ( ( A @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( pls @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(250,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_nat ) )
= ( A @ ( A @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_power3__eq__cube) ).
thf(1673,plain,
! [A: nat] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_nat ) )
= ( A @ ( A @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( zero_zero_nat @ ord_less_eq_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_zero__le__power) ).
thf(1480,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( zero_zero_nat @ ord_less_eq_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(733,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( A @ ( C @ dvd_dvd_nat ) )
| ~ ( C @ ( D @ ord_less_nat ) )
| ~ ( D @ ( zero_zero_nat @ ord_less_nat ) )
| ( A
!= ( D @ ( C @ ( B @ times_times_nat ) @ plus_plus_nat ) ) ) ),
inference(cnf,[status(esa)],[732]) ).
thf(734,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( A @ ( C @ dvd_dvd_nat ) )
| ~ ( C @ ( D @ ord_less_nat ) )
| ~ ( D @ ( zero_zero_nat @ ord_less_nat ) )
| ( A
!= ( D @ ( C @ ( B @ times_times_nat ) @ plus_plus_nat ) ) ) ),
inference(lifteq,[status(thm)],[733]) ).
thf(735,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( C @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) @ ( B @ dvd_dvd_nat ) )
| ~ ( B @ ( C @ ord_less_nat ) )
| ~ ( C @ ( zero_zero_nat @ ord_less_nat ) ) ),
inference(simp,[status(thm)],[734]) ).
thf(315,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_zadd__assoc) ).
thf(1908,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(691,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( A @ ( C @ plus_plus_int ) @ ( A @ ( B @ plus_plus_int ) @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zadd__strict__right__mono) ).
thf(3379,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_int ) )
=> ( A @ ( C @ plus_plus_int ) @ ( A @ ( B @ plus_plus_int ) @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(421,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_rel__simps_I46_J) ).
thf(2302,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(512,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( one_one_int @ ord_less_int ) )
=> ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_power__strict__increasing) ).
thf(2683,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ ord_less_nat ) )
=> ( ( A @ ( one_one_int @ ord_less_int ) )
=> ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(2382,plain,
! [B: int,A: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
| ( B != one_one_int )
| ( A != one_one_int ) ),
inference(cnfConj,[status(thm)],[2377]) ).
thf(2384,plain,
! [B: int,A: int] :
( ( ( B @ ( A @ times_times_int ) )
= one_one_int )
| ( B != one_one_int )
| ( A != one_one_int ) ),
inference(lifteq,[status(thm)],[2382]) ).
thf(2385,plain,
( ( one_one_int @ ( one_one_int @ times_times_int ) )
= one_one_int ),
inference(simp,[status(thm)],[2384]) ).
thf(252,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1678,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(5906,plain,
! [A: int] :
( ( ( zero_zero_nat @ ( A @ power_power_int ) )
!= ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) ) )
| ~ ( one_one_int @ ( zero_zero_int @ ord_less_int ) ) ),
inference(paramod_ordered,[status(thm)],[2139,5862]) ).
thf(5913,plain,
! [A: int] :
( ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat )
!= zero_zero_nat )
| ( A != zero_zero_int )
| ~ ( one_one_int @ ( zero_zero_int @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5906]) ).
thf(5928,plain,
( ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat )
!= zero_zero_nat )
| ~ ( one_one_int @ ( zero_zero_int @ ord_less_int ) ) ),
inference(simp,[status(thm)],[5913]) ).
thf(6667,plain,
( ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat )
!= zero_zero_nat )
| ~ $true ),
inference(rewrite,[status(thm)],[5928,3406]) ).
thf(6668,plain,
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat )
!= zero_zero_nat ),
inference(simp,[status(thm)],[6667]) ).
thf(6685,plain,
( ( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat )
!= ( zero_zero_int @ number_number_of_nat ) )
| ( zero_zero_nat != zero_zero_nat ) ),
inference(paramod_ordered,[status(thm)],[3472,6668]) ).
thf(6686,plain,
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat )
!= ( zero_zero_int @ number_number_of_nat ) ),
inference(simp,[status(thm)],[6685]) ).
thf(6693,plain,
( ( zero_zero_int @ bit1 @ bit0 )
!= zero_zero_int ),
inference(simp,[status(thm)],[6686]) ).
thf(668,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C
= ( B @ ( C @ times_times_int ) @ ( A @ plus_plus_int ) ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( one_one_int @ ( B @ ord_less_eq_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_self__quotient__aux2) ).
thf(3291,plain,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( C
= ( B @ ( C @ times_times_int ) @ ( A @ plus_plus_int ) ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( one_one_int @ ( B @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(111,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( B = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_zcong__zless__0) ).
thf(1097,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ( B @ zcong ) ) )
=> ( B = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1072,plain,
( ! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ) )
& ! [A: nat] :
( ( A = zero_zero_nat )
=> ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ) ) ),
inference(miniscope,[status(thm)],[1071]) ).
thf(1073,plain,
! [B: nat,A: nat] :
( ( ( ( B @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat )
| ( B = zero_zero_nat ) )
& ( ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat )
| ( A != zero_zero_nat ) ) ),
inference(cnf,[status(esa)],[1072]) ).
thf(1074,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat )
| ( A != zero_zero_nat ) ),
inference(cnfConj,[status(thm)],[1073]) ).
thf(1076,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat )
| ( A != zero_zero_nat ) ),
inference(lifteq,[status(thm)],[1074]) ).
thf(1077,plain,
( ( zero_zero_nat @ ( zero_zero_nat @ power_power_nat ) )
= one_one_nat ),
inference(simp,[status(thm)],[1076]) ).
thf(1216,plain,
( ! [A: nat,B: nat] :
( ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) )
=> ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat ) )
& ! [A: nat,B: nat] :
( ( ( B @ ( A @ power_power_nat ) )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B != zero_zero_nat ) ) ) ),
inference(miniscope,[status(thm)],[1215]) ).
thf(1217,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( ( D @ ( C @ power_power_nat ) )
= zero_zero_nat )
| ( C != zero_zero_nat )
| ( D = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
| ( ( B @ ( A @ power_power_nat ) )
!= zero_zero_nat ) )
& ( ( B != zero_zero_nat )
| ( ( B @ ( A @ power_power_nat ) )
!= zero_zero_nat ) ) ),
inference(cnf,[status(esa)],[1216]) ).
thf(1218,plain,
! [B: nat,A: nat] :
( ( B != zero_zero_nat )
| ( ( B @ ( A @ power_power_nat ) )
!= zero_zero_nat ) ),
inference(cnfConj,[status(thm)],[1217]) ).
thf(1221,plain,
! [B: nat,A: nat] :
( ( B != zero_zero_nat )
| ( ( B @ ( A @ power_power_nat ) )
!= zero_zero_nat ) ),
inference(lifteq,[status(thm)],[1218]) ).
thf(1222,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ power_power_nat ) )
!= zero_zero_nat ),
inference(simp,[status(thm)],[1221]) ).
thf(3732,plain,
! [A: nat] :
( ( ( zero_zero_nat @ ( zero_zero_nat @ power_power_nat ) )
!= ( zero_zero_nat @ ( A @ power_power_nat ) ) )
| ( zero_zero_nat != one_one_nat ) ),
inference(paramod_ordered,[status(thm)],[1077,1222]) ).
thf(3733,plain,
zero_zero_nat != one_one_nat,
inference(pattern_uni,[status(thm)],[3732:[bind(A,$thf( zero_zero_nat ))]]) ).
thf(487,axiom,
! [A: int,B: nat,C: int] :
( ( B @ ( C @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( C @ ( A @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_power__less__imp__less__base) ).
thf(2587,plain,
! [A: int,B: nat,C: int] :
( ( B @ ( C @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ ord_less_int ) )
=> ( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( C @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(523,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_semiring__mult__2__right) ).
thf(2736,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ times_times_nat ) )
= ( A @ ( A @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(41,axiom,
! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
=> ( ( A @ ( B @ ord_less_eq_real ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_real__le__antisym) ).
thf(854,plain,
! [A: real,B: real] :
( ( B @ ( A @ ord_less_eq_real ) )
=> ( ( A @ ( B @ ord_less_eq_real ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(498,axiom,
! [A: nat,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_nat ) )
= ( B @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2636,plain,
! [A: nat,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_nat ) )
= ( B @ ( A @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(527,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ times_times_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( zero_zero_int @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_pos__zmult__pos) ).
thf(2751,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ times_times_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( zero_zero_int @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(790,plain,
! [B: nat,A: nat] :
( ( ( B @ ( A @ power_power_nat ) @ ( A @ dvd_dvd_nat ) )
| ( A != one_one_nat ) )
& ( ( B @ ( A @ power_power_nat ) @ ( A @ dvd_dvd_nat ) )
| ~ ( B @ ( zero_zero_nat @ ord_less_nat ) ) ) ),
inference(cnf,[status(esa)],[789]) ).
thf(792,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ power_power_nat ) @ ( A @ dvd_dvd_nat ) )
| ( A != one_one_nat ) ),
inference(cnfConj,[status(thm)],[790]) ).
thf(793,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ power_power_nat ) @ ( A @ dvd_dvd_nat ) )
| ( A != one_one_nat ) ),
inference(lifteq,[status(thm)],[792]) ).
thf(794,plain,
! [A: nat] : ( A @ ( one_one_nat @ power_power_nat ) @ ( one_one_nat @ dvd_dvd_nat ) ),
inference(simp,[status(thm)],[793]) ).
thf(6627,plain,
one_one_nat @ ( one_one_nat @ dvd_dvd_nat ),
inference(rewrite,[status(thm)],[794,1107]) ).
thf(292,axiom,
! [A: int] :
( ( zero_zero_real @ ( A @ number267125858f_real @ ord_less_real ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_less__special_I3_J) ).
thf(1816,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( zero_zero_real @ ( A @ number267125858f_real @ ord_less_real ) ) )
& ( ( zero_zero_real @ ( A @ number267125858f_real @ ord_less_real ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(639,axiom,
! [A: int] :
( ( pls @ bit1 @ number_number_of_int @ ( A @ times_times_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_mult__numeral__1__right) ).
thf(3177,plain,
! [A: int] :
( ( pls @ bit1 @ number_number_of_int @ ( A @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(2177,plain,
( ! [A: int] :
( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ! [A: int] :
( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(miniscope,[status(thm)],[2176]) ).
thf(2178,plain,
! [B: int,A: int] :
( ( ( pls
= ( B @ bit0 ) )
| ( pls != B ) )
& ( ( pls = A )
| ( pls
!= ( A @ bit0 ) ) ) ),
inference(cnf,[status(esa)],[2177]) ).
thf(2180,plain,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
| ( pls != A ) ),
inference(cnfConj,[status(thm)],[2178]) ).
thf(2182,plain,
! [A: int] :
( ( ( A @ bit0 )
= pls )
| ( pls != A ) ),
inference(lifteq,[status(thm)],[2180]) ).
thf(2183,plain,
( ( pls @ bit0 )
= pls ),
inference(simp,[status(thm)],[2182]) ).
thf(3494,plain,
( ( zero_zero_int @ bit0 )
= zero_zero_int ),
inference(rewrite,[status(thm)],[2183,3057]) ).
thf(6712,plain,
( ( ( zero_zero_int @ bit1 @ bit0 )
!= ( zero_zero_int @ bit0 ) )
| ( zero_zero_int != zero_zero_int ) ),
inference(paramod_ordered,[status(thm)],[3494,6693]) ).
thf(6713,plain,
( ( zero_zero_int @ bit1 @ bit0 )
!= ( zero_zero_int @ bit0 ) ),
inference(simp,[status(thm)],[6712]) ).
thf(6714,plain,
( ( zero_zero_int @ bit1 )
!= zero_zero_int ),
inference(simp,[status(thm)],[6713]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) )
= ( C @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1056,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ times_times_nat ) @ ( A @ times_times_nat ) )
= ( C @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(437,axiom,
! [A: int] :
( ( A @ bit0 @ ( min @ ord_less_int ) )
<=> ( A @ ( min @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_rel__simps_I8_J) ).
thf(2366,plain,
! [A: int] :
( ( ( A @ ( min @ ord_less_int ) )
=> ( A @ bit0 @ ( min @ ord_less_int ) ) )
& ( ( A @ bit0 @ ( min @ ord_less_int ) )
=> ( A @ ( min @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(159,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) )
= ( B @ ( C @ times_times_real ) @ ( D @ ( A @ times_times_real ) @ plus_plus_real ) ) )
<=> ( ( B = D )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_crossproduct__eq) ).
thf(1288,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( B = D )
| ( A = C ) )
=> ( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) )
= ( B @ ( C @ times_times_real ) @ ( D @ ( A @ times_times_real ) @ plus_plus_real ) ) ) )
& ( ( ( D @ ( C @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) )
= ( B @ ( C @ times_times_real ) @ ( D @ ( A @ times_times_real ) @ plus_plus_real ) ) )
=> ( ( B = D )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(643,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_zadd__zmult__distrib2) ).
thf(3196,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(494,axiom,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( B @ times_times_int ) @ ( one_one_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_power__gt1__lemma) ).
thf(2619,plain,
! [A: nat,B: int] :
( ( B @ ( one_one_int @ ord_less_int ) )
=> ( A @ ( B @ power_power_int ) @ ( B @ times_times_int ) @ ( one_one_int @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(348,axiom,
! [A: int] :
( ( A @ ( A @ times_times_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(2040,plain,
! [A: int] :
( ( A @ ( A @ times_times_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(74,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A != B )
& ( C != D ) )
<=> ( ( B @ ( D @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ plus_plus_real ) )
!= ( A @ ( D @ times_times_real ) @ ( B @ ( C @ times_times_real ) @ plus_plus_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_crossproduct__noteq) ).
thf(955,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( B @ ( D @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ plus_plus_real ) )
!= ( A @ ( D @ times_times_real ) @ ( B @ ( C @ times_times_real ) @ plus_plus_real ) ) )
=> ( ( A != B )
& ( C != D ) ) )
& ( ( ( A != B )
& ( C != D ) )
=> ( ( B @ ( D @ times_times_real ) @ ( A @ ( C @ times_times_real ) @ plus_plus_real ) )
!= ( A @ ( D @ times_times_real ) @ ( B @ ( C @ times_times_real ) @ plus_plus_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(358,axiom,
! [A: int,B: int] :
( ( B @ ( A @ minus_minus_int ) @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ minus_minus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_zspecial__product) ).
thf(2063,plain,
! [A: int,B: int] :
( ( B @ ( A @ minus_minus_int ) @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ minus_minus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(397,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__int__code_I14_J) ).
thf(2201,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ ord_less_nat ) )
=> ( ( C @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( C @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_power__less__imp__less__base) ).
thf(801,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ power_power_nat ) @ ( B @ ( A @ power_power_nat ) @ ord_less_nat ) )
=> ( ( C @ ( zero_zero_nat @ ord_less_eq_nat ) )
=> ( C @ ( A @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(170,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ ord_less_real ) )
<=> ( B @ ( A @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_real__mult__less__iff1) ).
thf(1335,plain,
! [A: real,B: real,C: real] :
( ( C @ ( zero_zero_real @ ord_less_real ) )
=> ( ( ( B @ ( A @ ord_less_real ) )
=> ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ ord_less_real ) ) )
& ( ( C @ ( B @ times_times_real ) @ ( C @ ( A @ times_times_real ) @ ord_less_real ) )
=> ( B @ ( A @ ord_less_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(483,axiom,
! [A: real] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_real ) )
= ( A @ ( A @ ( A @ times_times_real ) @ times_times_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_power3__eq__cube) ).
thf(2572,plain,
! [A: real] :
( ( pls @ bit1 @ bit1 @ number_number_of_nat @ ( A @ power_power_real ) )
= ( A @ ( A @ ( A @ times_times_real ) @ times_times_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(132,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( ( D @ ( A @ ( C @ zcong ) ) )
=> ( D @ ( A @ ( B @ zcong ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_zcong__trans) ).
thf(1172,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ( B @ zcong ) ) )
=> ( ( D @ ( A @ ( C @ zcong ) ) )
=> ( D @ ( A @ ( B @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(896,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ times_times_nat ) )
= zero_zero_nat ),
inference(cnf,[status(esa)],[895]) ).
thf(897,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ times_times_nat ) )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[896]) ).
thf(766,plain,
! [B: nat,A: nat] :
( ( B @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) )
= ( B @ ( one_one_nat @ ( A @ plus_plus_nat ) @ times_times_nat ) ) ),
inference(cnf,[status(esa)],[765]) ).
thf(767,plain,
! [B: nat,A: nat] :
( ( B @ ( one_one_nat @ ( A @ plus_plus_nat ) @ times_times_nat ) )
= ( B @ ( B @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
inference(lifteq,[status(thm)],[766]) ).
thf(34,axiom,
! [A: real,B: real] : ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_sum__squares__ge__zero) ).
thf(828,plain,
! [A: real,B: real] : ( B @ ( B @ times_times_real ) @ ( A @ ( A @ times_times_real ) @ plus_plus_real ) @ ( zero_zero_real @ ord_less_eq_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3765,plain,
zero_zero_int @ bit1 @ bit0 @ number_number_of_int @ zprime,
inference(rewrite,[status(thm)],[2835,3057]) ).
thf(430,axiom,
! [A: int,B: int] :
( ( ~ ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ( ( ~ ( A @ ( B @ quadRes ) )
=> ( ( B @ ( A @ legendre ) )
= ( min @ number_number_of_int ) ) )
& ( ( A @ ( B @ quadRes ) )
=> ( ( B @ ( A @ legendre ) )
= one_one_int ) ) ) )
& ( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ( ( B @ ( A @ legendre ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_Legendre__def) ).
thf(2340,plain,
! [A: int,B: int] :
( ( ~ ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ( ( ~ ( A @ ( B @ quadRes ) )
=> ( ( B @ ( A @ legendre ) )
= ( min @ number_number_of_int ) ) )
& ( ( A @ ( B @ quadRes ) )
=> ( ( B @ ( A @ legendre ) )
= one_one_int ) ) ) )
& ( ( B @ ( zero_zero_int @ ( A @ zcong ) ) )
=> ( ( B @ ( A @ legendre ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(508,axiom,
! [A: nat,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ power_power_nat ) @ power_power_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_power__even__eq) ).
thf(2668,plain,
! [A: nat,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ power_power_nat ) @ power_power_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(267,axiom,
min @ number_number_of_int @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ quadRes ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(1742,plain,
min @ number_number_of_int @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ quadRes ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( D @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) @ ( C @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(928,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ times_times_nat ) @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) )
= ( D @ ( B @ ( A @ times_times_nat ) @ times_times_nat ) @ ( C @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(687,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_less__eq__int__code_I13_J) ).
thf(3362,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(152,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( C @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( A @ ord_less_int ) )
=> ( ( B @ ( A @ ( C @ zcong ) ) )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_zcong__zless__imp__eq) ).
thf(1261,plain,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( C @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( B @ ( A @ ord_less_int ) )
=> ( ( B @ ( A @ ( C @ zcong ) ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(588,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number267125858f_real @ ( B @ number267125858f_real @ times_times_real ) )
= ( A @ ( B @ times_times_int ) @ number267125858f_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_semiring__mult__number__of) ).
thf(2966,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number267125858f_real @ ( B @ number267125858f_real @ times_times_real ) )
= ( A @ ( B @ times_times_int ) @ number267125858f_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1146,plain,
( ! [A: real] :
( ( A = zero_zero_real )
=> ( ( A @ ( A @ plus_plus_real ) )
= zero_zero_real ) )
& ! [A: real] :
( ( ( A @ ( A @ plus_plus_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(miniscope,[status(thm)],[1145]) ).
thf(1147,plain,
! [B: real,A: real] :
( ( ( ( B @ ( B @ plus_plus_real ) )
= zero_zero_real )
| ( B != zero_zero_real ) )
& ( ( A = zero_zero_real )
| ( ( A @ ( A @ plus_plus_real ) )
!= zero_zero_real ) ) ),
inference(cnf,[status(esa)],[1146]) ).
thf(1149,plain,
! [A: real] :
( ( ( A @ ( A @ plus_plus_real ) )
= zero_zero_real )
| ( A != zero_zero_real ) ),
inference(cnfConj,[status(thm)],[1147]) ).
thf(1151,plain,
! [A: real] :
( ( ( A @ ( A @ plus_plus_real ) )
= zero_zero_real )
| ( A != zero_zero_real ) ),
inference(lifteq,[status(thm)],[1149]) ).
thf(1152,plain,
( ( zero_zero_real @ ( zero_zero_real @ plus_plus_real ) )
= zero_zero_real ),
inference(simp,[status(thm)],[1151]) ).
thf(567,axiom,
! [A: int] :
( ( A @ bit0 @ ( min @ minus_minus_int ) )
= ( A @ ( min @ minus_minus_int ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_diff__bin__simps_I5_J) ).
thf(2898,plain,
! [A: int] :
( ( A @ bit0 @ ( min @ minus_minus_int ) )
= ( A @ ( min @ minus_minus_int ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(91,axiom,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_real ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_power__less__imp__less__exp) ).
thf(1019,plain,
! [A: nat,B: nat,C: real] :
( ( C @ ( one_one_real @ ord_less_real ) )
=> ( ( B @ ( C @ power_power_real ) @ ( A @ ( C @ power_power_real ) @ ord_less_real ) )
=> ( B @ ( A @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(457,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_int @ ( A @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right) ).
thf(2467,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_int @ ( A @ times_times_int ) )
= ( A @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(659,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ product_Pair_int_int ) @ twoSqu2107342101sum2sq @ ( B @ ( A @ product_Pair_int_int ) @ twoSqu2107342101sum2sq @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( D @ ( A @ times_times_int ) @ minus_minus_int ) @ ( D @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) @ product_Pair_int_int ) @ twoSqu2107342101sum2sq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_mult__sum2sq) ).
thf(3259,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ product_Pair_int_int ) @ twoSqu2107342101sum2sq @ ( B @ ( A @ product_Pair_int_int ) @ twoSqu2107342101sum2sq @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( D @ ( A @ times_times_int ) @ minus_minus_int ) @ ( D @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) @ product_Pair_int_int ) @ twoSqu2107342101sum2sq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(32,axiom,
! [A: int,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ number267125858f_real @ times_times_real ) )
= ( C @ ( A @ number267125858f_real @ times_times_real ) @ ( B @ ( A @ number267125858f_real @ times_times_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_right__distrib__number__of) ).
thf(822,plain,
! [A: int,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ number267125858f_real @ times_times_real ) )
= ( C @ ( A @ number267125858f_real @ times_times_real ) @ ( B @ ( A @ number267125858f_real @ times_times_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(696,axiom,
! [A: int,B: int] :
( ( B @ number267125858f_real @ ( A @ number267125858f_real @ plus_plus_real ) )
= ( B @ ( A @ plus_plus_int ) @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__number__of__eq) ).
thf(3392,plain,
! [A: int,B: int] :
( ( B @ number267125858f_real @ ( A @ number267125858f_real @ plus_plus_real ) )
= ( B @ ( A @ plus_plus_int ) @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(2281,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[2280]) ).
thf(5821,plain,
( ( zero_zero_int @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
inference(rewrite,[status(thm)],[2281,3057]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( one_one_nat @ ( B @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ ( B @ times_times_nat ) @ ord_less_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_power__Suc__less) ).
thf(982,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ord_less_nat ) )
=> ( ( one_one_nat @ ( B @ ord_less_nat ) )
=> ( A @ ( B @ power_power_nat ) @ ( A @ ( B @ power_power_nat ) @ ( B @ times_times_nat ) @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(109,axiom,
! [A: nat,B: real] :
( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( A @ ( B @ power_power_real ) @ ( zero_zero_real @ ord_less_eq_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_zero__le__power) ).
thf(1093,plain,
! [A: nat,B: real] :
( ( B @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( A @ ( B @ power_power_real ) @ ( zero_zero_real @ ord_less_eq_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(321,axiom,
! [A: real] :
( ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_semiring__mult__2) ).
thf(1930,plain,
! [A: real] :
( ( A @ ( pls @ bit1 @ bit0 @ number267125858f_real @ times_times_real ) )
= ( A @ ( A @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(656,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_le__number__of) ).
thf(3244,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(217,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ times_times_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(1532,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ times_times_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(319,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(1923,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ ( A @ plus_plus_int ) @ power_power_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( B @ ( A @ ( pls @ bit1 @ bit0 @ number_number_of_int @ times_times_int ) @ times_times_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(599,axiom,
! [A: int] :
( ( one_one_real @ ( A @ number267125858f_real @ plus_plus_real ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number267125858f_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__special_I3_J) ).
thf(3020,plain,
! [A: int] :
( ( one_one_real @ ( A @ number267125858f_real @ plus_plus_real ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number267125858f_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(463,axiom,
! [A: int] :
( ( A @ ( zero_zero_int @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2484,plain,
! [A: int] :
( ( A @ ( zero_zero_int @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(515,axiom,
! [A: nat,B: int,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ dvd_dvd_int ) )
=> ( ( C @ ( B @ times_times_int ) @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) )
=> ( B @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_zprime__power__zdvd__cancel__right) ).
thf(2699,plain,
! [A: nat,B: int,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ dvd_dvd_int ) )
=> ( ( C @ ( B @ times_times_int ) @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) )
=> ( B @ ( A @ ( D @ power_power_int ) @ dvd_dvd_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(438,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ plus_plus_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2372,plain,
! [A: int] :
( ( zero_zero_int @ ( A @ plus_plus_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(236,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( B @ ( C @ ( A @ times_times_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1606,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( B @ ( C @ ( A @ times_times_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) )
= ( B @ ( A @ power_power_nat ) @ ( A @ times_times_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_power__commutes) ).
thf(803,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ power_power_nat ) @ times_times_nat ) )
= ( B @ ( A @ power_power_nat ) @ ( A @ times_times_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(479,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__number__of__eq) ).
thf(2563,plain,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(325,axiom,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(1945,plain,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(226,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ times_times_real ) )
= ( C @ ( A @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1565,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ plus_plus_real ) @ ( A @ times_times_real ) )
= ( C @ ( A @ times_times_real ) @ ( B @ ( A @ times_times_real ) @ plus_plus_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(449,axiom,
! [A: int] :
( ( A @ ( one_one_int @ times_times_int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2436,plain,
! [A: int] :
( ( A @ ( one_one_int @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(103,axiom,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_eq_real ) )
=> ( A @ ( B @ power_power_real ) @ ( one_one_real @ ord_less_eq_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_one__le__power) ).
thf(1069,plain,
! [A: nat,B: real] :
( ( B @ ( one_one_real @ ord_less_eq_real ) )
=> ( A @ ( B @ power_power_real ) @ ( one_one_real @ ord_less_eq_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(48,axiom,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( B @ dvd_dvd_int ) )
=> ( ( B @ ( A @ dvd_dvd_int ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_zdvd__antisym__nonneg) ).
thf(882,plain,
! [A: int,B: int] :
( ( B @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( ( A @ ( B @ dvd_dvd_int ) )
=> ( ( B @ ( A @ dvd_dvd_int ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(89,axiom,
! [A: real,B: nat,C: real] :
( ( B @ ( C @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ ord_less_real ) )
=> ( ( C @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( C @ ( A @ ord_less_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_power__less__imp__less__base) ).
thf(1014,plain,
! [A: real,B: nat,C: real] :
( ( B @ ( C @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ ord_less_real ) )
=> ( ( C @ ( zero_zero_real @ ord_less_eq_real ) )
=> ( C @ ( A @ ord_less_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(253,axiom,
! [A: int,B: nat,C: int] :
( ( ~ ( pls @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ ( C @ number_number_of_nat @ times_times_nat ) )
= ( B @ ( A @ ( C @ times_times_int ) @ number_number_of_nat @ times_times_nat ) ) ) )
& ( ( pls @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ ( C @ number_number_of_nat @ times_times_nat ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_nat__number__of__mult__left) ).
thf(1681,plain,
! [A: int,B: nat,C: int] :
( ( ~ ( pls @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ ( C @ number_number_of_nat @ times_times_nat ) )
= ( B @ ( A @ ( C @ times_times_int ) @ number_number_of_nat @ times_times_nat ) ) ) )
& ( ( pls @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ ( C @ number_number_of_nat @ times_times_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(137,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ( C @ zcong ) ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( C = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_zcong__less__eq) ).
thf(1184,plain,
! [A: int,B: int,C: int] :
( ( C @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( ( A @ ( B @ ( C @ zcong ) ) )
=> ( ( A @ ( C @ ord_less_int ) )
=> ( ( A @ ( B @ ord_less_int ) )
=> ( C = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(361,axiom,
! [A: int,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) )
= ( B @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(2074,plain,
! [A: int,B: nat] :
( ( B @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ times_times_nat ) @ ( A @ power_power_int ) )
= ( B @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(557,axiom,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_power__0) ).
thf(2866,plain,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(549,axiom,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Bit1__def) ).
thf(2832,plain,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( one_one_int @ plus_plus_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(674,axiom,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_nat__number__of__Pls) ).
thf(3316,plain,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(431,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ zprime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).
thf(2351,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(107,axiom,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ dvd_dvd_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_le__imp__power__dvd) ).
thf(1088,plain,
! [A: real,B: nat,C: nat] :
( ( C @ ( B @ ord_less_eq_nat ) )
=> ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ dvd_dvd_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(197,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ zcong ) ) )
<=> ( C @ ( A @ ( B @ zcong ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_zcong__sym) ).
thf(1449,plain,
! [A: int,B: int,C: int] :
( ( ( C @ ( A @ ( B @ zcong ) ) )
=> ( C @ ( B @ ( A @ zcong ) ) ) )
& ( ( C @ ( B @ ( A @ zcong ) ) )
=> ( C @ ( A @ ( B @ zcong ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(290,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__special_I2_J) ).
thf(1812,plain,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(373,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_rel__simps_I15_J) ).
thf(2106,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(366,axiom,
! [A: real] :
( ( pls @ bit1 @ number267125858f_real @ ( A @ times_times_real ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_mult__numeral__1__right) ).
thf(2087,plain,
! [A: real] :
( ( pls @ bit1 @ number267125858f_real @ ( A @ times_times_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(203,axiom,
! [A: real,B: real] :
( ( B @ ( A @ ord_less_real ) )
<=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_real__less__def) ).
thf(1468,plain,
! [A: real,B: real] :
( ( ( ( A != B )
& ( B @ ( A @ ord_less_eq_real ) ) )
=> ( B @ ( A @ ord_less_real ) ) )
& ( ( B @ ( A @ ord_less_real ) )
=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(458,axiom,
! [A: int,B: int,C: int] : ( B @ ( B @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ zcong ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_zcong__zmult__self) ).
thf(2470,plain,
! [A: int,B: int,C: int] : ( B @ ( B @ ( C @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ zcong ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(707,plain,
! [C: nat,B: nat,A: real] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_real ) )
= ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) ) ),
inference(cnf,[status(esa)],[706]) ).
thf(708,plain,
! [C: nat,B: nat,A: real] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_real ) )
= ( C @ ( A @ power_power_real ) @ ( B @ ( A @ power_power_real ) @ times_times_real ) ) ),
inference(lifteq,[status(thm)],[707]) ).
thf(138685,plain,
$false,
inference(e,[status(thm)],[1665,809,1411,3008,2263,1237,893,1982,1956,1879,1718,1369,2889,1190,2306,760,1559,1105,2921,1031,3830,2595,2544,941,2280,1110,762,3072,1882,2395,1443,741,1205,878,2363,2077,2117,2940,1596,2231,1068,994,3153,2947,2248,2671,2014,1728,3108,2099,2282,2114,1269,3017,1671,1137,1310,3332,2918,3044,2184,1999,1327,2459,1640,2901,2146,2360,2575,1426,3217,715,2448,3338,2434,2712,2627,2168,1761,913,3335,2723,2046,1243,4266,709,1613,2010,1650,2886,2082,1724,6102,2869,3370,1095,1746,898,2432,1914,973,885,3088,1046,2400,2825,1904,1518,1623,1482,2654,3221,3029,3131,719,785,2755,1871,2501,917,3125,1313,3845,934,2745,1792,1430,5759,2269,1330,1264,3410,1455,1059,1132,2857,5521,2049,1704,1609,770,1568,1773,3180,1100,1379,3385,969,1572,1115,2929,1815,1494,2222,1465,2090,1373,2259,937,2291,966,1051,6259,2950,2237,1302,1664,2794,3199,5526,789,1911,2782,2451,2236,1858,4147,1864,1828,2925,1960,806,2017,905,2964,1215,1886,2772,2002,2639,3327,2804,1975,1843,2058,1796,2530,1119,2424,774,3676,2137,2103,1405,1697,849,3211,2392,2718,3406,1438,1199,1153,3318,2093,1783,2011,3097,3265,925,5862,2296,2621,2790,2660,714,1868,2061,5281,1730,6200,2589,825,1042,1255,820,2969,2937,788,2032,2528,1900,910,1021,778,1355,2277,862,5579,1570,1174,1676,2133,2414,3250,729,2958,2464,1920,3090,1178,830,1159,1787,2327,2112,974,852,2663,1555,3314,2872,1951,757,3050,2547,2313,4104,1634,2228,3595,2769,1402,2100,1804,1121,3381,1587,1540,1138,3119,3078,3237,3205,989,857,1360,1350,1936,3467,742,1270,3122,1794,1953,2685,1082,3143,1942,3000,1461,6642,1424,2080,2613,1810,3194,1446,2666,1644,3294,706,3311,2877,3407,753,2830,1182,1016,2085,1612,2978,2472,3242,997,701,2536,738,2836,2487,3354,1668,2581,2566,1984,2813,3409,2052,3920,1324,2285,1478,2519,984,911,1979,779,3005,2140,6988,3083,3162,1333,3824,2788,2926,1202,2883,3321,1071,1187,773,2909,2043,3279,765,1846,2408,3190,2645,2189,2121,1135,2176,2292,1103,3042,1273,3262,3158,1278,1906,2253,2149,2570,2941,745,3289,1301,3523,5456,1007,1389,3240,3472,1752,1535,1701,2827,3234,2048,732,1884,2525,2657,2849,1652,3081,2674,2568,1520,3404,2695,1226,1488,3023,2293,3651,3208,1107,6649,2753,5703,1090,3302,2319,3002,1733,3594,1997,1897,919,1258,704,3091,2474,947,764,900,1408,5244,1894,1117,1574,3287,3270,1603,3106,1771,2802,3066,1376,2151,2642,3155,3779,3419,736,1589,1933,880,1801,3160,1307,890,1080,2742,3133,4911,1993,726,2757,1838,915,1112,1339,2605,2785,895,3451,2542,2647,1699,2139,1176,2390,1496,2156,2207,2069,1841,2439,1926,2962,768,2835,2765,1044,2550,2481,7002,868,2931,986,2592,1000,1435,2633,2022,3490,1562,3522,1034,2952,2096,1873,1758,944,2234,1509,749,939,754,836,1049,2054,722,1948,3031,2816,5538,5587,1467,2994,795,3395,2271,1145,2846,2513,776,1798,2715,2397,4490,2143,1647,3833,739,1780,2720,712,1003,1770,3376,6120,2863,705,2375,1156,1743,1400,2192,887,3214,971,954,3462,1267,3058,3642,717,3344,1785,2337,1763,2322,2354,1053,1499,1790,1716,3940,3305,1432,3114,3273,2219,2128,1538,2701,3359,3329,3174,3488,1543,1141,3356,2975,3224,3388,1585,3117,2728,2807,859,2056,1358,1353,2357,1485,1972,3256,2892,2584,3398,1240,991,2875,845,1421,3139,2352,1459,1966,931,2870,1321,3447,2209,3056,3171,2960,2310,903,2611,2325,759,2997,2490,2187,1866,2071,2792,1807,771,1108,3039,1276,1326,1721,2174,2855,2251,2554,3383,2431,1822,2934,3085,1903,2135,1523,2130,3331,3368,2447,1491,1689,2475,2796,1777,1440,2066,2162,2680,763,2739,2912,6181,3267,2462,1706,1193,5336,2019,716,1161,752,1774,1725,2534,1229,1546,3100,1673,1480,735,1908,3379,2302,2683,2385,1678,6693,3291,1097,3733,2587,2736,854,2008,2636,2751,6627,1816,3177,6714,1056,2366,1288,3196,2619,2040,955,2063,2201,801,1335,2572,1172,897,767,828,3765,720,2340,2668,1742,928,2127,3362,1261,2966,1152,2898,1019,2467,3259,908,822,3392,5821,982,1299,1093,1930,839,728,3244,3057,1532,1923,723,3020,2484,2699,3812,3494,5473,2372,1606,803,2563,1945,1565,2436,775,1069,882,1014,1681,1184,2074,2866,2832,3316,2351,1088,1449,6668,1812,2106,2087,1468,3047,2470,5574,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926_2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42 % Computer : n007.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 04:18:39 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.91/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.16/1.39 % [INFO] Parsing done (446ms).
% 2.65/1.40 % [INFO] Running in sequential loop mode.
% 3.40/1.79 % [INFO] eprover registered as external prover.
% 3.64/1.80 % [INFO] Scanning for conjecture ...
% 4.25/2.03 % [INFO] Found a conjecture (or negated_conjecture) and 698 axioms. Running axiom selection ...
% 4.90/2.29 % [INFO] Axiom selection finished. Selected 698 axioms (removed 0 axioms).
% 6.34/2.68 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.77/2.71 % [INFO] Type checking passed.
% 6.77/2.72 % [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 ...
% 232.11/65.05 % External prover 'e' found a proof!
% 232.11/65.06 % [INFO] Killing All external provers ...
% 232.11/65.06 % Time passed: 64510ms (effective reasoning time: 63648ms)
% 232.11/65.06 % 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)>
% 232.11/65.07 % Axioms used in derivation (698): fact_78_nat__numeral__1__eq__1, fact_507__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_310_power__eq__0__iff, fact_88_zle__add1__eq__le, fact_490_power__inject__exp, fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_449_power2__less__0, fact_440_zero__eq__power2, fact_7_zadd__power2, fact_204_Bit0__def, fact_279_semiring__mult__2__right, fact_457_power__commutes, fact_329_dvd__power__same, fact_557_zcong__sym, fact_47_zpower__zpower, fact_645_divides__exp2, fact_276_mult__2, fact_563_order__le__neq__implies__less, fact_154_rel__simps_I27_J, fact_153_rel__simps_I32_J, fact_369_zcong__zpower__zmult, fact_255_mult__numeral__1, fact_368_zero__less__power, fact_543_semiring__norm_I113_J, fact_580_zcong__iff__lin, fact_327_dvd__power__same, fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_352_add__0__iff, fact_283_semiring__one__add__one__is__two, fact_428_less__special_I1_J, fact_542_nat__number__of__Pls, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_483_one__le__power, fact_198_Bit0__Pls, fact_679_q__pos__lemma, fact_489_power__inject__exp, fact_653_zcong__zmult__prop3, fact_669_real__mult__left__cancel, fact_321_power__eq__imp__eq__base, fact_144_zadd__left__commute, fact_395_semiring__numeral__0__eq__0, fact_562_mult__nat__number__of, fact_74_less__eq__number__of__int__code, fact_655_zcong__zprime__prod__zero__contra, fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_218_left__distrib__number__of, fact_301_power__increasing__iff, fact_365_power__mono, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_498_power__strict__increasing, fact_681_unique__quotient__lemma, fact_360_zero__le__power, fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_432_le__special_I1_J, fact_514_rel__simps_I43_J, fact_374_power__less__imp__less__base, fact_564_order__le__neq__implies__less, fact_199_mult__Pls, fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_404_power__Suc__less, fact_641_nat__mult__dvd__cancel__disj_H, fact_607_diff__bin__simps_I4_J, fact_627_diff__square, fact_571_zcong__scalar, fact_208_zadd__zmult__distrib, fact_50_le__number__of__eq__not__less, fact_371_zdvd__period, fact_220_left__distrib__number__of, fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_145_zadd__commute, fact_598_number__of__diff, fact_419_number__of__Bit0, fact_246_add__number__of__eq, fact_203_add__Bit0__Bit0, fact_688_real__le__trans, fact_157_power__even__eq, fact_478_not__sum__power2__lt__zero, fact_216_semiring__add__number__of, fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_32_one__add__one__is__two, fact_594_diff__bin__simps_I7_J, fact_532_rel__simps_I23_J, fact_146_rel__simps_I12_J, fact_600_diff__bin__simps_I10_J, fact_622_divides__cases, fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_376_power__decreasing, fact_468_power__mult, fact_614_zspecial__product, fact_551_dvd__power, fact_159_power__even__eq, fact_677_real__two__squares__add__zero__iff, fact_233_add__numeral__0, fact_521_rel__simps_I24_J, fact_455_power__commutes, fact_499_power__strict__increasing, fact_502_Euler_Oaux____1, fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_316_dvd__power__le, fact_73_less__number__of__int__code, fact_586_zprime__zdvd__zmult, fact_210_plus__numeral__code_I9_J, fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_444_power2__le__imp__le, fact_274_semiring__mult__2, fact_9_power2__sum, fact_546_pos__zmult__eq__1__iff__lemma, fact_269_power3__eq__cube, fact_515_Bit1__Min, fact_71_less__eq__int__code_I13_J, fact_373_power__less__imp__less__base, fact_169_crossproduct__eq, fact_463_power__add, fact_626_power__eq__if, fact_628_divides__add__revr, fact_553_dvd__power, fact_265_one__is__num__one, fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_272_quartic__square__square, fact_680_q__neg__lemma, fact_625_mult__eq__if, fact_516_rel__simps_I37_J, fact_256_mult__numeral__1__right, fact_504_even__power__le__0__imp__0, fact_661_real__zero__not__eq__one, fact_525_rel__simps_I3_J, fact_378_power__strict__decreasing, fact_284_semiring__one__add__one__is__two, fact_386_add__scale__eq__noteq, fact_381_even__less__0__iff, fact_451_zero__less__power2, fact_492_power__strict__increasing__iff, fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_431_le__special_I1_J, fact_268_double__number__of__Bit0, fact_40_zle__antisym, fact_403_odd__nonzero, fact_605_Euler_Oaux1, fact_666_real__mult__commute, fact_139_rel__simps_I48_J, fact_38_zless__linear, fact_382_even__less__0__iff, fact_494_power__strict__increasing__iff, fact_162_less__special_I2_J, fact_442_zero__le__power2, fact_355_double__eq__0__iff, fact_482_zero__le__even__power_H, fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_518_rel__simps_I45_J, fact_460_power__mult__distrib, fact_500_power__strict__increasing, fact_305_s0p, fact_548_one__less__power, fact_567_IntPrimes_Ozcong__zero, fact_72_rel__simps_I31_J, fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_576_power__eq__0__iff__number__of, fact_685_self__quotient__aux2, fact_418_le__nat__number__of, fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_294_power__less__power__Suc, fact_544_rel__simps_I25_J, fact_364_power__mono, fact_37_zless__le, fact_415_not__sum__squares__lt__zero, fact_260_semiring__numeral__1__eq__1, 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fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_200_mult__Bit0, fact_651_Int2_Ozcong__zero, fact_633_Int2_Oaux1, fact_262_numeral__1__eq__1, fact_654_divides__div__not, fact_247_number__of__add, fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_140_zmult__assoc, fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_574_power__m1__even, fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_332_power__0__left, fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_682_zdiv__mono2__lemma, fact_469_power__mult, fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_330_field__power__not__zero, fact_333_power__0__left, fact_437_zero__power2, fact_307__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_, fact_271_power3__eq__cube, fact_390_semiring__norm_I112_J, fact_642_zcong__not__zero, fact_388_zprime__zdvd__power, fact_664_less__eq__real__def, fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_209_zadd__zmult__distrib2, fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_222_right__distrib__number__of, fact_396_bin__less__0__simps_I4_J, fact_436_zero__power2, fact_317_dvd__power__le, fact_443_power2__le__imp__le, fact_133_eq__number__of, fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_541_power__0, fact_411_sum__squares__le__zero__iff, fact_534_eq__number__of__Pls__Min, fact_509_nat__zero__less__power__iff, fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_22_power2__eq__square, fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_617_neg__one__power, fact_309_power__eq__0__iff, fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_662_real__le__eq__diff, fact_141_zmult__commute, fact_616_zdiff__power3, fact_52_less__number__of, fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_24_power2__eq__square, fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_610_inv__not__p__minus__1__aux, fact_17_one__power2, fact_477_not__sum__power2__lt__zero, fact_448_power2__eq__imp__eq, fact_646_divides__rev, fact_142_number__of__is__id, fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_416_sum__squares__gt__zero__iff, fact_150_rel__simps_I4_J, fact_621_Legendre__def, fact_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_313_le__imp__power__dvd, fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_650_zprime__zdvd__zmult__better, fact_234_add__numeral__0, fact_424_int__one__le__iff__zero__less, fact_263_semiring__norm_I110_J, fact_632_nat__mult__eq__one, fact_384_sum__squares__eq__zero__iff, fact_484_one__le__power, fact_435_le__imp__0__less, fact_331_field__power__not__zero, fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_461_power__add, fact_4_p, fact_634_zcong__zmult__prop2, fact_414_not__sum__squares__lt__zero, fact_678_two__realpow__ge__one, fact_549_one__less__power, fact_163_less__special_I2_J, fact_495_power__less__imp__less__exp, fact_533_rel__simps_I28_J, fact_248_number__of__add, fact_462_power__add, fact_644_zdvd__bounds, fact_241_number__of__mult, fact_30_add__special_I3_J, fact_278_semiring__mult__2__right, fact_282_mult__2__right, fact_476_sum__power2__le__zero__iff, fact_487_power__increasing, fact_143_zadd__assoc, fact_579_zcong__not, fact_540_power__0, 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fact_458_power__mult__distrib, fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_429_less__special_I3_J, fact_506_zprime__def, fact_87_add1__zle__eq, fact_166_le__special_I2_J, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_66_rel__simps_I34_J, fact_205_zmult__1__right, fact_64_rel__simps_I17_J, fact_675_real__mult__le__cancel__iff1, fact_334_power__0__left, fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_493_power__strict__increasing__iff, fact_629_divides__mul__l, fact_606_zle__diff1__eq, fact_623_divides__antisym, fact_659_realpow__two__sum__zero__iff, fact_158_power__even__eq, fact_5_t, fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096, fact_315_dvd__power__le, fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_689_real__le__linear, fact_438_zero__power2, fact_335_zdvd__imp__le, fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_275_semiring__mult__2, fact_62_nat__1__add__1, fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_83_rel__simps_I33_J, fact_195_rel__simps_I49_J, fact_361_zero__le__power, fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_480_sum__power2__gt__zero__iff, fact_147_less__int__code_I15_J, fact_11_power2__sum, fact_367_zero__less__power, fact_575_power__m1__even, fact_303_power__increasing__iff, fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_249_add__Bit1__Bit0, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_608_diff__bin__simps_I6_J, fact_280_semiring__mult__2__right, fact_65_less__eq__int__code_I16_J, fact_358_zadd__0, fact_619_one__not__neg__one__mod__m, fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_485_one__le__power, fact_517_rel__simps_I40_J, fact_86_zless__imp__add1__zle, fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096, fact_261_numeral__1__eq__1, fact_479_sum__power2__gt__zero__iff, fact_337_power__strict__mono, fact_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_297_power__gt1__lemma, fact_402_zmult__zless__mono2, fact_178_crossproduct__noteq, fact_245_add__number__of__eq, fact_156_zless__add1__eq, fact_270_power3__eq__cube, fact_60_nat__mult__2, fact_375_power__decreasing, fact_370_zdvd__reduce, fact_292_power__less__power__Suc, fact_670_real__mult__right__cancel, fact_219_left__distrib__number__of, fact_473_sum__power2__ge__zero, fact_54_le__number__of, fact_286_p0, fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_6_qf1pt, fact_665_real__mult__1, fact_592_zcong__zdiff, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_423_power__one__right, fact_328_dvd__power__same, fact_597_zdvd__zdiffD, fact_453_sum__power2__eq__zero__iff, fact_674_real__mult__le__cancel__iff2, fact_522_not__real__square__gt__zero, fact_36_zle__linear, fact_28_add__special_I2_J, fact_531_rel__simps_I20_J, fact_417_sum__squares__gt__zero__iff, fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_8_zadd__power3, fact_604_zcong__def, fact_565_order__le__neq__implies__less, fact_211_semiring__mult__number__of, fact_385_add__scale__eq__noteq, fact_300_power__le__imp__le__exp, fact_359_zadd__0__right, fact_578_power__eq__0__iff__number__of, fact_236_add__numeral__0__right, fact_217_power2__ge__self, fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_215_semiring__add__number__of, fact_454_sum__power2__eq__zero__iff, fact_550_one__less__power, fact_164_le__special_I4_J, fact_635_zcong__zmult__prop1, fact_206_zmult__1, fact_430_less__special_I3_J, fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_474_sum__power2__ge__zero, fact_16_one__power2, fact_155_rel__simps_I21_J, fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_558_zcong__refl, fact_589_neg__one__power__eq__mod__m, fact_496_power__less__imp__less__exp, fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_213_semiring__mult__number__of, fact_76_zadd__left__mono, fact_684_zdiv__mono2__neg__lemma, fact_486_power__increasing, fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_401_pos__zmult__pos, fact_197_rel__simps_I38_J
% 232.11/65.07 % No. of inferences in proof: 1721
% 232.11/65.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 64510 ms resp. 63648 ms w/o parsing
% 220.54/65.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 220.94/65.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------