TSTP Solution File: SWV621_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV621_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Fri May 19 12:17:35 EDT 2023
% Result : Theorem 30.67s 17.02s
% Output : Refutation 31.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 210
% Syntax : Number of formulae : 372 ( 156 unt; 50 typ; 0 def)
% Number of atoms : 1077 ( 234 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 5499 ( 68 ~; 18 |; 74 &;4977 @)
% ( 24 <=>; 338 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 6 con; 0-5 aty)
% Number of variables : 611 ( 0 ^; 552 !; 10 ?; 611 :)
% ( 49 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(power_type,type,
power:
!>[TA: $tType] : $o ).
thf(field_type,type,
field:
!>[TA: $tType] : $o ).
thf(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_0_type,type,
semiring_0:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(ab_group_add_type,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(division_ring_type,type,
division_ring:
!>[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(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_type,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(field_inverse_zero_type,type,
field_inverse_zero:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_type,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_type,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(divisi14063676e_zero_type,type,
divisi14063676e_zero:
!>[TA: $tType] : $o ).
thf(linord1117847801e_zero_type,type,
linord1117847801e_zero:
!>[TA: $tType] : $o ).
thf(big_co1399186613setsum_type,type,
big_co1399186613setsum:
!>[TA: $tType,TB: $tType] : ( fun @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) ) ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(fFT_Mirabelle_root_type,type,
fFT_Mirabelle_root: nat > complex ).
thf(inverse_divide_type,type,
inverse_divide:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ TA ) ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ TA ) ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : 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(power_power_type,type,
power_power:
!>[TA: $tType] : ( TA > ( fun @ nat @ TA ) ) ).
thf(ord_atLeastLessThan_type,type,
ord_atLeastLessThan:
!>[TA: $tType] : ( TA > TA > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(k_type,type,
k: nat ).
thf(n_type,type,
n: nat ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_linorder__neqE__nat) ).
thf(518,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(80,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(333,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType] :
( ( ab_group_add @ TB )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ ( combs @ TA @ TB @ TB @ ( combb @ TB @ ( fun @ TB @ TB ) @ TA @ ( minus_minus @ TB ) @ C ) @ B ) ) @ A )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( minus_minus @ TB ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ C ) @ A ) ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_setsum__subtractf) ).
thf(249,plain,
! [TA: $tType,TB: $tType] :
( ( ab_group_add @ TB )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ ( combs @ TA @ TB @ TB @ ( combb @ TB @ ( fun @ TB @ TB ) @ TA @ ( minus_minus @ TB ) @ C ) @ B ) ) @ A )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( minus_minus @ TB ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ C ) @ A ) ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(9,axiom,
linordered_field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Olinordered__field) ).
thf(170,plain,
linordered_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(136,axiom,
! [TA: $tType] :
( ( field_inverse_zero @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_power__divide) ).
thf(523,plain,
! [TA: $tType] :
( ( field_inverse_zero @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(36,axiom,
ring_n68954251visors @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors) ).
thf(217,plain,
ring_n68954251visors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(96,axiom,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: nat,B: TA] :
( ( ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( A
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_power__eq__0__iff) ).
thf(385,plain,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: nat,B: TA] :
( ( ( ( aa @ nat @ 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 ) ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(95,axiom,
mult_zero @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(384,plain,
mult_zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(140,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_eq__iff__diff__eq__0) ).
thf(533,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) ) )
& ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(340,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(21,axiom,
linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(185,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(174,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(102,axiom,
power @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(404,plain,
power @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(20,axiom,
ring_11004092258visors @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(184,plain,
ring_11004092258visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(87,axiom,
group_add @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ogroup__add) ).
thf(357,plain,
group_add @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(116,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( one_one @ nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_power__one__right) ).
thf(460,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( one_one @ nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(25,axiom,
linordered_semidom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(189,plain,
linordered_semidom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(60,axiom,
! [A: nat,B: real] :
( ( B
!= ( one_one @ real ) )
=> ( ( aa @ ( fun @ nat @ bool ) @ real @ ( aa @ ( fun @ nat @ real ) @ ( fun @ ( fun @ nat @ bool ) @ real ) @ ( big_co1399186613setsum @ nat @ real ) @ ( power_power @ real @ B ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ A ) )
= ( aa @ real @ real @ ( aa @ real @ ( fun @ real @ real ) @ ( inverse_divide @ real ) @ ( aa @ real @ real @ ( aa @ real @ ( fun @ real @ real ) @ ( minus_minus @ real ) @ ( aa @ nat @ real @ ( power_power @ real @ B ) @ A ) ) @ ( one_one @ real ) ) ) @ ( aa @ real @ real @ ( aa @ real @ ( fun @ real @ real ) @ ( minus_minus @ real ) @ B ) @ ( one_one @ real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_sumr__geometric) ).
thf(284,plain,
! [A: nat,B: real] :
( ( B
!= ( one_one @ real ) )
=> ( ( aa @ ( fun @ nat @ bool ) @ real @ ( aa @ ( fun @ nat @ real ) @ ( fun @ ( fun @ nat @ bool ) @ real ) @ ( big_co1399186613setsum @ nat @ real ) @ ( power_power @ real @ B ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ A ) )
= ( aa @ real @ real @ ( aa @ real @ ( fun @ real @ real ) @ ( inverse_divide @ real ) @ ( aa @ real @ real @ ( aa @ real @ ( fun @ real @ real ) @ ( minus_minus @ real ) @ ( aa @ nat @ real @ ( power_power @ real @ B ) @ A ) ) @ ( one_one @ real ) ) ) @ ( aa @ real @ real @ ( aa @ real @ ( fun @ real @ real ) @ ( minus_minus @ real ) @ B ) @ ( one_one @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zero__less__power) ).
thf(325,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_less__not__refl3) ).
thf(228,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: fun @ TB @ TA,B: fun @ TB @ bool] :
( ! [C: TB] :
( ( member @ TB @ C @ B )
=> ( ( aa @ TB @ TA @ A @ C )
= ( zero_zero @ TA ) ) )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ ( big_co1399186613setsum @ TB @ TA ) @ A ) @ B )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_setsum__0_H) ).
thf(289,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: fun @ TB @ TA,B: fun @ TB @ bool] :
( ! [C: TB] :
( ( member @ TB @ C @ B )
=> ( ( aa @ TB @ TA @ A @ C )
= ( zero_zero @ TA ) ) )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ ( big_co1399186613setsum @ TB @ TA ) @ A ) @ B )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ nat @ ( power_power @ nat @ B ) @ A ) )
<=> ( ( A
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__less__power__nat__eq) ).
thf(448,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ nat @ ( power_power @ nat @ B ) @ A ) )
=> ( ( A
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) )
& ( ( ( A
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ nat @ ( power_power @ nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ nat @ B @ A )
=> ( ( aa @ ( fun @ nat @ bool ) @ complex @ ( aa @ ( fun @ nat @ complex ) @ ( fun @ ( fun @ nat @ bool ) @ complex ) @ ( big_co1399186613setsum @ nat @ complex ) @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ A ) ) @ B ) ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ A ) )
= ( zero_zero @ complex ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_root__summation) ).
thf(321,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ nat @ B @ A )
=> ( ( aa @ ( fun @ nat @ bool ) @ complex @ ( aa @ ( fun @ nat @ complex ) @ ( fun @ ( fun @ nat @ bool ) @ complex ) @ ( big_co1399186613setsum @ nat @ complex ) @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ A ) ) @ B ) ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ A ) )
= ( zero_zero @ complex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(33,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_power__strict__mono) ).
thf(211,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(132,axiom,
one @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oone) ).
thf(514,plain,
one @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(147,axiom,
ring_11004092258visors @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(574,plain,
ring_11004092258visors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(124,axiom,
division_ring @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring) ).
thf(492,plain,
division_ring @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(3,axiom,
divisi14063676e_zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero) ).
thf(164,plain,
divisi14063676e_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A )
= ( zero_zero @ nat ) )
=> ( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B )
= ( zero_zero @ nat ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_diffs0__imp__equal) ).
thf(602,plain,
! [A: nat,B: nat] :
( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A )
= ( zero_zero @ nat ) )
=> ( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B )
= ( zero_zero @ nat ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(39,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_one__less__power) ).
thf(221,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(98,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__eq__nat_Osimps_I1_J) ).
thf(396,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(46,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(243,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(50,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(248,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ k,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(56,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( one_one @ nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(270,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( one_one @ nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(90,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ( ( ord_atLeastLessThan @ TA @ D @ C )
= ( ord_atLeastLessThan @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_atLeastLessThan__eq__iff) ).
thf(366,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ( ( ( ord_atLeastLessThan @ TA @ D @ C )
= ( ord_atLeastLessThan @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( ord_atLeastLessThan @ TA @ D @ C )
= ( ord_atLeastLessThan @ TA @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(130,axiom,
semiring_0 @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__0) ).
thf(512,plain,
semiring_0 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(111,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_right__minus__eq) ).
thf(439,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(145,axiom,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_diff__self__eq__0) ).
thf(561,plain,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(107,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_gr0I) ).
thf(424,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(28,axiom,
comm_semiring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(192,plain,
comm_semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(58,axiom,
! [TA: $tType] :
( ( field_inverse_zero @ TA )
=> ! [A: nat,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( one_one @ TA ) ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) )
= ( aa @ nat @ TA @ ( power_power @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( one_one @ TA ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_power__one__over) ).
thf(275,plain,
! [TA: $tType] :
( ( field_inverse_zero @ TA )
=> ! [A: nat,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( one_one @ TA ) ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) )
= ( aa @ nat @ TA @ ( power_power @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( one_one @ TA ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(4,axiom,
field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield) ).
thf(165,plain,
field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(121,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ A )
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_divide__self) ).
thf(484,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ A )
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ ( times_times @ nat @ C @ B ) ) ) @ ( times_times @ nat @ C @ A ) )
= ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_root__cancel) ).
thf(252,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ ( times_times @ nat @ C @ B ) ) ) @ ( times_times @ nat @ C @ A ) )
= ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(493,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(143,axiom,
zero_neq_one @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(551,plain,
zero_neq_one @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(74,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(324,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(24,axiom,
no_zero_divisors @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(188,plain,
no_zero_divisors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
mult_zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(169,plain,
mult_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( combc @ TC @ TA @ TB @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(593,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( combc @ TC @ TA @ TB @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(127,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_diff__0__right) ).
thf(499,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( field @ TB )
=> ! [A: TB,B: fun @ TA @ bool,C: fun @ TA @ TB] :
( ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( inverse_divide @ TB ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ C ) @ B ) ) @ A )
= ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ ( aa @ TB @ ( fun @ TA @ TB ) @ ( combc @ TA @ TB @ TB @ ( combb @ TB @ ( fun @ TB @ TB ) @ TA @ ( inverse_divide @ TB ) @ C ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_setsum__divide__distrib) ).
thf(328,plain,
! [TA: $tType,TB: $tType] :
( ( field @ TB )
=> ! [A: TB,B: fun @ TA @ bool,C: fun @ TA @ TB] :
( ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( inverse_divide @ TB ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ C ) @ B ) ) @ A )
= ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ ( aa @ TB @ ( fun @ TA @ TB ) @ ( combc @ TA @ TB @ TB @ ( combb @ TB @ ( fun @ TB @ TB ) @ TA @ ( inverse_divide @ TB ) @ C ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(193,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(120,axiom,
! [A: fun @ nat @ bool,B: nat] :
( ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ( pp @ ( aa @ nat @ bool @ A @ C ) ) )
<=> ? [C: nat] :
( ( member @ nat @ C @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ B ) )
& ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_ex__nat__less__eq) ).
thf(476,plain,
! [A: fun @ nat @ bool,B: nat] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ( pp @ ( aa @ nat @ bool @ A @ C ) ) )
=> ? [C: nat] :
( ( member @ nat @ C @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ B ) )
& ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) )
& ( ? [C: nat] :
( ( member @ nat @ C @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ B ) )
& ( pp @ ( aa @ nat @ bool @ A @ C ) ) )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(137,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) )
=> ( ( ord_less @ TA @ D @ C )
<=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_diff__eq__diff__less) ).
thf(526,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) )
=> ( ( ( ord_less @ TA @ D @ C )
=> ( ord_less @ TA @ B @ A ) )
& ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(150,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_divide__1) ).
thf(590,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(133,axiom,
! [A: nat] :
( ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ A ) ) @ A )
= ( one_one @ complex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_root__unity) ).
thf(515,plain,
! [A: nat] :
( ( aa @ nat @ complex @ ( power_power @ complex @ ( fFT_Mirabelle_root @ A ) ) @ A )
= ( one_one @ complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(115,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zero__neq__one) ).
thf(457,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(12,axiom,
power @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(173,plain,
power @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(155,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__irrefl__nat) ).
thf(605,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(343,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(47,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(244,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(142,axiom,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_nat__less__cases) ).
thf(541,plain,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: fun @ TB @ bool] :
( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ ( big_co1399186613setsum @ TB @ TA ) @ ( combk @ TA @ TB @ ( zero_zero @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_setsum__0) ).
thf(398,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: fun @ TB @ bool] :
( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ ( big_co1399186613setsum @ TB @ TA ) @ ( combk @ TA @ TB @ ( zero_zero @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ ( one_one @ TA ) )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ B ) @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_power__strict__decreasing) ).
thf(298,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ ( one_one @ TA ) )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ B ) @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(104,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ A ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_diff__divide__distrib) ).
thf(412,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ A ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(131,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(513,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(5,axiom,
ring_n68954251visors @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) ).
thf(166,plain,
ring_n68954251visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(180,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(92,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) )
<=> ( ord_less @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_power__strict__increasing__iff) ).
thf(375,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ( ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(14,axiom,
ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__group__add) ).
thf(176,plain,
ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(27,axiom,
comm_monoid_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__add) ).
thf(191,plain,
comm_monoid_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ nat @ C @ A )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_diff__less__mono2) ).
thf(402,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ nat @ C @ A )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(112,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_not__one__less__zero) ).
thf(445,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(94,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le0) ).
thf(382,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(69,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_power__less__imp__less__exp) ).
thf(313,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(17,axiom,
division_ring @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring) ).
thf(181,plain,
division_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(85,axiom,
ord_less @ nat @ k @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(350,plain,
ord_less @ nat @ k @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(23,axiom,
linord1117847801e_zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) ).
thf(187,plain,
linord1117847801e_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
one @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oone) ).
thf(172,plain,
one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ A ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_divide__strict__right__mono) ).
thf(219,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ A ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(48,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(245,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(71,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(318,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(109,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_not__less0) ).
thf(434,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(67,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(303,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(32,axiom,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_minus__nat_Odiff__0) ).
thf(208,plain,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(153,axiom,
! [TA: $tType] :
( ( divisi14063676e_zero @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_divide__zero) ).
thf(599,plain,
! [TA: $tType] :
( ( divisi14063676e_zero @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ nat @ ( power_power @ nat @ B ) @ A ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nat__zero__less__power__iff) ).
thf(552,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ 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 ) @ ( aa @ nat @ nat @ ( power_power @ nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(157,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
<=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_less__iff__diff__less__0) ).
thf(609,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(34,axiom,
monoid_mult @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(213,plain,
monoid_mult @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(135,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_zero__less__one) ).
thf(521,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ( power @ TA )
& ( semiring_0 @ TA ) )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ ( zero_zero @ TA ) ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ ( zero_zero @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_power__0__left) ).
thf(278,plain,
! [TA: $tType] :
( ( ( power @ TA )
& ( semiring_0 @ TA ) )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ ( zero_zero @ TA ) ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ ( zero_zero @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_divide__pos__pos) ).
thf(394,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__imp__diff__less) ).
thf(226,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(129,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_one__reorient) ).
thf(505,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(6,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(167,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: nat,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_field__power__not__zero) ).
thf(223,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: nat,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(156,axiom,
field @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield) ).
thf(608,plain,
field @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(119,axiom,
! [TA: $tType] :
( ( power @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_power__0) ).
thf(473,plain,
! [TA: $tType] :
( ( power @ TA )
=> ! [A: TA] :
( ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less @ nat @ ( aa @ nat @ nat @ ( power_power @ nat @ C ) @ B ) @ ( aa @ nat @ nat @ ( power_power @ nat @ C ) @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_nat__power__less__imp__less) ).
thf(490,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less @ nat @ ( aa @ nat @ nat @ ( power_power @ nat @ C ) @ B ) @ ( aa @ nat @ nat @ ( power_power @ nat @ C ) @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(91,axiom,
field_inverse_zero @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield__inverse__zero) ).
thf(374,plain,
field_inverse_zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(53,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ C ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_nonzero__power__divide) ).
thf(255,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ C ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) @ ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(122,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( zero_zero @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_divide__zero__left) ).
thf(487,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( zero_zero @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(159,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__0__eq) ).
thf(617,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)],[159]) ).
thf(30,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ( ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B )
= ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_power__inject__exp) ).
thf(194,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ( ( ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B )
= ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ B )
= ( aa @ nat @ TA @ ( power_power @ TA @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
( ( aa @ ( fun @ nat @ bool ) @ complex @ ( aa @ ( fun @ nat @ complex ) @ ( fun @ ( fun @ nat @ bool ) @ complex ) @ ( big_co1399186613setsum @ nat @ complex ) @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ n ) )
= ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( minus_minus @ complex ) @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) @ n ) ) @ ( one_one @ complex ) ) ) @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( minus_minus @ complex ) @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) @ ( one_one @ complex ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( aa @ ( fun @ nat @ bool ) @ complex @ ( aa @ ( fun @ nat @ complex ) @ ( fun @ ( fun @ nat @ bool ) @ complex ) @ ( big_co1399186613setsum @ nat @ complex ) @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ n ) )
!= ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( minus_minus @ complex ) @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) @ n ) ) @ ( one_one @ complex ) ) ) @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( minus_minus @ complex ) @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) @ ( one_one @ complex ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(162,plain,
( ( aa @ ( fun @ nat @ bool ) @ complex @ ( aa @ ( fun @ nat @ complex ) @ ( fun @ ( fun @ nat @ bool ) @ complex ) @ ( big_co1399186613setsum @ nat @ complex ) @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ n ) )
!= ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( minus_minus @ complex ) @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) @ n ) ) @ ( one_one @ complex ) ) ) @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( minus_minus @ complex ) @ ( aa @ nat @ complex @ ( power_power @ complex @ ( aa @ complex @ complex @ ( aa @ complex @ ( fun @ complex @ complex ) @ ( inverse_divide @ complex ) @ ( one_one @ complex ) ) @ ( fFT_Mirabelle_root @ n ) ) ) @ k ) ) @ ( one_one @ complex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(138,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(531,plain,
semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(64,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_less__not__refl) ).
thf(295,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(76,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(327,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(55,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_diff__eq__diff__eq) ).
thf(263,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(78,axiom,
no_zero_divisors @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(331,plain,
no_zero_divisors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(128,axiom,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( zero_zero @ nat ) ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_diff__0__eq__0) ).
thf(502,plain,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( zero_zero @ nat ) ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linord1117847801e_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) )
<=> ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_divide__less__0__iff) ).
thf(463,plain,
! [TA: $tType] :
( ( linord1117847801e_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) )
=> ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) )
& ( ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(89,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zero__reorient) ).
thf(359,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)],[89]) ).
thf(15,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_linorder__neqE__linordered__idom) ).
thf(177,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__group__add) ).
thf(182,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(118,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_atLeastLessThan @ TA @ D @ C )
= ( ord_atLeastLessThan @ TA @ B @ A ) )
=> ( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_atLeastLessThan__inj_I2_J) ).
thf(470,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_atLeastLessThan @ TA @ D @ C )
= ( ord_atLeastLessThan @ TA @ B @ A ) )
=> ( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linord1117847801e_zero @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ B ) )
<=> ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ C @ A ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ C ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_divide__less__cancel) ).
thf(576,plain,
! [TA: $tType] :
( ( linord1117847801e_zero @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ B ) )
=> ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ C @ A ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ C ) )
& ( B
!= ( zero_zero @ TA ) ) ) )
& ( ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ C @ A ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ C ) )
& ( B
!= ( zero_zero @ TA ) ) )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__not__refl2) ).
thf(336,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_gr__implies__not0) ).
thf(612,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(161,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( aa @ nat @ TA @ ( power_power @ TA @ ( one_one @ TA ) ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_power__one) ).
thf(627,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( aa @ nat @ TA @ ( power_power @ TA @ ( one_one @ TA ) ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_diff__less) ).
thf(539,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(37,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(218,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(72,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_divide__neg__neg) ).
thf(319,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_97_mult__eq__0__iff) ).
thf(304,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)],[68]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) )
<=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_zero__less__diff) ).
thf(258,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) )
=> ( ord_less @ nat @ A @ B ) )
& ( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(86,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ B )
= ( one_one @ TA ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_right__inverse__eq) ).
thf(351,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ B )
= ( one_one @ TA ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ B )
= ( one_one @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(22,axiom,
zero_neq_one @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(186,plain,
zero_neq_one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(100,axiom,
comm_monoid_add @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__add) ).
thf(401,plain,
comm_monoid_add @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10,axiom,
semiring_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__0) ).
thf(171,plain,
semiring_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(106,axiom,
! [TA: $tType] :
( ( divisi14063676e_zero @ TA )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ A )
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_divide__self__if) ).
thf(418,plain,
! [TA: $tType] :
( ( divisi14063676e_zero @ TA )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ A ) @ A )
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(93,axiom,
! [A: real,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( aa @ nat @ real @ ( power_power @ real @ C ) @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_realpow__pos__nth) ).
thf(378,plain,
! [A: real,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( aa @ nat @ real @ ( power_power @ real @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(84,axiom,
! [A: nat] :
( ( fFT_Mirabelle_root @ A )
!= ( zero_zero @ complex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_root__nonzero) ).
thf(346,plain,
! [A: nat] :
( ( fFT_Mirabelle_root @ A )
!= ( zero_zero @ complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(44,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_neq0__conv) ).
thf(235,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)],[44]) ).
thf(49,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_divide__pos__neg) ).
thf(246,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(35,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_one__neq__zero) ).
thf(214,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(61,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ C ) @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_power__strict__increasing) ).
thf(287,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ C ) @ ( aa @ nat @ TA @ ( power_power @ TA @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(66,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_less__nat__zero__code) ).
thf(300,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(113,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(447,plain,
no_zero_divisors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(70,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_atLeastLessThan @ TA @ D @ C )
= ( ord_atLeastLessThan @ TA @ B @ A ) )
=> ( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( D = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_atLeastLessThan__inj_I1_J) ).
thf(315,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_atLeastLessThan @ TA @ D @ C )
= ( ord_atLeastLessThan @ TA @ B @ A ) )
=> ( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(7,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(168,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(103,axiom,
! [TA: $tType] :
( ( linord1117847801e_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) )
<=> ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zero__less__divide__iff) ).
thf(405,plain,
! [TA: $tType] :
( ( linord1117847801e_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) )
=> ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) )
& ( ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(26,axiom,
field_inverse_zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield__inverse__zero) ).
thf(190,plain,
field_inverse_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ogroup__add) ).
thf(183,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(57,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_divide__strict__right__mono__neg) ).
thf(273,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_nat__neq__iff) ).
thf(564,plain,
! [A: nat,B: nat] :
( ( ( B != A )
=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) )
& ( ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(45,axiom,
divisi14063676e_zero @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero) ).
thf(242,plain,
divisi14063676e_zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(63,axiom,
ab_group_add @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__group__add) ).
thf(294,plain,
ab_group_add @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(88,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(358,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_divide__neg__pos) ).
thf(437,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ B ) @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(139,axiom,
power @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(532,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(105,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_less__zeroE) ).
thf(415,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B ) ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_diff__commute) ).
thf(624,plain,
! [A: nat,B: nat,C: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B ) ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(79,axiom,
comm_semiring_1 @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(332,plain,
comm_semiring_1 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(148,axiom,
zero @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(575,plain,
zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(108,axiom,
! [A: real,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( aa @ nat @ real @ ( power_power @ real @ C ) @ B )
= A )
& ! [D: real] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( aa @ nat @ real @ ( power_power @ real @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_realpow__pos__nth__unique) ).
thf(427,plain,
! [A: real,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( aa @ nat @ real @ ( power_power @ real @ C ) @ B )
= A )
& ! [D: real] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( aa @ nat @ real @ ( power_power @ real @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TB )
=> ! [A: fun @ TC @ bool,B: fun @ TA @ bool,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( fun @ TC @ bool ) @ TB @ ( aa @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TC @ bool ) @ TB ) @ ( big_co1399186613setsum @ TC @ TB ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TC @ TB ) @ ( combc @ TC @ ( fun @ TA @ bool ) @ TB @ ( combb @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ TC @ ( big_co1399186613setsum @ TA @ TB ) @ C ) ) @ B ) ) @ A )
= ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ ( aa @ ( fun @ TC @ bool ) @ ( fun @ TA @ TB ) @ ( combc @ TA @ ( fun @ TC @ bool ) @ TB @ ( combb @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TC @ bool ) @ TB ) @ TA @ ( big_co1399186613setsum @ TC @ TB ) @ ( combc @ TC @ TA @ TB @ C ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_setsum__commute) ).
thf(596,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TB )
=> ! [A: fun @ TC @ bool,B: fun @ TA @ bool,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( fun @ TC @ bool ) @ TB @ ( aa @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TC @ bool ) @ TB ) @ ( big_co1399186613setsum @ TC @ TB ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TC @ TB ) @ ( combc @ TC @ ( fun @ TA @ bool ) @ TB @ ( combb @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ TC @ ( big_co1399186613setsum @ TA @ TB ) @ C ) ) @ B ) ) @ A )
= ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ ( big_co1399186613setsum @ TA @ TB ) @ ( aa @ ( fun @ TC @ bool ) @ ( fun @ TA @ TB ) @ ( combc @ TA @ ( fun @ TC @ bool ) @ TB @ ( combb @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TC @ bool ) @ TB ) @ TA @ ( big_co1399186613setsum @ TC @ TB ) @ ( combc @ TC @ TA @ TB @ C ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(31,axiom,
! [A: fun @ nat @ bool,B: nat] :
( ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) )
<=> ! [C: nat] :
( ( member @ nat @ C @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ B ) )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_all__nat__less__eq) ).
thf(200,plain,
! [A: fun @ nat @ bool,B: nat] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) )
=> ! [C: nat] :
( ( member @ nat @ C @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ B ) )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) )
& ( ! [C: nat] :
( ( member @ nat @ C @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ B ) )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(126,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: nat,B: TA] :
( ( B
!= ( one_one @ TA ) )
=> ( ( aa @ ( fun @ nat @ bool ) @ TA @ ( aa @ ( fun @ nat @ TA ) @ ( fun @ ( fun @ nat @ bool ) @ TA ) @ ( big_co1399186613setsum @ nat @ TA ) @ ( power_power @ TA @ B ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) @ ( one_one @ TA ) ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ ( one_one @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_geometric__sum) ).
thf(496,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: nat,B: TA] :
( ( B
!= ( one_one @ TA ) )
=> ( ( aa @ ( fun @ nat @ bool ) @ TA @ ( aa @ ( fun @ nat @ TA ) @ ( fun @ ( fun @ nat @ bool ) @ TA ) @ ( big_co1399186613setsum @ nat @ TA ) @ ( power_power @ TA @ B ) ) @ ( ord_atLeastLessThan @ nat @ ( zero_zero @ nat ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( inverse_divide @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ nat @ TA @ ( power_power @ TA @ B ) @ A ) ) @ ( one_one @ TA ) ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ ( one_one @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(43,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_diff__self) ).
thf(232,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(630,plain,
$false,
inference(e,[status(thm)],[518,333,249,170,523,217,385,384,533,340,185,174,404,184,357,460,189,284,325,228,289,448,321,211,514,574,492,164,602,221,396,243,248,270,366,512,439,561,424,192,275,165,484,252,493,551,324,188,169,593,499,328,193,476,526,590,515,457,173,605,343,244,541,398,298,412,513,166,180,375,176,191,402,445,382,313,181,350,187,172,219,245,318,434,303,208,599,552,609,213,521,278,394,226,505,167,223,608,473,490,374,255,487,617,194,162,531,295,327,263,331,502,463,359,177,182,470,576,336,612,627,539,218,319,304,258,351,186,401,171,418,378,346,235,246,214,287,300,447,315,168,405,190,183,273,564,242,294,358,437,532,415,624,332,575,427,596,200,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SWV621_5 : TPTP v8.1.2. Released v6.0.0.
% 0.09/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:32:59 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.87/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.08 % [INFO] Parsing done (216ms).
% 1.46/1.08 % [INFO] Running in sequential loop mode.
% 2.10/1.28 % [INFO] eprover registered as external prover.
% 2.10/1.29 % [INFO] cvc4 registered as external prover.
% 2.10/1.29 % [INFO] Scanning for conjecture ...
% 2.55/1.42 % [INFO] Found a conjecture and 159 axioms. Running axiom selection ...
% 2.99/1.50 % [INFO] Axiom selection finished. Selected 159 axioms (removed 0 axioms).
% 3.47/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.47/1.65 % [INFO] Type checking passed.
% 3.47/1.66 % [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 ...
% 30.67/17.01 % External prover 'e' found a proof!
% 30.67/17.01 % [INFO] Killing All external provers ...
% 30.67/17.01 % Time passed: 16505ms (effective reasoning time: 15927ms)
% 30.67/17.02 % 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)>
% 30.67/17.02 % Axioms used in derivation (159): arity_Complex_Ocomplex___Groups_Oone, fact_36_divide__less__cancel, arity_RealDef_Oreal___Groups_Oordered__ab__group__add, fact_92_root__cancel, arity_Nat_Onat___Groups_Omonoid__mult, help_COMBS_1_1_U, fact_8_power__one, fact_41_zero__reorient, fact_58_zero__less__diff, fact_81_one__neq__zero, arity_RealDef_Oreal___Fields_Olinordered__field, fact_84_gr__implies__not0, fact_7_setsum__0, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero, arity_RealDef_Oreal___Rings_Osemiring__0, fact_29_zero__less__power, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, fact_23_power__strict__increasing, arity_Complex_Ocomplex___Power_Opower, fact_61_neq0__conv, fact_63_ex__nat__less__eq, arity_RealDef_Oreal___Groups_Ozero, fact_45_setsum__commute, arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero, fact_11_diff__self, fact_3_geometric__sum, fact_50_divide__1, fact_59_less__zeroE, arity_Nat_Onat___Power_Opower, fact_52_power__divide, fact_28_less__iff__diff__less__0, arity_RealDef_Oreal___Fields_Ofield__inverse__zero, fact_96_le0, arity_RealDef_Oreal___Rings_Oring__no__zero__divisors, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, fact_44_root__summation, fact_34_divide__pos__neg, fact_64_zero__less__one, fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_6_power__eq__0__iff, fact_86_diff__less, fact_24_power__less__imp__less__exp, fact_4_power__0, fact_35_divide__pos__pos, fact_75_less__not__refl3, arity_HOL_Obool___Orderings_Olinorder, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_22_atLeastLessThan__eq__iff, fact_95_less__eq__nat_Osimps_I1_J, arity_Nat_Onat___Rings_Omult__zero, fact_74_less__imp__diff__less, fact_76_less__not__refl2, arity_Complex_Ocomplex___Groups_Ocomm__monoid__add, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_57_nonzero__power__divide, fact_21_atLeastLessThan__inj_I1_J, fact_80_less__not__refl, fact_77_less__irrefl__nat, fact_17_diff__eq__diff__less, fact_83_not__less0, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, help_COMBB_1_1_U, arity_Complex_Ocomplex___Fields_Ofield__inverse__zero, fact_56_divide__self, fact_60_less__nat__zero__code, fact_94_le__0__eq, fact_15_nat__zero__less__power__iff, arity_Nat_Onat___Orderings_Olinorder, arity_Complex_Ocomplex___Rings_Osemiring__0, fact_85_gr0I, fact_55_right__inverse__eq, arity_RealDef_Oreal___Fields_Odivision__ring, fact_62_all__nat__less__eq, fact_70_minus__nat_Odiff__0, arity_Nat_Onat___Rings_Osemiring__0, fact_72_nat__less__cases, fact_65_not__one__less__zero, fact_30_divide__strict__right__mono__neg, arity_RealDef_Oreal___Fields_Ofield, fact_16_nat__power__less__imp__less, fact_51_diff__divide__distrib, fact_89_setsum__0_H, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_53_setsum__subtractf, fact_20_atLeastLessThan__inj_I2_J, arity_Complex_Ocomplex___Rings_Omult__zero, arity_Nat_Onat___Rings_Olinordered__semidom, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_42_one__reorient, fact_1_assms_I2_J, fact_27_one__less__power, fact_5_divide__self__if, fact_32_divide__neg__neg, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_46_right__minus__eq, fact_73_diff__less__mono2, fact_48_diff__0__right, arity_Nat_Onat___Groups_Ozero, arity_RealDef_Oreal___Rings_Omult__zero, fact_43_diff__eq__diff__eq, arity_RealDef_Oreal___Groups_Oab__group__add, help_COMBK_1_1_U, arity_Complex_Ocomplex___Fields_Ofield, fact_40_root__nonzero, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Groups_Ocomm__monoid__add, fact_66_diff__0__eq__0, arity_RealDef_Oreal___Orderings_Olinorder, fact_67_diff__self__eq__0, fact_54_setsum__divide__distrib, help_COMBC_1_1_U, arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_69_linorder__neqE__linordered__idom, fact_91_realpow__pos__nth__unique, arity_RealDef_Oreal___Groups_Oone, fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_37_divide__less__0__iff, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_82_zero__neq__one, arity_Nat_Onat___Groups_Oone, fact_19_power__one__right, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_9_divide__zero__left, fact_47_eq__iff__diff__eq__0, fact_68_diff__commute, fact_13_power__one__over, arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero, arity_RealDef_Oreal___Power_Opower, fact_49_field__power__not__zero, help_pp_1_1_U, fact_33_divide__neg__pos, fact_87_zero__less__power__nat__eq, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_2_root__unity, arity_Complex_Ocomplex___Groups_Oab__group__add, fact_93_power__strict__mono, fact_12_power__0__left, fact_38_zero__less__divide__iff, fact_39_power__inject__exp, fact_0_assms_I1_J, fact_78_linorder__neqE__nat, fact_88_sumr__geometric, help_pp_2_1_U, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Complex_Ocomplex___Groups_Ozero, fact_97_mult__eq__0__iff, fact_25_power__strict__increasing__iff, fact_71_diffs0__imp__equal, arity_Complex_Ocomplex___Fields_Odivision__ring, fact_31_divide__strict__right__mono, arity_RealDef_Oreal___Groups_Ogroup__add, arity_Complex_Ocomplex___Groups_Ogroup__add, fact_10_divide__zero, fact_79_nat__neq__iff, fact_90_realpow__pos__nth, fact_26_power__strict__decreasing
% 30.67/17.02 % No. of inferences in proof: 322
% 30.67/17.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16505 ms resp. 15927 ms w/o parsing
% 31.29/17.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.29/17.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------