TSTP Solution File: NUM925+5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 13:03:14 EDT 2024
% Result : Theorem 8.10s 3.71s
% Output : Refutation 8.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 153
% Syntax : Number of formulae : 308 ( 148 unt; 0 typ; 0 def)
% Number of atoms : 660 ( 271 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2959 ( 43 ~; 10 |; 104 &;2564 @)
% ( 38 <=>; 200 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 6 con; 0-3 aty)
% Number of variables : 420 ( 0 ^ 420 !; 0 ?; 420 :)
% Comments :
%------------------------------------------------------------------------------
thf(power_power_type,type,
power_power: $i > $i > $i > $i ).
thf(int_type,type,
int: $i ).
thf(plus_plus_type,type,
plus_plus: $i > $i > $i > $i ).
thf(one_one_type,type,
one_one: $i > $i ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat: $i > $i > $i ).
thf(n_type,type,
n: $i ).
thf(number_number_of_type,type,
number_number_of: $i > $i > $i ).
thf(nat_type,type,
nat: $i ).
thf(bit0_type,type,
bit0: $i > $i ).
thf(bit1_type,type,
bit1: $i > $i ).
thf(pls_type,type,
pls: $i ).
thf(zero_zero_type,type,
zero_zero: $i > $i ).
thf(linordered_idom_type,type,
linordered_idom: $i > $o ).
thf(ord_less_type,type,
ord_less: $i > $i > $i > $o ).
thf(ti_type,type,
ti: $i > $i > $i ).
thf(undefined_type,type,
undefined: $i > $i ).
thf(number_ring_type,type,
number_ring: $i > $o ).
thf(number_semiring_type,type,
number_semiring: $i > $o ).
thf(ring_char_0_type,type,
ring_char_0: $i > $o ).
thf(power_type,type,
power: $i > $o ).
thf(mult_zero_type,type,
mult_zero: $i > $o ).
thf(no_zero_divisors_type,type,
no_zero_divisors: $i > $o ).
thf(zero_neq_one_type,type,
zero_neq_one: $i > $o ).
thf(number_type,type,
number: $i > $o ).
thf(semiring_1_type,type,
semiring_1: $i > $o ).
thf(t_type,type,
t: $i ).
thf(ring_11004092258visors_type,type,
ring_11004092258visors: $i > $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add: $i > $o ).
thf(semiring_0_type,type,
semiring_0: $i > $o ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( number_semiring @ B )
=> ( ( semiring_1_of_nat @ B @ ( ti @ nat @ A ) )
= ( semiring_1_of_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1) ).
thf(645,plain,
! [A: $i,B: $i] :
( ( number_semiring @ B )
=> ( ( semiring_1_of_nat @ B @ ( ti @ nat @ A ) )
= ( semiring_1_of_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_int__int__eq) ).
thf(365,plain,
! [A: $i,B: $i] :
( ( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ A ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ B ) ) )
& ( ~ ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__nat__number__of) ).
thf(666,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ A ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ B ) ) )
& ( ~ ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(85,axiom,
! [A: $i] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__Pls) ).
thf(449,plain,
! [A: $i] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( number_semiring @ B )
=> ( ( ti @ B @ ( semiring_1_of_nat @ B @ A ) )
= ( semiring_1_of_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).
thf(511,plain,
! [A: $i,B: $i] :
( ( number_semiring @ B )
=> ( ( ti @ B @ ( semiring_1_of_nat @ B @ A ) )
= ( semiring_1_of_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(135,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_semiring__one__add__one__is__two) ).
thf(614,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(70,axiom,
! [A: $i] :
( ( ring_11004092258visors @ A )
=> ! [B: $i] :
( ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) )
<=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
thf(408,plain,
! [A: $i] :
( ( ring_11004092258visors @ A )
=> ! [B: $i] :
( ( ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) )
& ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
=> ( ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(7,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bin__less__0__simps_I1_J) ).
thf(170,plain,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nat__numeral__1__eq__1) ).
thf(384,plain,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(114,axiom,
! [A: $i] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
thf(533,plain,
! [A: $i] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( semiring_1_of_nat @ int @ ( power_power @ nat @ A @ B ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_int__power) ).
thf(500,plain,
! [A: $i,B: $i] :
( ( semiring_1_of_nat @ int @ ( power_power @ nat @ A @ B ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( number_semiring @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
thf(288,plain,
! [A: $i,B: $i,C: $i] :
( ( number_semiring @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__Bit1__Bit0) ).
thf(436,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( semiring_0 @ C ) )
=> ( ( power_power @ C @ ( ti @ C @ A ) @ B )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_arg1) ).
thf(570,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( semiring_0 @ C ) )
=> ( ( power_power @ C @ ( ti @ C @ A ) @ B )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(60,axiom,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zero__power2) ).
thf(372,plain,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rel__simps_I51_J) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( ( ( bit1 @ A )
= ( bit1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit1 @ A )
= ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(117,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(542,plain,
semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ord_less @ int @ ( plus_plus @ int @ B @ A ) @ ( plus_plus @ int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zadd__strict__right__mono) ).
thf(638,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less @ int @ B @ C )
=> ( ord_less @ int @ ( plus_plus @ int @ B @ A ) @ ( plus_plus @ int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(72,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
thf(416,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(84,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(448,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(95,axiom,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ! [B: $i] :
( ( ( ( number_number_of @ nat @ B )
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( one_one @ A ) ) )
& ( ( ( number_number_of @ nat @ B )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_power__0__left__number__of) ).
thf(475,plain,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ! [B: $i] :
( ( ( ( number_number_of @ nat @ B )
= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( one_one @ A ) ) )
& ( ( ( number_number_of @ nat @ B )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ A @ ( zero_zero @ A ) @ ( number_number_of @ nat @ B ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(82,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(443,plain,
no_zero_divisors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(109,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I12_J) ).
thf(514,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(101,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_semiring__numeral__0__eq__0) ).
thf(492,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( linordered_idom @ C )
=> ( ( ord_less @ C @ ( ti @ C @ A ) @ B )
<=> ( ord_less @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg1) ).
thf(164,plain,
! [A: $i,B: $i,C: $i] :
( ( linordered_idom @ C )
=> ( ( ( ord_less @ C @ ( ti @ C @ A ) @ B )
=> ( ord_less @ C @ A @ B ) )
& ( ( ord_less @ C @ A @ B )
=> ( ord_less @ C @ ( ti @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(53,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_int__0) ).
thf(348,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(125,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(574,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(67,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_number__of__add) ).
thf(397,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).
thf(280,plain,
! [A: $i,B: $i] :
( ( ( ( bit0 @ A )
= ( bit0 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit0 @ A )
= ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(38,axiom,
! [A: $i] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
thf(293,plain,
! [A: $i] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I16_J) ).
thf(660,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(77,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) )
<=> ( ord_less @ int @ B @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__special_I3_J) ).
thf(428,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) )
=> ( ord_less @ int @ B @ pls ) )
& ( ( ord_less @ int @ B @ pls )
=> ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(44,axiom,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_int__1) ).
thf(312,plain,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(43,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
<=> ( ord_less @ int @ B @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__special_I4_J) ).
thf(307,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
=> ( ord_less @ int @ B @ ( bit1 @ pls ) ) )
& ( ( ord_less @ int @ B @ ( bit1 @ pls ) )
=> ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__Bit0__Bit0) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(80,axiom,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( one_one @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_one__power2) ).
thf(439,plain,
! [A: $i] :
( ( semiring_1 @ A )
=> ( ( power_power @ A @ ( one_one @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(33,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
~ ( ord_less @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_power2__less__0) ).
thf(270,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
~ ( ord_less @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(24,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(233,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( ti @ A @ C )
= ( zero_zero @ A ) ) )
=> ( ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zadd__int) ).
thf(452,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_rel__simps_I50_J) ).
thf(302,plain,
! [A: $i,B: $i] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( ti @ B @ ( number_number_of @ B @ A ) )
= ( number_number_of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( ti @ B @ ( number_number_of @ B @ A ) )
= ( number_number_of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(141,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( one_one @ A )
= ( number_number_of @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_semiring__norm_I110_J) ).
thf(630,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( one_one @ A )
= ( number_number_of @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( linord219039673up_add @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
thf(467,plain,
! [A: $i,B: $i,C: $i] :
( ( linord219039673up_add @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( mult_zero @ C )
& ( no_zero_divisors @ C )
& ( zero_neq_one @ C ) )
=> ( ( power_power @ C @ ( ti @ C @ A ) @ B )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_arg1) ).
thf(484,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( mult_zero @ C )
& ( no_zero_divisors @ C )
& ( zero_neq_one @ C ) )
=> ( ( power_power @ C @ ( ti @ C @ A ) @ B )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(138,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(625,plain,
ring_11004092258visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(48,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(329,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(153,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(665,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( linord219039673up_add @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(456,plain,
! [A: $i,B: $i,C: $i] :
( ( linord219039673up_add @ C )
=> ( ( plus_plus @ C @ ( ti @ C @ A ) @ B )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(128,axiom,
! [A: $i] :
( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_int__eq__0__conv) ).
thf(583,plain,
! [A: $i] :
( ( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( semiring_0 @ C ) )
=> ( ( ti @ C @ ( power_power @ C @ A @ B ) )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_res) ).
thf(522,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( semiring_0 @ C ) )
=> ( ( ti @ C @ ( power_power @ C @ A @ B ) )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(110,axiom,
! [A: $i] :
( ( bit0 @ ( ti @ int @ A ) )
= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
thf(519,plain,
! [A: $i] :
( ( bit0 @ ( ti @ int @ A ) )
= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I14_J) ).
thf(403,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(56,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(356,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(130,axiom,
! [A: $i] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).
thf(593,plain,
! [A: $i] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(94,axiom,
! [A: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_odd__nonzero) ).
thf(471,plain,
! [A: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( mult_zero @ C )
& ( no_zero_divisors @ C )
& ( zero_neq_one @ C ) )
=> ( ( ti @ C @ ( power_power @ C @ A @ B ) )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_res) ).
thf(488,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( mult_zero @ C )
& ( no_zero_divisors @ C )
& ( zero_neq_one @ C ) )
=> ( ( ti @ C @ ( power_power @ C @ A @ B ) )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ int @ B @ ( plus_plus @ int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_zadd__left__commute) ).
thf(193,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) )
= ( plus_plus @ int @ B @ ( plus_plus @ int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(146,axiom,
! [A: $i] :
( ( power_power @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_quartic__square__square) ).
thf(642,plain,
! [A: $i] :
( ( power_power @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( number_number_of @ B @ ( ti @ int @ A ) )
= ( number_number_of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(590,plain,
! [A: $i,B: $i] :
( ( number @ B )
=> ( ( number_number_of @ B @ ( ti @ int @ A ) )
= ( number_number_of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(150,axiom,
! [A: $i] :
( ( plus_plus @ int @ A @ ( zero_zero @ int ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_zadd__0__right) ).
thf(654,plain,
! [A: $i] :
( ( plus_plus @ int @ A @ ( zero_zero @ int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(105,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
thf(503,plain,
( pls
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_less__int__code_I13_J) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(31,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(266,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(142,axiom,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_2_res) ).
thf(633,plain,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(17,axiom,
( ( ti @ nat @ n )
= n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_n_____res) ).
thf(205,plain,
( ( ti @ nat @ n )
= n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__Bit0__Bit1) ).
thf(657,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(76,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ ( number_number_of @ A @ pls ) )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__numeral__0__right) ).
thf(425,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ B @ ( number_number_of @ A @ pls ) )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(124,axiom,
ord_less @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
thf(573,plain,
ord_less @ int @ ( one_one @ int ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(83,axiom,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I39_J) ).
thf(444,plain,
! [A: $i] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(61,axiom,
! [A: $i] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I44_J) ).
thf(375,plain,
! [A: $i] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(10,axiom,
! [A: $i] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I38_J) ).
thf(180,plain,
! [A: $i] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( zero_zero @ A )
= ( number_number_of @ A @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring__norm_I112_J) ).
thf(296,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( zero_zero @ A )
= ( number_number_of @ A @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(13,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
thf(191,plain,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(37,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_semiring__norm_I113_J) ).
thf(291,plain,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(204,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(62,axiom,
( ( ti @ int @ t )
= t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(382,plain,
( ( ti @ int @ t )
= t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(134,axiom,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ( ( ti @ A @ ( one_one @ A ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
thf(611,plain,
! [A: $i] :
( ( ( power @ A )
& ( semiring_0 @ A ) )
=> ( ( ti @ A @ ( one_one @ A ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(50,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ pls ) @ B )
= ( ti @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
thf(335,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ pls ) @ B )
= ( ti @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(54,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_n0) ).
thf(350,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(133,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( ring_char_0 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( number_number_of @ A @ B )
= ( number_number_of @ A @ C ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_eq__number__of) ).
thf(604,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( ring_char_0 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ( number_number_of @ A @ B )
= ( number_number_of @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( number_number_of @ A @ B )
= ( number_number_of @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(11,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( plus_plus @ int @ ( bit1 @ pls ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__special_I2_J) ).
thf(187,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
= ( number_number_of @ A @ ( plus_plus @ int @ ( bit1 @ pls ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ord_less @ A @ ( plus_plus @ A @ B @ B ) @ ( zero_zero @ A ) )
<=> ( ord_less @ A @ B @ ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_even__less__0__iff) ).
thf(172,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( plus_plus @ A @ B @ B ) @ ( zero_zero @ A ) )
=> ( ord_less @ A @ B @ ( zero_zero @ A ) ) )
& ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
=> ( ord_less @ A @ ( plus_plus @ A @ B @ B ) @ ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( number_semiring @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
thf(419,plain,
! [A: $i,B: $i,C: $i] :
( ( number_semiring @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(23,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__number__of__eq) ).
thf(230,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( semiring_0 @ C ) )
=> ( ( power_power @ C @ A @ ( ti @ nat @ B ) )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_arg2) ).
thf(567,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( semiring_0 @ C ) )
=> ( ( power_power @ C @ A @ ( ti @ nat @ B ) )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(26,axiom,
! [A: $i] :
( ( ti @ int @ ( bit0 @ A ) )
= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
thf(245,plain,
! [A: $i] :
( ( ti @ int @ ( bit0 @ A ) )
= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( ord_less @ nat @ A @ ( ti @ nat @ B ) )
<=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg2) ).
thf(599,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ nat @ A @ ( ti @ nat @ B ) )
=> ( ord_less @ nat @ A @ B ) )
& ( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( ti @ nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zless__add1__eq) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) )
=> ( ( ord_less @ int @ A @ B )
| ( A = B ) ) )
& ( ( ( ord_less @ int @ A @ B )
| ( A = B ) )
=> ( ord_less @ int @ A @ ( plus_plus @ int @ B @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(139,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(626,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1,conjecture,
( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(155,plain,
~ ( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__int__code_I16_J) ).
thf(330,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(90,axiom,
! [A: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zadd__0) ).
thf(462,plain,
! [A: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(143,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Numeral1__eq1__nat) ).
thf(636,plain,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(87,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(455,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(42,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(306,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(121,axiom,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rel__simps_I46_J) ).
thf(563,plain,
! [A: $i] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(40,axiom,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_0_res) ).
thf(299,plain,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( plus_plus @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( plus_plus @ A @ ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__number__of__left) ).
thf(267,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( plus_plus @ A @ ( number_number_of @ A @ C ) @ D ) )
= ( plus_plus @ A @ ( number_number_of @ A @ ( plus_plus @ int @ B @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(106,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(505,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(149,axiom,
semiring_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(653,plain,
semiring_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(6,axiom,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(167,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(119,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_bin__less__0__simps_I4_J) ).
thf(548,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(136,axiom,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ! [B: $i] :
( ( ( plus_plus @ A @ B @ B )
= ( zero_zero @ A ) )
<=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_double__eq__0__iff) ).
thf(617,plain,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ! [B: $i] :
( ( ( ( plus_plus @ A @ B @ B )
= ( zero_zero @ A ) )
=> ( ( ti @ A @ B )
= ( zero_zero @ A ) ) )
& ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
=> ( ( plus_plus @ A @ B @ B )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(120,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_sum__power2__gt__zero__iff) ).
thf(553,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i,C: $i] :
( ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) ) )
& ( ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
| ( ( ti @ A @ C )
!= ( zero_zero @ A ) ) )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ A @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(148,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I10_J) ).
thf(648,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(98,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(487,plain,
no_zero_divisors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ C ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zadd__int__left) ).
thf(525,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ C ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( mult_zero @ C )
& ( no_zero_divisors @ C )
& ( zero_neq_one @ C ) )
=> ( ( power_power @ C @ A @ ( ti @ nat @ B ) )
= ( power_power @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_arg2) ).
thf(580,plain,
! [A: $i,B: $i,C: $i] :
( ( ( power @ C )
& ( mult_zero @ C )
& ( no_zero_divisors @ C )
& ( zero_neq_one @ C ) )
=> ( ( power_power @ C @ A @ ( ti @ nat @ B ) )
= ( power_power @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(145,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
thf(640,plain,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(30,axiom,
! [A: $i] :
( ( ti @ int @ ( bit1 @ A ) )
= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
thf(263,plain,
! [A: $i] :
( ( ti @ int @ ( bit1 @ A ) )
= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
= ( number_number_of @ int @ ( plus_plus @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_plus__numeral__code_I9_J) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
= ( number_number_of @ int @ ( plus_plus @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__special_I2_J) ).
thf(338,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) )
=> ( ord_less @ int @ ( bit1 @ pls ) @ B ) )
& ( ( ord_less @ int @ ( bit1 @ pls ) @ B )
=> ( ord_less @ A @ ( one_one @ A ) @ ( number_number_of @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(93,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(470,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(57,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i,C: $i] :
( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
<=> ( ord_less @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_less__number__of) ).
thf(359,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) )
=> ( ord_less @ int @ B @ C ) )
& ( ( ord_less @ int @ B @ C )
=> ( ord_less @ A @ ( number_number_of @ A @ B ) @ ( number_number_of @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rel__simps_I49_J) ).
thf(386,plain,
! [A: $i,B: $i] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ord_less @ nat @ ( ti @ nat @ A ) @ B )
<=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg1) ).
thf(314,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ nat @ ( ti @ nat @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) )
& ( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( ti @ nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(103,axiom,
! [A: $i] :
( ( bit1 @ ( ti @ int @ A ) )
= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
thf(497,plain,
! [A: $i] :
( ( bit1 @ ( ti @ int @ A ) )
= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(91,axiom,
( ( ti @ int @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(465,plain,
( ( ti @ int @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
| ( A = B )
| ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zless__linear) ).
thf(627,plain,
! [A: $i,B: $i] :
( ( ord_less @ int @ A @ B )
| ( A = B )
| ( ord_less @ int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(116,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add__special_I3_J) ).
thf(539,plain,
! [A: $i] :
( ( number_ring @ A )
=> ! [B: $i] :
( ( plus_plus @ A @ ( number_number_of @ A @ B ) @ ( one_one @ A ) )
= ( number_number_of @ A @ ( plus_plus @ int @ B @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(96,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_nat__number__of__Pls) ).
thf(482,plain,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(102,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
thf(495,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(21,axiom,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ! [B: $i,C: $i] :
( ( ( power_power @ A @ B @ ( number_number_of @ nat @ C ) )
= ( zero_zero @ A ) )
<=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( number_number_of @ nat @ C )
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_power__eq__0__iff__number__of) ).
thf(218,plain,
! [A: $i] :
( ( ( power @ A )
& ( mult_zero @ A )
& ( no_zero_divisors @ A )
& ( zero_neq_one @ A ) )
=> ! [B: $i,C: $i] :
( ( ( ( power_power @ A @ B @ ( number_number_of @ nat @ C ) )
= ( zero_zero @ A ) )
=> ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( number_number_of @ nat @ C )
!= ( zero_zero @ nat ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( zero_zero @ A ) )
& ( ( number_number_of @ nat @ C )
!= ( zero_zero @ nat ) ) )
=> ( ( power_power @ A @ B @ ( number_number_of @ nat @ C ) )
= ( zero_zero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(46,axiom,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( ( ti @ A @ B )
!= ( zero_zero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__less__power2) ).
thf(319,plain,
! [A: $i] :
( ( linordered_idom @ A )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ti @ A @ B )
!= ( zero_zero @ A ) ) )
& ( ( ( ti @ A @ B )
!= ( zero_zero @ A ) )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(65,axiom,
! [A: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_odd__less__0) ).
thf(390,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(73,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(418,plain,
mult_zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( linordered_idom @ C )
=> ( ( ord_less @ C @ A @ ( ti @ C @ B ) )
<=> ( ord_less @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg2) ).
thf(158,plain,
! [A: $i,B: $i,C: $i] :
( ( linordered_idom @ C )
=> ( ( ( ord_less @ C @ A @ ( ti @ C @ B ) )
=> ( ord_less @ C @ A @ B ) )
& ( ( ord_less @ C @ A @ B )
=> ( ord_less @ C @ A @ ( ti @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_less__number__of__int__code) ).
thf(351,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( number_number_of @ int @ A ) @ ( number_number_of @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(78,axiom,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_1_res) ).
thf(433,plain,
! [A: $i] :
( ( linord219039673up_add @ A )
=> ( ( ti @ A @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(18,axiom,
( ( zero_zero @ int )
!= ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_int__0__neq__1) ).
thf(207,plain,
( ( zero_zero @ int )
!= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( linord219039673up_add @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ( linord219039673up_add @ C )
=> ( ( ti @ C @ ( plus_plus @ C @ A @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(12,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(190,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(75,axiom,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
thf(422,plain,
! [A: $i] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(34,axiom,
! [A: $i] :
( ( number @ A )
=> ! [B: $i,C: $i] :
( ( ( number_number_of @ A @ B )
= ( ti @ A @ C ) )
<=> ( ( ti @ A @ C )
= ( number_number_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_number__of__reorient) ).
thf(273,plain,
! [A: $i] :
( ( number @ A )
=> ! [B: $i,C: $i] :
( ( ( ( number_number_of @ A @ B )
= ( ti @ A @ C ) )
=> ( ( ti @ A @ C )
= ( number_number_of @ A @ B ) ) )
& ( ( ( ti @ A @ C )
= ( number_number_of @ A @ B ) )
=> ( ( number_number_of @ A @ B )
= ( ti @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__int__code_I15_J) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(47,axiom,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i] :
( ( number_number_of @ A @ ( semiring_1_of_nat @ int @ B ) )
= ( semiring_1_of_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_number__of__int) ).
thf(326,plain,
! [A: $i] :
( ( number_semiring @ A )
=> ! [B: $i] :
( ( number_number_of @ A @ ( semiring_1_of_nat @ int @ B ) )
= ( semiring_1_of_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ A ) @ B )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_zpower__int) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ A ) @ B )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less @ int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I17_J) ).
thf(506,plain,
! [A: $i,B: $i] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less @ int @ A @ B ) )
& ( ( ord_less @ int @ A @ B )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(68,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_number__of__Pls) ).
thf(400,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ pls )
= ( zero_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(71,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(415,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(126,axiom,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ord_less @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) )
<=> ( ord_less @ int @ pls @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_less__special_I1_J) ).
thf(575,plain,
! [A: $i] :
( ( ( number_ring @ A )
& ( linordered_idom @ A ) )
=> ! [B: $i] :
( ( ( ord_less @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) )
=> ( ord_less @ int @ pls @ B ) )
& ( ( ord_less @ int @ pls @ B )
=> ( ord_less @ A @ ( zero_zero @ A ) @ ( number_number_of @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( plus_plus @ int @ A @ B )
= ( plus_plus @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
thf(596,plain,
! [A: $i,B: $i] :
( ( plus_plus @ int @ A @ B )
= ( plus_plus @ int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(113,axiom,
! [A: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I4_J) ).
thf(528,plain,
! [A: $i] :
( ( ( ord_less @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(89,axiom,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ ( bit1 @ pls ) )
= ( one_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
thf(459,plain,
! [A: $i] :
( ( number_ring @ A )
=> ( ( number_number_of @ A @ ( bit1 @ pls ) )
= ( one_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(81,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(442,plain,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(66,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
thf(395,plain,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(137,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(624,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ A @ B ) @ C )
= ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zadd__assoc) ).
thf(227,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ A @ B ) @ C )
= ( plus_plus @ int @ A @ ( plus_plus @ int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,axiom,
! [A: $i] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_bin__less__0__simps_I3_J) ).
thf(543,plain,
! [A: $i] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( number_semiring @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
thf(215,plain,
! [A: $i,B: $i,C: $i] :
( ( number_semiring @ C )
=> ( ( plus_plus @ C @ A @ ( ti @ C @ B ) )
= ( plus_plus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(100,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(491,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(58,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_int__0__less__1) ).
thf(364,plain,
ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(676,plain,
$false,
inference(e,[status(thm)],[645,365,666,449,511,614,408,170,384,533,500,288,436,570,372,196,542,638,416,448,475,443,514,492,164,348,574,397,280,293,660,428,312,307,248,439,270,233,452,302,260,630,467,484,625,329,665,456,583,522,519,403,356,593,471,488,193,642,590,654,503,343,266,633,205,657,425,161,573,444,375,180,296,191,291,204,382,611,335,350,604,187,172,419,230,567,245,599,251,626,155,330,462,636,455,306,563,299,267,505,653,167,548,617,553,648,487,525,580,640,263,177,338,470,359,386,314,497,465,627,539,482,495,218,319,390,418,158,351,433,207,536,190,422,273,210,326,242,506,400,415,575,596,528,459,442,395,624,227,543,215,491,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 23:53:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.07/1.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.59/1.30 % [INFO] Parsing done (248ms).
% 1.59/1.32 % [INFO] Running in sequential loop mode.
% 2.35/1.72 % [INFO] eprover registered as external prover.
% 2.35/1.72 % [INFO] Scanning for conjecture ...
% 2.69/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 152 axioms. Running axiom selection ...
% 2.96/1.98 % [INFO] Axiom selection finished. Selected 152 axioms (removed 0 axioms).
% 3.43/2.15 % [INFO] Problem is first-order (TPTP FOF).
% 3.48/2.17 % [INFO] Type checking passed.
% 3.48/2.17 % [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 ...
% 8.10/3.70 % External prover 'e' found a proof!
% 8.10/3.70 % [INFO] Killing All external provers ...
% 8.10/3.70 % Time passed: 3176ms (effective reasoning time: 2376ms)
% 8.10/3.70 % 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)>
% 8.10/3.71 % Axioms used in derivation (152): fact_73_Pls__def, fact_46_zadd__left__commute, fact_70_rel__simps_I44_J, fact_2_sum__power2__eq__zero__iff, fact_77_add__Bit0__Bit0, fact_36_add__nat__number__of, fact_61_int__less__0__conv, tsy_c_Groups_Oplus__class_Oplus_0_arg2, fact_50_less__special_I1_J, fact_13_numeral__1__eq__1, fact_29_nat__1__add__1, arity_Int_Oint___Rings_Olinordered__idom, arity_Nat_Onat___Rings_Osemiring__1, fact_9_semiring__one__add__one__is__two, tsy_c_Groups_Oplus__class_Oplus_1_arg2, fact_12_semiring__norm_I110_J, fact_4_zero__power2, arity_Int_Oint___Int_Oring__char__0, tsy_c_Int_OPls_res, fact_20_zpower__int, fact_44_even__less__0__iff, fact_68_rel__simps_I50_J, fact_31_rel__simps_I17_J, tsy_c_Groups_Oplus__class_Oplus_0_res, tsy_c_Orderings_Oord__class_Oless_1_arg2, tsy_c_Power_Opower__class_Opower_0_arg1, fact_91_add__Bit0__Bit1, fact_88_add__number__of__eq, fact_22_zadd__int__left, arity_Nat_Onat___Int_Onumber__semiring, fact_56_bin__less__0__simps_I4_J, fact_7_add__special_I3_J, fact_97_sum__power2__gt__zero__iff, arity_Nat_Onat___Power_Opower, fact_26_semiring__norm_I113_J, fact_75_add__Pls__right, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, tsy_c_Int_Onumber__class_Onumber__of_res, fact_33_less__int__code_I13_J, tsy_c_Groups_Oplus__class_Oplus_1_res, fact_5_zero__eq__power2, fact_60_zless__add1__eq, fact_40_eq__number__of, fact_48_int__int__eq, tsy_c_Groups_Oplus__class_Oplus_1_arg1, fact_47_zadd__commute, arity_Int_Oint___Int_Onumber__semiring, tsy_c_Groups_Ozero__class_Ozero_1_res, arity_Int_Oint___Int_Onumber__ring, tsy_c_Groups_Ozero__class_Ozero_0_res, arity_Int_Oint___Rings_Osemiring__1, arity_Nat_Onat___Rings_Omult__zero, fact_66_rel__simps_I46_J, fact_52_less__int__code_I15_J, tsy_c_Power_Opower__class_Opower_1_arg1, fact_21_int__power, fact_6_add__special_I2_J, fact_80_zadd__0, fact_1_t1, fact_57_bin__less__0__simps_I1_J, fact_59_int__0__less__1, fact_96_power2__less__0, fact_64_odd__less__0, tsy_c_Power_Opower__class_Opower_0_arg2, fact_93_odd__nonzero, fact_95_zero__less__power2, fact_83_semiring__norm_I112_J, fact_34_rel__simps_I14_J, tsy_c_Orderings_Oord__class_Oless_0_arg2, tsy_c_Groups_Oplus__class_Oplus_0_arg1, fact_67_rel__simps_I39_J, fact_87_add__number__of__left, arity_Nat_Onat___Rings_Osemiring__0, tsy_c_Int_OBit1_res, fact_25_nat__number__of__Pls, tsy_c_Orderings_Oord__class_Oless_1_arg1, tsy_c_Power_Opower__class_Opower_1_arg2, fact_54_rel__simps_I10_J, fact_79_zadd__0__right, tsy_c_HOL_Oundefined_res, fact_78_Bit0__def, fact_49_less__special_I3_J, help_ti_idem, fact_86_power__eq__0__iff__number__of, fact_39_Numeral1__eq1__nat, fact_51_rel__simps_I12_J, fact_82_number__of__Pls, fact_45_zadd__assoc, fact_10_quartic__square__square, fact_41_number__of__reorient, arity_Int_Oint___Power_Opower, fact_62_less__special_I4_J, fact_85_add__numeral__0__right, arity_Int_Oint___Rings_Osemiring__0, fact_55_rel__simps_I4_J, fact_69_rel__simps_I49_J, fact_18_less__number__of, fact_8_one__add__one__is__two, fact_72_Bit0__Pls, fact_42_rel__simps_I51_J, fact_11_power__0__left__number__of, arity_Nat_Onat___Int_Onumber, fact_23_zadd__int, fact_14_n0, tsy_c_Groups_Ozero__class_Ozero_2_res, arity_Int_Oint___Rings_Ozero__neq__one, fact_90_add__Bit1__Bit0, fact_28_int__0, tsy_c_Int_Onumber__class_Onumber__of_arg1, tsy_c_Nat_Osemiring__1__class_Oof__nat_res, fact_24_int__1, tsy_c_Int_OBit0_res, fact_43_rel__simps_I48_J, fact_32_rel__simps_I2_J, tsy_c_Power_Opower__class_Opower_1_res, tsy_c_Groups_Oone__class_Oone_res, fact_94_number__of__int, fact_15_zless__linear, fact_30_less__int__code_I16_J, tsy_c_Power_Opower__class_Opower_0_res, fact_81_semiring__numeral__0__eq__0, fact_76_add__Pls, tsy_c_Orderings_Oord__class_Oless_0_arg1, fact_65_double__eq__0__iff, fact_16_less__number__of__int__code, arity_Nat_Onat___Rings_Ono__zero__divisors, tsy_v_t_____res, fact_37_one__is__num__one, fact_92_Bit1__def, fact_63_less__special_I2_J, fact_58_bin__less__0__simps_I3_J, tsy_c_Int_OBit0_arg1, fact_89_number__of__add, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_35_zadd__strict__right__mono, tsy_v_n_____res, tsy_c_Int_OBit1_arg1, arity_Int_Oint___Rings_Omult__zero, fact_0_n1pos, fact_74_int__0__neq__1, fact_27_int__eq__0__conv, fact_53_rel__simps_I16_J, arity_Nat_Onat___Rings_Ozero__neq__one, fact_38_nat__numeral__1__eq__1, fact_84_add__numeral__0, fact_71_rel__simps_I38_J, fact_3_one__power2, tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1, fact_17_plus__numeral__code_I9_J, fact_19_zero__is__num__zero
% 8.10/3.71 % No. of inferences in proof: 308
% 8.10/3.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3176 ms resp. 2376 ms w/o parsing
% 8.53/3.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.53/3.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------