TSTP Solution File: SWW499_5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW499_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 18:23:29 EDT 2024
% Result : Theorem 6.81s 2.58s
% Output : Refutation 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 190
% Syntax : Number of formulae : 382 ( 208 unt; 0 typ; 0 def)
% Number of atoms : 724 ( 270 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2378 ( 45 ~; 23 |; 49 &;2034 @)
% ( 27 <=>; 200 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 5 con; 0-3 aty)
% Number of variables : 446 ( 0 ^ 440 !; 6 ?; 446 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(comm_ring_1_type,type,
comm_ring_1:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_type,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(idom_type,type,
idom:
!>[TA: $tType] : $o ).
thf(number_type,type,
number:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(power_type,type,
power:
!>[TA: $tType] : $o ).
thf(number_ring_type,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(number_semiring_type,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_type,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_type,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_type,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_type,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(ab_sem1668676832m_mult_type,type,
ab_sem1668676832m_mult:
!>[TA: $tType] : $o ).
thf(fundam1563812824_csqrt_type,type,
fundam1563812824_csqrt: complex > complex ).
thf(fundam1280195782_psize_type,type,
fundam1280195782_psize:
!>[TA: $tType] : ( ( poly @ TA ) > nat ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_type,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(even_odd_even_type,type,
even_odd_even:
!>[TA: $tType] : ( TA > $o ) ).
thf(power_power_type,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(n_type,type,
n: nat ).
thf(na_type,type,
na: nat ).
thf(33,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(234,plain,
ring_11004092258visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(151,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(555,plain,
no_zero_divisors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(167,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zero__eq__power2) ).
thf(628,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(40,axiom,
ab_semigroup_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(249,plain,
ab_semigroup_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(111,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ B )
= ( times_times @ TA @ B @ ( power_power @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_power__commutes) ).
thf(408,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ B )
= ( times_times @ TA @ B @ ( power_power @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(38,axiom,
zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(247,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(56,axiom,
power @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(269,plain,
power @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(9,axiom,
ab_semigroup_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__mult) ).
thf(202,plain,
ab_semigroup_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(217,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(61,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_n68954251visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oring__no__zero__divisors) ).
thf(276,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_n68954251visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(104,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(385,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(145,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_less__eq__nat_Osimps_I1_J) ).
thf(538,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(116,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_mult__is__0) ).
thf(417,plain,
! [A: nat,B: nat] :
( ( ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
| ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
| ( A
= ( zero_zero @ nat ) ) )
=> ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(69,axiom,
ring_11004092258visors @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(288,plain,
ring_11004092258visors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(81,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(301,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(47,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_monoid_mult @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocomm__monoid__mult) ).
thf(257,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_monoid_mult @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(100,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(372,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(139,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I14_J) ).
thf(504,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(164,axiom,
! [TA: $tType] :
( ( ( monoid_mult @ TA )
& ( number @ TA ) )
=> ! [A: int] :
( ( power_power @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_power2__eq__square__number__of) ).
thf(619,plain,
! [TA: $tType] :
( ( ( monoid_mult @ TA )
& ( number @ TA ) )
=> ! [A: int] :
( ( power_power @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(4,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(196,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(153,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_rel__simps_I49_J) ).
thf(559,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(115,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(416,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(70,axiom,
zero @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(289,plain,
zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(124,axiom,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: int,B: TA] :
( ( ( power_power @ TA @ B @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_power__eq__0__iff__number__of) ).
thf(448,plain,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: int,B: TA] :
( ( ( ( power_power @ TA @ B @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
& ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
& ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) ) )
=> ( ( power_power @ TA @ B @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(50,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( number @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Onumber) ).
thf(261,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( number @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
ring_n68954251visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) ).
thf(216,plain,
ring_n68954251visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) )
<=> ( ( C
= ( zero_zero @ nat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_nat__mult__eq__cancel__disj) ).
thf(591,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) )
=> ( ( C
= ( zero_zero @ nat ) )
| ( B = A ) ) )
& ( ( ( C
= ( zero_zero @ nat ) )
| ( B = A ) )
=> ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(133,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_eq__number__of) ).
thf(485,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(36,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(238,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(132,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_rel__simps_I17_J) ).
thf(480,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(15,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(211,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(172,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_mult__zero__left) ).
thf(646,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(43,axiom,
mult_zero @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(253,plain,
mult_zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(63,axiom,
comm_monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) ).
thf(280,plain,
comm_monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(168,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rel__simps_I31_J) ).
thf(634,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(186,axiom,
comm_monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(692,plain,
comm_monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(24,axiom,
comm_semiring_1 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(221,plain,
comm_semiring_1 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(73,axiom,
comm_semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(293,plain,
comm_semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(108,axiom,
! [A: complex] :
( ( power_power @ complex @ ( fundam1563812824_csqrt @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_csqrt) ).
thf(396,plain,
! [A: complex] :
( ( power_power @ complex @ ( fundam1563812824_csqrt @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(112,axiom,
( n
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).
thf(411,plain,
( n
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ A @ B ) )
<=> ( ( C = A )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_mult__cancel2) ).
thf(307,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ A @ B ) )
=> ( ( C = A )
| ( B
= ( zero_zero @ nat ) ) ) )
& ( ( ( C = A )
| ( B
= ( zero_zero @ nat ) ) )
=> ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(32,axiom,
ring_n68954251visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(233,plain,
ring_n68954251visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(248,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(102,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(380,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(141,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit1 @ pls ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_mult__numeral__1) ).
thf(512,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit1 @ pls ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(181,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mult__left__idem) ).
thf(678,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(57,axiom,
comm_semiring_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__0) ).
thf(270,plain,
comm_semiring_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(177,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zero__power2) ).
thf(661,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(148,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rel__simps_I2_J) ).
thf(546,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(8,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(201,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,axiom,
no_zero_divisors @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(220,plain,
no_zero_divisors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(82,axiom,
comm_ring_1 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__ring__1) ).
thf(302,plain,
comm_ring_1 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(77,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(297,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(49,axiom,
comm_monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(260,plain,
comm_monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(94,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: nat,B: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zero__le__even__power_H) ).
thf(349,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: nat,B: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1,conjecture,
? [A: nat] :
( na
= ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: nat] :
( na
= ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(192,plain,
~ ? [A: nat] :
( na
= ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(187,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(693,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(129,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( ( fundam1280195782_psize @ TA @ A )
= ( zero_zero @ nat ) )
<=> ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_psize__eq__0__iff) ).
thf(467,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( ( ( fundam1280195782_psize @ TA @ A )
= ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ ( poly @ TA ) ) ) )
& ( ( A
= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( fundam1280195782_psize @ TA @ A )
= ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(42,axiom,
semiring_1 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__1) ).
thf(252,plain,
semiring_1 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(5,axiom,
monoid_mult @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(197,plain,
monoid_mult @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(97,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( times_times @ nat @ C @ B ) @ A )
= ( times_times @ nat @ C @ ( times_times @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_nat__mult__assoc) ).
thf(361,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( times_times @ nat @ C @ B ) @ A )
= ( times_times @ nat @ C @ ( times_times @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(166,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( power_power @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_power__mult__distrib) ).
thf(625,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( power_power @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(143,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I51_J) ).
thf(522,plain,
! [A: int,B: int] :
( ( ( ( bit1 @ B )
= ( bit1 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit1 @ B )
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(150,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_rel__simps_I39_J) ).
thf(551,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(125,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_arith__simps_I32_J) ).
thf(456,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(87,axiom,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_number__of__is__id) ).
thf(324,plain,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(30,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: nat,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ B @ A )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_field__power__not__zero) ).
thf(229,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: nat,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ B @ A )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(155,axiom,
! [A: real] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ A @ A ) )
<=> ( A
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_not__real__square__gt__zero) ).
thf(566,plain,
! [A: real] :
( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ A @ A ) )
=> ( A
= ( zero_zero @ real ) ) )
& ( ( A
= ( zero_zero @ real ) )
=> ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(67,axiom,
comm_ring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring__1) ).
thf(285,plain,
comm_ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,axiom,
zero_neq_one @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(224,plain,
zero_neq_one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(189,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(697,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(86,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__0__eq) ).
thf(317,plain,
! [A: nat] :
( ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(174,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(650,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(105,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_nat__number__of__Pls) ).
thf(388,plain,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(46,axiom,
number @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber) ).
thf(256,plain,
number @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(28,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( monoid_mult @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Omonoid__mult) ).
thf(225,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( monoid_mult @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(16,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(212,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(184,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_mult__number__of__left) ).
thf(686,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(131,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_rel__simps_I46_J) ).
thf(476,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(165,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(622,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(107,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_times__numeral__code_I5_J) ).
thf(393,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(142,axiom,
! [A: nat] :
( ( even_odd_even @ nat @ A )
<=> ? [B: nat] :
( A
= ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_even__mult__two__ex) ).
thf(515,plain,
! [A: nat] :
( ( ( even_odd_even @ nat @ A )
=> ? [B: nat] :
( A
= ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) )
& ( ? [B: nat] :
( A
= ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
=> ( even_odd_even @ nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(99,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(371,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(53,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(266,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(11,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( ab_semigroup_mult @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oab__semigroup__mult) ).
thf(205,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( ab_semigroup_mult @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(144,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I48_J) ).
thf(530,plain,
! [A: int,B: int] :
( ( ( ( bit0 @ B )
= ( bit0 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit0 @ B )
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(78,axiom,
number_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(298,plain,
number_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(118,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(430,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(52,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( zero_neq_one @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ozero__neq__one) ).
thf(264,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( zero_neq_one @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(156,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(573,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(161,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_semiring__norm_I113_J) ).
thf(601,plain,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(185,axiom,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_mult__Pls) ).
thf(689,plain,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(76,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(296,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(188,axiom,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_mult__0) ).
thf(694,plain,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_zero__less__power2) ).
thf(402,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( A
!= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(68,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__1) ).
thf(286,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(64,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(281,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(48,axiom,
no_zero_divisors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(259,plain,
no_zero_divisors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(158,axiom,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: nat,B: TA] :
( ( ( power_power @ TA @ B @ A )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( A
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_power__eq__0__iff) ).
thf(579,plain,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: nat,B: TA] :
( ( ( ( power_power @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
& ( A
!= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
& ( A
!= ( zero_zero @ nat ) ) )
=> ( ( power_power @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(72,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( number_semiring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Onumber__semiring) ).
thf(291,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( number_semiring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(137,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__zero__right) ).
thf(498,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(91,axiom,
ab_semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(335,plain,
ab_semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(35,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( mult_zero @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Omult__zero) ).
thf(236,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( mult_zero @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(146,axiom,
! [A: nat,B: nat,C: int] :
( ( power_power @ int @ ( power_power @ int @ C @ B ) @ A )
= ( power_power @ int @ C @ ( times_times @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zpower__zpower) ).
thf(540,plain,
! [A: nat,B: nat,C: int] :
( ( power_power @ int @ ( power_power @ int @ C @ B ) @ A )
= ( power_power @ int @ C @ ( times_times @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(182,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( power_power @ TA @ ( power_power @ TA @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_power__even__eq) ).
thf(681,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( power_power @ TA @ ( power_power @ TA @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(60,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(274,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(83,axiom,
idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oidom) ).
thf(303,plain,
idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(140,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_number__of__Pls) ).
thf(509,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(173,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(649,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(120,axiom,
( na
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_n) ).
thf(434,plain,
( na
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(58,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
thf(271,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(13,axiom,
number_ring @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__ring) ).
thf(208,plain,
number_ring @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(135,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(494,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(17,axiom,
ring_11004092258visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(213,plain,
ring_11004092258visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(190,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit1 @ pls ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_mult__numeral__1__right) ).
thf(700,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit1 @ pls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(37,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_zero__reorient) ).
thf(240,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
ring_n68954251visors @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors) ).
thf(198,plain,
ring_n68954251visors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(89,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rel__simps_I19_J) ).
thf(330,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(127,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_less__zeroE) ).
thf(462,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(109,axiom,
! [A: real] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_four__x__squared) ).
thf(399,plain,
! [A: real] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(62,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( no_zero_divisors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ono__zero__divisors) ).
thf(278,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( no_zero_divisors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(26,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(223,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(154,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(563,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(79,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(299,plain,
no_zero_divisors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(267,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(122,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_power2__eq__square) ).
thf(438,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(175,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ D @ B ) @ ( times_times @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(653,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ D @ B ) @ ( times_times @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(130,axiom,
! [TA: $tType] :
( ( no_zero_divisors @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ B @ A )
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_no__zero__divisors) ).
thf(473,plain,
! [TA: $tType] :
( ( no_zero_divisors @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ B @ A )
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(149,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( power_power @ TA @ C @ ( times_times @ nat @ B @ A ) )
= ( power_power @ TA @ ( power_power @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_power__mult) ).
thf(548,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( power_power @ TA @ C @ ( times_times @ nat @ B @ A ) )
= ( power_power @ TA @ ( power_power @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(45,axiom,
mult_zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(255,plain,
mult_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(14,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( power @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Power_Opower) ).
thf(209,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( power @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(170,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_semiring__numeral__0__eq__0) ).
thf(640,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(75,axiom,
comm_semiring_0 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).
thf(295,plain,
comm_semiring_0 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(65,axiom,
zero_neq_one @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(282,plain,
zero_neq_one @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(113,axiom,
even_odd_even @ nat @ ( zero_zero @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_even__zero__nat) ).
thf(414,plain,
even_odd_even @ nat @ ( zero_zero @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(88,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_mult__0__right) ).
thf(327,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(51,axiom,
power @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(263,plain,
power @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(7,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
thf(199,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(90,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_rel__simps_I50_J) ).
thf(331,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(123,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_rel__simps_I38_J) ).
thf(441,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(157,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( power_power @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(576,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( power_power @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(171,axiom,
! [A: nat,B: nat] :
( ( times_times @ nat @ B @ A )
= ( times_times @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nat__mult__commute) ).
thf(643,plain,
! [A: nat,B: nat] :
( ( times_times @ nat @ B @ A )
= ( times_times @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) )
<=> ( ( B = A )
| ( C
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_mult__cancel1) ).
thf(336,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) )
=> ( ( B = A )
| ( C
= ( zero_zero @ nat ) ) ) )
& ( ( ( B = A )
| ( C
= ( zero_zero @ nat ) ) )
=> ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(191,axiom,
even_odd_even @ nat @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_e) ).
thf(703,plain,
even_odd_even @ nat @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(176,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_rel__simps_I34_J) ).
thf(656,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(163,axiom,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( number_number_of @ TA @ B )
= A )
<=> ( A
= ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_number__of__reorient) ).
thf(612,plain,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( ( number_number_of @ TA @ B )
= A )
=> ( A
= ( number_number_of @ TA @ B ) ) )
& ( ( A
= ( number_number_of @ TA @ B ) )
=> ( ( number_number_of @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(152,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ D @ ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(556,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ D @ ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(10,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_11004092258visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oring__1__no__zero__divisors) ).
thf(203,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_11004092258visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(136,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( zero_zero @ TA )
= ( number_number_of @ TA @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_semiring__norm_I112_J) ).
thf(495,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( zero_zero @ TA )
= ( number_number_of @ TA @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(22,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(218,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(41,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( semiring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Osemiring__1) ).
thf(250,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( semiring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(128,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le0) ).
thf(465,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(159,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__nat__zero__code) ).
thf(588,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(84,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( power_power @ TA @ ( power_power @ TA @ C @ B ) @ A )
= ( power_power @ TA @ C @ ( times_times @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(304,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( power_power @ TA @ ( power_power @ TA @ C @ B ) @ A )
= ( power_power @ TA @ C @ ( times_times @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(95,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(351,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(106,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( times_times @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(390,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( times_times @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(71,axiom,
number_semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(290,plain,
number_semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(34,axiom,
number_semiring @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__semiring) ).
thf(235,plain,
number_semiring @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(119,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(433,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(12,axiom,
comm_monoid_mult @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult) ).
thf(207,plain,
comm_monoid_mult @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(179,axiom,
! [TA: $tType] :
( ( ring_n68954251visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_mult__eq__0__iff) ).
thf(667,plain,
! [TA: $tType] :
( ( ring_n68954251visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) )
=> ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(103,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zero__is__num__zero) ).
thf(383,plain,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(183,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Bit0__Pls) ).
thf(684,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(93,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( times_times @ int @ B @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_number__of__mult) ).
thf(346,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( times_times @ int @ B @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(18,axiom,
number @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(214,plain,
number @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(80,axiom,
comm_semiring_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__0) ).
thf(300,plain,
comm_semiring_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(59,axiom,
comm_ring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__ring__1) ).
thf(273,plain,
comm_ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(101,axiom,
! [A: nat,B: nat] :
( ( even_odd_even @ nat @ ( times_times @ nat @ B @ A ) )
<=> ( ( even_odd_even @ nat @ B )
| ( even_odd_even @ nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_even__product__nat) ).
thf(373,plain,
! [A: nat,B: nat] :
( ( ( even_odd_even @ nat @ ( times_times @ nat @ B @ A ) )
=> ( ( even_odd_even @ nat @ B )
| ( even_odd_even @ nat @ A ) ) )
& ( ( ( even_odd_even @ nat @ B )
| ( even_odd_even @ nat @ A ) )
=> ( even_odd_even @ nat @ ( times_times @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ B @ A ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_nat__zero__less__power__iff) ).
thf(603,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ B @ A ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( A
= ( zero_zero @ nat ) ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(74,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(294,plain,
mult_zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(55,axiom,
idom @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oidom) ).
thf(268,plain,
idom @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(3,axiom,
idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oidom) ).
thf(195,plain,
idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(121,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(437,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(178,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_times_Oidem) ).
thf(664,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(66,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__ring__1) ).
thf(283,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(114,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(415,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(117,axiom,
! [TA: $tType] :
( ( no_zero_divisors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_divisors__zero) ).
thf(427,plain,
! [TA: $tType] :
( ( no_zero_divisors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(126,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_mult__Bit0) ).
thf(459,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(138,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_mult__idem) ).
thf(501,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(96,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_rel__simps_I44_J) ).
thf(354,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(147,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(543,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(19,axiom,
ring_char_0 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(215,plain,
ring_char_0 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(169,axiom,
comm_semiring_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__0) ).
thf(639,plain,
comm_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(180,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Pls__def) ).
thf(676,plain,
( pls
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(134,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_power3__eq__cube) ).
thf(491,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(25,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(222,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(98,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_neq0__conv) ).
thf(364,plain,
! [A: nat] :
( ( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
!= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(31,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(232,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(44,axiom,
ab_semigroup_mult @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__semigroup__mult) ).
thf(254,plain,
ab_semigroup_mult @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(29,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( number_ring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Onumber__ring) ).
thf(227,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( number_ring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(708,plain,
$false,
inference(e,[status(thm)],[234,555,628,249,408,247,269,202,217,276,385,538,417,288,301,257,372,504,619,196,559,416,289,448,261,216,591,485,238,480,211,646,253,280,634,692,221,293,396,411,307,233,248,380,512,678,270,661,546,201,220,302,297,260,349,192,693,467,252,197,361,625,522,551,456,324,229,566,285,224,697,317,650,388,256,225,212,686,476,622,393,515,371,266,205,530,298,430,264,573,601,689,296,694,402,286,281,259,579,291,498,335,236,540,681,274,303,509,649,434,271,208,494,213,700,240,198,330,462,399,278,223,563,299,267,438,653,473,548,255,209,640,295,282,414,327,263,199,331,441,576,643,336,703,656,612,556,203,495,218,250,465,588,304,351,390,290,235,433,207,667,383,684,346,214,300,273,373,603,294,268,195,437,664,283,415,427,459,501,354,543,215,639,676,491,222,364,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWW499_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.11 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Jun 19 07:09:10 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.91/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/1.01 % [INFO] Parsing done (170ms).
% 1.39/1.02 % [INFO] Running in sequential loop mode.
% 1.86/1.21 % [INFO] eprover registered as external prover.
% 1.86/1.21 % [INFO] Scanning for conjecture ...
% 2.06/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 191 axioms. Running axiom selection ...
% 2.38/1.38 % [INFO] Axiom selection finished. Selected 189 axioms (removed 2 axioms).
% 2.83/1.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.83/1.50 % [INFO] Type checking passed.
% 2.83/1.50 % [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 ...
% 6.81/2.58 % External prover 'e' found a proof!
% 6.81/2.58 % [INFO] Killing All external provers ...
% 6.81/2.58 % Time passed: 2074ms (effective reasoning time: 1557ms)
% 6.81/2.58 % 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)>
% 6.81/2.58 % Axioms used in derivation (189): arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_83_nat__zero__less__power__iff, fact_33_mult__zero__left, arity_Polynomial_Opoly___Rings_Ocomm__ring__1, arity_Polynomial_Opoly___Rings_Oring__no__zero__divisors, fact_48_power2__eq__square__number__of, arity_Nat_Onat___Groups_Omonoid__mult, arity_Complex_Ocomplex___Rings_Ocomm__semiring__0, arity_Nat_Onat___Groups_Oab__semigroup__mult, fact_32_mult__eq__0__iff, fact_46_mult__left__idem, arity_Nat_Onat___Rings_Osemiring__1, fact_74_field__power__not__zero, arity_Int_Oint___Int_Oring__char__0, arity_Int_Oint___Rings_Ocomm__semiring__0, fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_4_rel__simps_I38_J, fact_13_mult__numeral__1, arity_Int_Oint___Rings_Olinordered__idom, fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_24_nat__number__of__Pls, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_47_nat__mult__eq__cancel__disj, arity_Polynomial_Opoly___Power_Opower, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, arity_Polynomial_Opoly___Rings_Ono__zero__divisors, arity_Complex_Ocomplex___Power_Opower, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, arity_RealDef_Oreal___Groups_Ozero, fact_16_rel__simps_I48_J, arity_Nat_Onat___Int_Onumber__semiring, fact_42_even__zero__nat, fact_54_ab__semigroup__mult__class_Omult__ac_I1_J, arity_RealDef_Oreal___Int_Onumber__semiring, arity_Nat_Onat___Power_Opower, arity_RealDef_Oreal___Groups_Ocomm__monoid__mult, fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_60_power__eq__0__iff, arity_Complex_Ocomplex___Rings_Oidom, fact_38_nat__mult__commute, arity_Int_Oint___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Rings_Oring__no__zero__divisors, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, fact_50_zero__eq__power2, arity_Complex_Ocomplex___Int_Oring__char__0, fact_17_mult__Pls, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, fact_86_le0, fact_0_e, arity_Polynomial_Opoly___Groups_Omonoid__mult, arity_Polynomial_Opoly___Int_Onumber__ring, arity_Int_Oint___Int_Onumber__semiring, fact_55_mult__idem, arity_Int_Oint___Int_Onumber__ring, arity_Polynomial_Opoly___Rings_Omult__zero, arity_Int_Oint___Rings_Osemiring__1, fact_87_less__zeroE, fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, arity_Nat_Onat___Rings_Omult__zero, arity_Polynomial_Opoly___Rings_Oidom, fact_81_zero__less__power2, fact_5_rel__simps_I44_J, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_85_less__eq__nat_Osimps_I1_J, fact_23_number__of__mult, fact_43_semiring__norm_I112_J, arity_Polynomial_Opoly___Rings_Ozero__neq__one, fact_49_power__eq__0__iff__number__of, arity_Polynomial_Opoly___Groups_Ozero, fact_63_csqrt, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, arity_Polynomial_Opoly___Int_Oring__char__0, fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_40_no__zero__divisors, fact_37_zero__is__num__zero, fact_28_mult__cancel1, arity_RealDef_Oreal___Rings_Osemiring__1, fact_88_less__nat__zero__code, fact_14_eq__number__of, fact_82_zero__le__even__power_H, fact_56_times_Oidem, arity_Polynomial_Opoly___Rings_Ocomm__semiring__1, fact_22_number__of__reorient, fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Polynomial_Opoly___Groups_Ocomm__monoid__mult, fact_89_neq0__conv, fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_9_rel__simps_I46_J, fact_44_semiring__norm_I113_J, arity_RealDef_Oreal___Int_Onumber__ring, fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_95_rel__simps_I14_J, arity_Polynomial_Opoly___Rings_Olinordered__idom, arity_Int_Oint___Groups_Omonoid__mult, fact_6_rel__simps_I49_J, fact_10_arith__simps_I32_J, arity_Polynomial_Opoly___Int_Onumber__semiring, fact_31_mult__0, fact_84_le__0__eq, fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, arity_Int_Oint___Rings_Oring__no__zero__divisors, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_7_rel__simps_I50_J, arity_Complex_Ocomplex___Rings_Omult__zero, fact_58_power2__eq__square, arity_RealDef_Oreal___Rings_Oidom, arity_Nat_Onat___Groups_Ozero, arity_Complex_Ocomplex___Groups_Oab__semigroup__mult, fact_19_number__of__Pls, fact_18_mult__Bit0, fact_52_zpower__zpower, arity_RealDef_Oreal___Rings_Omult__zero, arity_RealDef_Oreal___Int_Oring__char__0, arity_Polynomial_Opoly___Groups_Oab__semigroup__mult, arity_RealDef_Oreal___Rings_Ocomm__semiring__0, fact_3_Bit0__Pls, arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_8_rel__simps_I39_J, arity_RealDef_Oreal___Rings_Ocomm__ring__1, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_Nat_Onat___Rings_Ocomm__semiring__0, fact_92_rel__simps_I19_J, fact_12_mult__numeral__1__right, arity_Int_Oint___Power_Opower, arity_Int_Oint___Rings_Oidom, fact_2_assms_I2_J, arity_Complex_Ocomplex___Int_Onumber__ring, fact_30_mult__0__right, arity_Polynomial_Opoly___Rings_Osemiring__1, fact_35_number__of__is__id, fact_90_rel__simps_I34_J, fact_20_times__numeral__code_I5_J, arity_Complex_Ocomplex___Rings_Osemiring__1, arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors, arity_RealDef_Oreal___Rings_Ozero__neq__one, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_96_not__real__square__gt__zero, fact_59_power__even__eq, arity_Nat_Onat___Int_Onumber, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_1_n, fact_25_even__mult__two__ex, fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_36_Pls__def, fact_79_power__mult, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_21_semiring__numeral__0__eq__0, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_80_four__x__squared, fact_91_rel__simps_I17_J, fact_93_rel__simps_I2_J, fact_41_divisors__zero, arity_RealDef_Oreal___Power_Opower, fact_51_zero__power2, arity_Int_Oint___Rings_Ocomm__ring__1, fact_45_psize__eq__0__iff, fact_11_mult__number__of__left, fact_27_mult__cancel2, arity_Nat_Onat___Rings_Ono__zero__divisors, arity_Complex_Ocomplex___Int_Onumber__semiring, arity_Polynomial_Opoly___Rings_Oring__1__no__zero__divisors, fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_57_power3__eq__cube, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_29_mult__is__0, fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, arity_Complex_Ocomplex___Int_Onumber, arity_Polynomial_Opoly___Int_Onumber, arity_RealDef_Oreal___Int_Onumber, fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, arity_RealDef_Oreal___Groups_Oab__semigroup__mult, fact_53_zero__reorient, arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Rings_Omult__zero, arity_Complex_Ocomplex___Rings_Ocomm__ring__1, fact_76_power__mult__distrib, fact_26_even__product__nat, fact_77_power__commutes, fact_15_rel__simps_I51_J, fact_39_nat__mult__assoc, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_94_rel__simps_I31_J, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, arity_Complex_Ocomplex___Groups_Ozero, fact_34_mult__zero__right
% 6.81/2.58 % No. of inferences in proof: 382
% 6.81/2.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2074 ms resp. 1557 ms w/o parsing
% 7.21/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.21/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------