TSTP Solution File: DAT153^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT153^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 : Tue May 7 07:39:37 EDT 2024
% Result : Theorem 15.77s 4.92s
% Output : Refutation 16.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 346
% Syntax : Number of formulae : 641 ( 291 unt; 53 typ; 0 def)
% Number of atoms : 1572 ( 599 equ; 0 cnn)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 6493 ( 203 ~; 41 |; 66 &;5587 @)
% ( 0 <=>; 596 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 269 ( 269 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 8 con; 0-4 aty)
% Number of variables : 1507 ( 124 ^1287 !; 52 ?;1507 :)
% ( 44 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(field_type,type,
field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(division_ring_type,type,
division_ring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_mult_type,type,
semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_ring_type,type,
linordered_ring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord581940658strict_type,type,
linord581940658strict:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(archim1727834104eiling_type,type,
archim1727834104eiling:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri1193490041visors_type,type,
semiri1193490041visors:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord20386208strict_type,type,
linord20386208strict:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(archim1804426504_field_type,type,
archim1804426504_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord893533164strict_type,type,
linord893533164strict:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri1923998003cancel_type,type,
semiri1923998003cancel:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(archimedean_ceiling_type,type,
archimedean_ceiling:
!>[TA: $tType] : ( TA > int ) ).
thf(coindu1365464361scount_type,type,
coindu1365464361scount:
!>[TA: $tType] : ( ( ( stream @ TA ) > $o ) > ( stream @ TA ) > extended_enat ) ).
thf(coindu76177514sfirst_type,type,
coindu76177514sfirst:
!>[TA: $tType] : ( ( ( stream @ TA ) > $o ) > ( stream @ TA ) > extended_enat ) ).
thf(extended_enat2_type,type,
extended_enat2: nat > extended_enat ).
thf(extended_case_enat_type,type,
extended_case_enat:
!>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).
thf(extended_rec_enat_type,type,
extended_rec_enat:
!>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).
thf(extended_size_enat_type,type,
extended_size_enat: extended_enat > nat ).
thf(extend1396239628finity_type,type,
extend1396239628finity:
!>[TA: $tType] : TA ).
thf(extended_the_enat_type,type,
extended_the_enat: extended_enat > nat ).
thf(inverse_inverse_type,type,
inverse_inverse:
!>[TA: $tType] : ( TA > TA ) ).
thf(finite_card_type,type,
finite_card:
!>[TA: $tType] : ( ( set @ TA ) > nat ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(nat2_type,type,
nat2: int > nat ).
thf(linear1341015445_UNTIL_type,type,
linear1341015445_UNTIL:
!>[TA: $tType] : ( ( ( stream @ TA ) > $o ) > ( ( stream @ TA ) > $o ) > ( stream @ TA ) > $o ) ).
thf(linear1386806755on_alw_type,type,
linear1386806755on_alw:
!>[TA: $tType] : ( ( ( stream @ TA ) > $o ) > ( stream @ TA ) > $o ) ).
thf(linear505997466_on_ev_type,type,
linear505997466_on_ev:
!>[TA: $tType] : ( ( ( stream @ TA ) > $o ) > ( stream @ TA ) > $o ) ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(nat_tr1645093318rphism_type,type,
nat_tr1645093318rphism:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > $o ) > $o ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(type_type,type,
type:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(sdrop_type,type,
sdrop:
!>[TA: $tType] : ( nat > ( stream @ TA ) > ( stream @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: ( stream @ a ) > $o ).
thf(omega_type,type,
omega: stream @ a ).
thf(129,axiom,
! [A: nat] :
~ ( ord_less @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extended_enat2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_infinity__ilessE) ).
thf(645,plain,
! [A: nat] :
~ ( ord_less @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extended_enat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(30,axiom,
! [TA: $tType] :
( ( extended_case_enat @ TA )
= ( extended_rec_enat @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_case__enat__def) ).
thf(365,plain,
! [TA: $tType] :
( ( extended_case_enat @ TA )
= ( extended_rec_enat @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(18,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear1386806755on_alw @ TA @ A @ B ) )
= ( linear505997466_on_ev @ TA
@ ^ [B: stream @ TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_not__alw) ).
thf(333,plain,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear1386806755on_alw @ TA @ A @ B ) )
= ( linear505997466_on_ev @ TA
@ ^ [B: stream @ TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(174,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_mult__strict__right__mono) ).
thf(777,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(136,axiom,
! [TA: $tType,A: TA > extended_enat,B: nat] :
( ! [C: TA] :
? [D: TA] : ( ord_less @ extended_enat @ ( A @ C ) @ ( A @ D ) )
=> ? [C: TA] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_chain__incr) ).
thf(666,plain,
! [TA: $tType,A: TA > extended_enat,B: nat] :
( ! [C: TA] :
? [D: TA] : ( ord_less @ extended_enat @ ( A @ C ) @ ( A @ D ) )
=> ? [C: TA] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(76,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_semiring__normalization__rules_I13_J) ).
thf(479,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(276,axiom,
! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extended_enat2 @ A ) )
= ( zero_zero @ extended_enat ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extended_enat2 @ A ) )
= ( extend1396239628finity @ extended_enat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_times__enat__simps_I3_J) ).
thf(1105,plain,
! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extended_enat2 @ A ) )
= ( zero_zero @ extended_enat ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extended_enat2 @ A ) )
= ( extend1396239628finity @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(219,axiom,
( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extend1396239628finity @ extended_enat ) )
= ( extend1396239628finity @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_times__enat__simps_I2_J) ).
thf(962,plain,
( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ ( extend1396239628finity @ extended_enat ) )
= ( extend1396239628finity @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(73,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o,D: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ! [E: stream @ TA] :
( ( A @ E )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( linear505997466_on_ev @ TA @ C @ B )
= ( linear505997466_on_ev @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ev__cong) ).
thf(468,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o,D: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ! [E: stream @ TA] :
( ( A @ E )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( linear505997466_on_ev @ TA @ C @ B )
= ( linear505997466_on_ev @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(142,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( times_times @ nat @ A @ B ) )
= ( times_times @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_of__nat__mult) ).
thf(683,plain,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( times_times @ nat @ A @ B ) )
= ( times_times @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(115,axiom,
( nat_tr1645093318rphism @ nat @ int @ ( semiring_1_of_nat @ int )
@ ^ [A: nat] : $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_transfer__morphism__int__nat) ).
thf(597,plain,
( nat_tr1645093318rphism @ nat @ int @ ( semiring_1_of_nat @ int )
@ ^ [A: nat] : $true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(204,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_semiring__normalization__rules_I9_J) ).
thf(861,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(293,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_inverse__negative__iff__negative) ).
thf(1158,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(170,axiom,
! [A: extended_enat] :
( ( A
!= ( extend1396239628finity @ extended_enat ) )
= ( ? [B: nat] :
( A
= ( extended_enat2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_not__infinity__eq) ).
thf(762,plain,
! [A: extended_enat] :
( ( A
!= ( extend1396239628finity @ extended_enat ) )
= ( ? [B: nat] :
( A
= ( extended_enat2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(210,axiom,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ~ ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_enat3__cases) ).
thf(878,plain,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ~ ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( ( B
= ( extend1396239628finity @ extended_enat ) )
=> ( C
!= ( extend1396239628finity @ extended_enat ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(132,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_measure__induct) ).
thf(655,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(88,axiom,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_enat_Osimps_I6_J) ).
thf(511,plain,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_mult__is__0) ).
thf(1078,plain,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(38,axiom,
semigroup_mult @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__mult) ).
thf(385,plain,
semigroup_mult @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(37,axiom,
zero @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(384,plain,
zero @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(285,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B )
=> ( ( coindu1365464361scount @ TA @ A @ B )
= ( extend1396239628finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_scount__infinite) ).
thf(1137,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B )
=> ( ( coindu1365464361scount @ TA @ A @ B )
= ( extend1396239628finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(97,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_divisors__zero) ).
thf(533,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(182,axiom,
! [TA: $tType] :
( ( zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zero__reorient) ).
thf(797,plain,
! [TA: $tType] :
( ( zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(148,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_mult__less__cancel2) ).
thf(698,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(21,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o,D: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ! [E: stream @ TA] :
( ( A @ E )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( linear1386806755on_alw @ TA @ C @ B )
= ( linear1386806755on_alw @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_alw__cong) ).
thf(340,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o,D: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ! [E: stream @ TA] :
( ( A @ E )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( linear1386806755on_alw @ TA @ C @ B )
= ( linear1386806755on_alw @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(235,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_nat__mult__less__cancel__disj) ).
thf(1001,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_inverse__negative__imp__negative) ).
thf(782,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(223,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_mult__pos__neg2) ).
thf(973,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(13,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) )
= ( linear1386806755on_alw @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_not__ev__not) ).
thf(320,plain,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) )
= ( linear1386806755on_alw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(61,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
@ B )
=> ( linear1386806755on_alw @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_alw__mp) ).
thf(436,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
@ B )
=> ( linear1386806755on_alw @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__not__refl2) ).
thf(651,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(194,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_mult__left__cancel) ).
thf(829,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(46,axiom,
linord581940658strict @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(404,plain,
linord581940658strict @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(199,axiom,
( ( nat2 @ ( zero_zero @ int ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_nat__0) ).
thf(841,plain,
( ( nat2 @ ( zero_zero @ int ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(52,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ! [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( linear1386806755on_alw @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_alw__mono) ).
thf(417,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( ! [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( linear1386806755on_alw @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(177,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_mult__strict__right__mono__neg) ).
thf(785,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_enat__ord__simps_I2_J) ).
thf(504,plain,
! [A: nat,B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(166,axiom,
( extended_size_enat
= ( extended_rec_enat @ nat
@ ^ [A: nat] : ( zero_zero @ nat )
@ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_size__enat__def) ).
thf(751,plain,
( extended_size_enat
= ( extended_rec_enat @ nat
@ ^ [A: nat] : ( zero_zero @ nat )
@ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(211,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ C ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_mult__less__cancel__left__disj) ).
thf(934,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ C ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(27,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B )
=> ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
( ( A @ C )
& ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ C ) )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_alw__ev__imp__ev__alw) ).
thf(357,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B )
=> ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
( ( A @ C )
& ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ C ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(107,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_inverse__positive__iff__positive) ).
thf(559,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(127,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_enat__iless) ).
thf(638,plain,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(268,axiom,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_enat__0__iff_I1_J) ).
thf(1087,plain,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(119,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_inverse__zero) ).
thf(606,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(239,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_less__imp__of__nat__less) ).
thf(1013,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(172,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zero__less__imp__eq__int) ).
thf(770,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(82,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_semiring__normalization__rules_I10_J) ).
thf(492,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(179,axiom,
semiring_1 @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_10) ).
thf(789,plain,
semiring_1 @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(248,axiom,
( ( size_size @ extended_enat )
= ( extended_rec_enat @ nat
@ ^ [A: nat] : ( zero_zero @ nat )
@ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_size__enat__overloaded__def) ).
thf(1040,plain,
( ( size_size @ extended_enat )
= ( extended_rec_enat @ nat
@ ^ [A: nat] : ( zero_zero @ nat )
@ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(89,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_mult__less__cancel__left__neg) ).
thf(514,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(212,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_not__less0) ).
thf(937,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(186,axiom,
semiri1193490041visors @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__no__zero__divisors_14) ).
thf(806,plain,
semiri1193490041visors @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(25,axiom,
ab_semigroup_mult @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(353,plain,
ab_semigroup_mult @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(284,axiom,
ab_semigroup_mult @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult_6) ).
thf(1136,plain,
ab_semigroup_mult @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(196,axiom,
( ( zero_zero @ extended_enat )
= ( extended_enat2 @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_zero__enat__def) ).
thf(834,plain,
( ( zero_zero @ extended_enat )
= ( extended_enat2 @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(242,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_mult__less__cancel__left__pos) ).
thf(1020,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(23,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(348,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(206,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ord_less @ extended_enat @ ( coindu76177514sfirst @ TA @ A @ B ) @ ( extend1396239628finity @ extended_enat ) )
= ( linear505997466_on_ev @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_sfirst__finite) ).
thf(866,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ord_less @ extended_enat @ ( coindu76177514sfirst @ TA @ A @ B ) @ ( extend1396239628finity @ extended_enat ) )
= ( linear505997466_on_ev @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(261,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B )
=> ( ( coindu1365464361scount @ TA @ A @ B )
= ( zero_zero @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_scount__eq__0I) ).
thf(1072,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B )
=> ( ( coindu1365464361scount @ TA @ A @ B )
= ( zero_zero @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(173,axiom,
! [TA: $tType,A: stream @ TA] :
( ( sdrop @ TA @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_sdrop_Osimps_I1_J) ).
thf(774,plain,
! [TA: $tType,A: stream @ TA] :
( ( sdrop @ TA @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(134,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_inverse__positive__imp__positive) ).
thf(660,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(233,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_reals__Archimedean2) ).
thf(998,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(50,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( ! [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_ev__mono) ).
thf(411,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( ! [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(275,axiom,
linordered_semidom @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom_5) ).
thf(1104,plain,
linordered_semidom @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_nat__mult__less__cancel1) ).
thf(507,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(8,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( A @ B )
=> ( linear1341015445_UNTIL @ TA @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_UNTIL_Obase) ).
thf(307,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( A @ B )
=> ( linear1341015445_UNTIL @ TA @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(67,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(452,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(35,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ~ ( linear1386806755on_alw @ TA @ A @ B ) )
= ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_not__alw__iff) ).
thf(380,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ~ ( linear1386806755on_alw @ TA @ A @ B ) )
= ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(140,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_less__imp__inverse__less) ).
thf(678,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(102,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_positive__imp__inverse__positive) ).
thf(546,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(188,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_not__gr__zero) ).
thf(810,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(259,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_negative__imp__inverse__negative) ).
thf(1067,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_enat_Oinject) ).
thf(714,plain,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(251,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [C: nat] : ( ord_less @ TA @ B @ ( times_times @ TA @ ( semiring_1_of_nat @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_ex__less__of__nat__mult) ).
thf(1047,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [C: nat] : ( ord_less @ TA @ B @ ( times_times @ TA @ ( semiring_1_of_nat @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(217,axiom,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_transfer__int__nat__numerals_I1_J) ).
thf(957,plain,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(192,axiom,
semigroup_mult @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult_8) ).
thf(825,plain,
semigroup_mult @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(249,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_not__less__zero) ).
thf(1042,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(5,axiom,
linordered_semidom @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semidom) ).
thf(302,plain,
linordered_semidom @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(116,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__zeroE) ).
thf(598,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(191,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nat__less__induct) ).
thf(820,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(42,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_linordered__field__class_Osign__simps_I25_J) ).
thf(392,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3,axiom,
! [TA: $tType,A: stream @ TA] :
~ ( linear1386806755on_alw @ TA
@ ^ [B: stream @ TA] : $false
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_alw__False) ).
thf(297,plain,
! [TA: $tType,A: stream @ TA] :
~ ( linear1386806755on_alw @ TA
@ ^ [B: stream @ TA] : $false
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(159,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA
@ ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C ) )
@ B )
=> ( ( coindu1365464361scount @ TA @ A @ B )
= ( extended_enat2
@ ( finite_card @ nat
@ ( collect @ nat
@ ^ [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_scount__eq__card) ).
thf(729,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA
@ ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C ) )
@ B )
=> ( ( coindu1365464361scount @ TA @ A @ B )
= ( extended_enat2
@ ( finite_card @ nat
@ ( collect @ nat
@ ^ [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(48,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( inverse_inverse @ TA @ ( times_times @ TA @ A @ B ) )
= ( times_times @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_inverse__mult__distrib) ).
thf(407,plain,
! [TA: $tType] :
( ( field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( inverse_inverse @ TA @ ( times_times @ TA @ A @ B ) )
= ( times_times @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(146,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: nat,C: stream @ TA] :
( ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ ( sdrop @ TA @ B @ C ) )
=> ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_alw__ev__sdrop) ).
thf(693,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: nat,C: stream @ TA] :
( ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ ( sdrop @ TA @ B @ C ) )
=> ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(78,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mult_Oleft__commute) ).
thf(484,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(16,axiom,
! [A: nat] :
( ( nat2 @ ( semiring_1_of_nat @ int @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_nat__int) ).
thf(329,plain,
! [A: nat] :
( ( nat2 @ ( semiring_1_of_nat @ int @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(93,axiom,
! [A: nat] :
( ( finite_card @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ nat @ B @ A ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_card__Collect__less__nat) ).
thf(522,plain,
! [A: nat] :
( ( finite_card @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ nat @ B @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(69,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_semiring__normalization__rules_I15_J) ).
thf(456,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(201,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ( times_times @ extended_enat @ A @ B )
= ( extend1396239628finity @ extended_enat ) )
= ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
& ( B
!= ( zero_zero @ extended_enat ) ) )
| ( ( B
= ( extend1396239628finity @ extended_enat ) )
& ( A
!= ( zero_zero @ extended_enat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_imult__is__infinity) ).
thf(852,plain,
! [A: extended_enat,B: extended_enat] :
( ( ( times_times @ extended_enat @ A @ B )
= ( extend1396239628finity @ extended_enat ) )
= ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
& ( B
!= ( zero_zero @ extended_enat ) ) )
| ( ( B
= ( extend1396239628finity @ extended_enat ) )
& ( A
!= ( zero_zero @ extended_enat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(60,axiom,
semiri1923998003cancel @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__no__zero__divisors__cancel) ).
thf(435,plain,
semiri1923998003cancel @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(104,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_zero__less__mult__pos) ).
thf(551,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(281,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_mult__0__right) ).
thf(1128,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(287,axiom,
! [A: nat] : ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extend1396239628finity @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_enat__ord__code_I4_J) ).
thf(1143,plain,
! [A: nat] : ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extend1396239628finity @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(12,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_semiring__normalization__rules_I7_J) ).
thf(317,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(241,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu1365464361scount @ TA @ A @ B )
= ( extend1396239628finity @ extended_enat ) )
= ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_scount__infinite__iff) ).
thf(1017,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu1365464361scount @ TA @ A @ B )
= ( extend1396239628finity @ extended_enat ) )
= ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(227,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ int @ ( zero_zero @ int ) @ ( archimedean_ceiling @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_zero__less__ceiling) ).
thf(980,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ int @ ( zero_zero @ int ) @ ( archimedean_ceiling @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(272,axiom,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
= ( A
!= ( zero_zero @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_i0__less) ).
thf(1096,plain,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
= ( A
!= ( zero_zero @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(207,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_less__irrefl__nat) ).
thf(869,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(53,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: nat,B: TA] :
( ( times_times @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B )
= ( times_times @ TA @ B @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_mult__of__nat__commute) ).
thf(420,plain,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: nat,B: TA] :
( ( times_times @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B )
= ( times_times @ TA @ B @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(230,axiom,
! [A: int] :
( ( times_times @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_times__int__code_I2_J) ).
thf(989,plain,
! [A: int] :
( ( times_times @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(91,axiom,
canoni770627133id_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(519,plain,
canoni770627133id_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_linorder__neqE__linordered__idom) ).
thf(742,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(266,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_of__nat__less__0__iff) ).
thf(1082,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(80,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B )
=> ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_ev__alw__imp__alw__ev) ).
thf(488,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B )
=> ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(167,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__numeral__extra_I3_J) ).
thf(753,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(99,axiom,
! [A: nat] :
( ( extended_size_enat @ ( extended_enat2 @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_enat_Osize_I1_J) ).
thf(537,plain,
! [A: nat] :
( ( extended_size_enat @ ( extended_enat2 @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(128,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu76177514sfirst @ TA @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_sfirst__eq__0) ).
thf(642,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu76177514sfirst @ TA @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(126,axiom,
mult_zero @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero_11) ).
thf(637,plain,
mult_zero @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(222,axiom,
! [A: int,B: int,C: int] :
( ( ord_less @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ord_less @ int @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_zmult__zless__mono2) ).
thf(970,plain,
! [A: int,B: int,C: int] :
( ( ord_less @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ord_less @ int @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(292,axiom,
! [A: int] :
( ( times_times @ int @ A @ ( zero_zero @ int ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_times__int__code_I1_J) ).
thf(1155,plain,
! [A: int] :
( ( times_times @ int @ A @ ( zero_zero @ int ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(143,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_inverse__less__imp__less__neg) ).
thf(686,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(262,axiom,
comm_semiring_1 @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1_7) ).
thf(1075,plain,
comm_semiring_1 @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(75,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear505997466_on_ev @ TA @ A @ B ) )
= ( linear1386806755on_alw @ TA
@ ^ [B: stream @ TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_not__ev) ).
thf(476,plain,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear505997466_on_ev @ TA @ A @ B ) )
= ( linear1386806755on_alw @ TA
@ ^ [B: stream @ TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(273,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_mult__pos__neg) ).
thf(1099,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(149,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_neq0__conv) ).
thf(701,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(282,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_gr0I) ).
thf(1131,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(253,axiom,
( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_the__enat__0) ).
thf(1050,plain,
( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(175,axiom,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ A @ ( extend1396239628finity @ extended_enat ) )
= ( A
!= ( extend1396239628finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_enat__ord__simps_I4_J) ).
thf(779,plain,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ A @ ( extend1396239628finity @ extended_enat ) )
= ( A
!= ( extend1396239628finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(32,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA,D: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A @ B @ C )
=> ( ! [E: stream @ TA] :
( ( A @ E )
=> ( D @ E ) )
=> ( linear1341015445_UNTIL @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_until__monoL) ).
thf(371,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA,D: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A @ B @ C )
=> ( ! [E: stream @ TA] :
( ( A @ E )
=> ( D @ E ) )
=> ( linear1341015445_UNTIL @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(311,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_of__nat__eq__iff) ).
thf(398,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(244,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ~ ! [C: nat] :
( ( A
= ( extended_enat2 @ C ) )
=> ~ ( ord_less @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_less__enatE) ).
thf(1026,plain,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ~ ! [C: nat] :
( ( A
= ( extended_enat2 @ C ) )
=> ~ ( ord_less @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(171,axiom,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_enat__less__induct) ).
thf(765,plain,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(255,axiom,
! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extend1396239628finity @ extended_enat ) )
= ( zero_zero @ extended_enat ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extend1396239628finity @ extended_enat ) )
= ( extend1396239628finity @ extended_enat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_times__enat__simps_I4_J) ).
thf(1054,plain,
! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extend1396239628finity @ extended_enat ) )
= ( zero_zero @ extended_enat ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extend1396239628finity @ extended_enat ) )
= ( extend1396239628finity @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(124,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ TA @ ( inverse_inverse @ TA @ ( semiring_1_of_nat @ TA @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_ex__inverse__of__nat__less) ).
thf(618,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ TA @ ( inverse_inverse @ TA @ ( semiring_1_of_nat @ TA @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(57,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( linear1386806755on_alw @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_alw__alwD) ).
thf(430,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( linear1386806755on_alw @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_gr__implies__not0) ).
thf(745,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(64,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( archimedean_ceiling @ TA @ ( semiring_1_of_nat @ TA @ A ) )
= ( semiring_1_of_nat @ int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_ceiling__of__nat) ).
thf(444,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( archimedean_ceiling @ TA @ ( semiring_1_of_nat @ TA @ A ) )
= ( semiring_1_of_nat @ int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_mult__strict__left__mono__neg) ).
thf(601,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( zero @ TB @ ( type @ TB ) )
=> ! [A: ( TC > TB ) > TA,B: TA] :
( ( A
= ( ^ [C: TC > TB] : B ) )
=> ( ( A
@ ^ [C: TC] : ( zero_zero @ TB ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_fun__cong__unused__0) ).
thf(584,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( zero @ TB @ ( type @ TB ) )
=> ! [A: ( TC > TB ) > TA,B: TA] :
( ( A
= ( ^ [C: TC > TB] : B ) )
=> ( ( A
@ ^ [C: TC] : ( zero_zero @ TB ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(54,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ~ ( linear505997466_on_ev @ TA @ A @ B ) )
= ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_not__ev__iff) ).
thf(423,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ~ ( linear505997466_on_ev @ TA @ A @ B ) )
= ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(237,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_inverse__less__iff__less__neg) ).
thf(1007,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( B = C )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_mult__cancel1) ).
thf(732,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( B = C )
| ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(108,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ( B
!= ( extend1396239628finity @ extended_enat ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ~ ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( B
!= ( extend1396239628finity @ extended_enat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_enat2__cases) ).
thf(562,plain,
! [A: extended_enat,B: extended_enat] :
( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ( B
!= ( extend1396239628finity @ extended_enat ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ~ ( ( A
= ( extend1396239628finity @ extended_enat ) )
=> ( B
!= ( extend1396239628finity @ extended_enat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(224,axiom,
semiri1193490041visors @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_4) ).
thf(975,plain,
semiri1193490041visors @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(200,axiom,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ C )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_int__if__cong) ).
thf(843,plain,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ C )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(280,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_of__nat__eq__0__iff) ).
thf(1125,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(209,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_infinite__descent__measure) ).
thf(875,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(193,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_inverse__less__iff__less) ).
thf(826,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(152,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_less__nat__zero__code) ).
thf(711,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(178,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( A @ ( sdrop @ TA @ ( linear1335279038n_wait @ TA @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_sdrop__wait) ).
thf(787,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( A @ ( sdrop @ TA @ ( linear1335279038n_wait @ TA @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_zero__less__mult__iff) ).
thf(498,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(269,axiom,
( ( ord_less @ extended_enat )
= ( ^ [A: extended_enat,B: extended_enat] :
( extended_case_enat @ $o
@ ^ [C: nat] : ( extended_case_enat @ $o @ ( ord_less @ nat @ C ) @ $true @ B )
@ $false
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__enat__def) ).
thf(1090,plain,
( ( ord_less @ extended_enat )
= ( ^ [A: extended_enat,B: extended_enat] :
( extended_case_enat @ $o
@ ^ [C: nat] : ( extended_case_enat @ $o @ ( ord_less @ nat @ C ) @ $true @ B )
@ $false
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(185,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_mult__neg__pos) ).
thf(804,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_nat__mult__eq__cancel1) ).
thf(704,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(215,axiom,
! [TA: $tType] :
( ( coindu1365464361scount @ TA )
= ( ^ [A: ( stream @ TA ) > $o,B: stream @ TA] :
( if @ extended_enat @ ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B ) @ ( extend1396239628finity @ extended_enat )
@ ( extended_enat2
@ ( finite_card @ nat
@ ( collect @ nat
@ ^ [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_scount__eq) ).
thf(947,plain,
! [TA: $tType] :
( ( coindu1365464361scount @ TA )
= ( ^ [A: ( stream @ TA ) > $o,B: stream @ TA] :
( if @ extended_enat @ ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ A ) @ B ) @ ( extend1396239628finity @ extended_enat )
@ ( extended_enat2
@ ( finite_card @ nat
@ ( collect @ nat
@ ^ [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(100,axiom,
! [A: nat] :
( ( extend1396239628finity @ extended_enat )
!= ( extended_enat2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_enat_Odistinct_I2_J) ).
thf(540,plain,
! [A: nat] :
( ( extend1396239628finity @ extended_enat )
!= ( extended_enat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(72,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ! [C: stream @ TA] : ( A @ C )
=> ( linear1386806755on_alw @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_all__imp__alw) ).
thf(466,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ! [C: stream @ TA] : ( A @ C )
=> ( linear1386806755on_alw @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(270,axiom,
semiri1923998003cancel @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel_1) ).
thf(1092,plain,
semiri1923998003cancel @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(226,axiom,
comm_semiring_1 @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_16) ).
thf(979,plain,
comm_semiring_1 @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(34,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A
@ ^ [B: stream @ TA] : $false )
= ( linear1386806755on_alw @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_until__false) ).
thf(377,plain,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A
@ ^ [B: stream @ TA] : $false )
= ( linear1386806755on_alw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
! [TA: $tType] :
( ( semigroup_mult @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mult_Oassoc) ).
thf(362,plain,
! [TA: $tType] :
( ( semigroup_mult @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_linordered__field__no__lb) ).
thf(616,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(303,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(279,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_nat__mult__eq__cancel__disj) ).
thf(1122,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(387,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(190,axiom,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) )
=> ( A
= ( extend1396239628finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_enat_Oexhaust) ).
thf(816,plain,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) )
=> ( A
= ( extend1396239628finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(120,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_mult__right__cancel) ).
thf(609,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_transfer__int__nat__relations_I1_J) ).
thf(323,plain,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(114,axiom,
! [A: extended_enat] :
~ ( ord_less @ extended_enat @ A @ ( zero_zero @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_not__iless0) ).
thf(594,plain,
! [A: extended_enat] :
~ ( ord_less @ extended_enat @ A @ ( zero_zero @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(157,axiom,
linord20386208strict @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semiring__strict_3) ).
thf(726,plain,
linord20386208strict @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(125,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_infinite__descent0) ).
thf(621,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(92,axiom,
! [TA: $tType,A: nat,B: ( stream @ TA ) > $o,C: stream @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu76177514sfirst @ TA @ B @ C ) )
=> ~ ( B @ ( sdrop @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_less__sfirstD) ).
thf(520,plain,
! [TA: $tType,A: nat,B: ( stream @ TA ) > $o,C: stream @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu76177514sfirst @ TA @ B @ C ) )
=> ~ ( B @ ( sdrop @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_nat__0__less__mult__iff) ).
thf(668,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(22,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ C )
& ( linear1386806755on_alw @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_alw__aand) ).
thf(345,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ C )
& ( linear1386806755on_alw @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(203,axiom,
! [A: nat] :
( ( size_size @ extended_enat @ ( extended_enat2 @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_enat_Osize_I3_J) ).
thf(858,plain,
! [A: nat] :
( ( size_size @ extended_enat @ ( extended_enat2 @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(290,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ ( times_times @ extended_enat @ A @ B ) )
= ( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
& ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_enat__0__less__mult__iff) ).
thf(1149,plain,
! [A: extended_enat,B: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ ( times_times @ extended_enat @ A @ B ) )
= ( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
& ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(220,axiom,
! [TA: $tType] :
( ( mult_zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_mult__zero__left) ).
thf(964,plain,
! [TA: $tType] :
( ( mult_zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(228,axiom,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
=> ( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ A )
= ( extend1396239628finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_imult__infinity) ).
thf(983,plain,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
=> ( ( times_times @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ A )
= ( extend1396239628finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(218,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_mult__less__0__iff) ).
thf(959,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(258,axiom,
semigroup_mult @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_17) ).
thf(1066,plain,
semigroup_mult @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(68,axiom,
mult_zero @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Omult__zero) ).
thf(455,plain,
mult_zero @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(240,axiom,
( ( '?' @ extended_enat )
= ( ^ [A: extended_enat > $o] :
( ( A @ ( extend1396239628finity @ extended_enat ) )
| ? [B: nat] : ( A @ ( extended_enat2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_enat__ex__split) ).
thf(1015,plain,
( ( '?' @ extended_enat )
= ( ^ [A: extended_enat > $o] :
( ( A @ ( extend1396239628finity @ extended_enat ) )
| ? [B: nat] : ( A @ ( extended_enat2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(277,axiom,
! [TA: $tType] :
( ( mult_zero @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_mult__not__zero) ).
thf(1113,plain,
! [TA: $tType] :
( ( mult_zero @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(234,axiom,
semiring_char_0 @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_18) ).
thf(1000,plain,
semiring_char_0 @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(4,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_linordered__field__class_Osign__simps_I24_J) ).
thf(299,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_semiring__normalization__rules_I16_J) ).
thf(438,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(133,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA
@ ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C ) )
@ B )
=> ( ord_less @ extended_enat @ ( coindu1365464361scount @ TA @ A @ B ) @ ( extend1396239628finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_scount__finite) ).
thf(658,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear505997466_on_ev @ TA
@ ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C ) )
@ B )
=> ( ord_less @ extended_enat @ ( coindu1365464361scount @ TA @ A @ B ) @ ( extend1396239628finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(250,axiom,
! [A: nat,B: nat] :
( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( times_times @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_times__enat__simps_I1_J) ).
thf(1044,plain,
! [A: nat,B: nat] :
( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( times_times @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(147,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_gr__zeroI) ).
thf(695,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(229,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type @ TA ) )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_of__nat__0) ).
thf(986,plain,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type @ TA ) )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(7,axiom,
linordered_ring @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__ring) ).
thf(306,plain,
linordered_ring @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(246,axiom,
! [A: nat] :
( ( ( zero_zero @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_enat__0__iff_I2_J) ).
thf(1034,plain,
! [A: nat] :
( ( ( zero_zero @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(81,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_mult__pos__pos) ).
thf(490,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(55,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(426,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(112,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_not__gr0) ).
thf(589,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(141,axiom,
! [A: nat] :
( ( extended_the_enat @ ( extended_enat2 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_the__enat_Osimps) ).
thf(680,plain,
! [A: nat] :
( ( extended_the_enat @ ( extended_enat2 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(33,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_semiring__normalization__rules_I19_J) ).
thf(374,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(288,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( A @ B )
=> ( ( coindu76177514sfirst @ TA @ A @ B )
= ( zero_zero @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_sfirst__0) ).
thf(1145,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( A @ B )
=> ( ( coindu76177514sfirst @ TA @ A @ B )
= ( zero_zero @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(105,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_of__nat__less__iff) ).
thf(553,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(197,axiom,
! [A: nat,B: nat] :
( ( times_times @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( semiring_1_of_nat @ int @ ( times_times @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
thf(836,plain,
! [A: nat,B: nat] :
( ( times_times @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( semiring_1_of_nat @ int @ ( times_times @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(252,axiom,
ab_semigroup_mult @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_15) ).
thf(1049,plain,
ab_semigroup_mult @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(74,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ C )
=> ( linear505997466_on_ev @ TA @ B @ C ) ) )
= ( ^ [C: stream @ TA] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ C )
=> ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_alw__alw__impl__ev) ).
thf(473,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ C )
=> ( linear505997466_on_ev @ TA @ B @ C ) ) )
= ( ^ [C: stream @ TA] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ C )
=> ( linear1386806755on_alw @ TA @ ( linear505997466_on_ev @ TA @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(263,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_linordered__field__no__ub) ).
thf(1076,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(96,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_mult__neg__neg) ).
thf(531,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(214,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_inverse__nonzero__iff__nonzero) ).
thf(944,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_nat__neq__iff) ).
thf(663,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(103,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_measure__induct__rule) ).
thf(548,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(283,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_less__imp__inverse__less__neg) ).
thf(1134,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(130,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_less__not__refl) ).
thf(648,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(79,axiom,
semiri1193490041visors @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__no__zero__divisors) ).
thf(487,plain,
semiri1193490041visors @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(265,axiom,
zero @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_21) ).
thf(1081,plain,
zero @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(165,axiom,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_less__int__code_I1_J) ).
thf(749,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ C @ B ) )
= ( ( A = C )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_mult__cancel2) ).
thf(525,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ C @ B ) )
= ( ( A = C )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(202,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_of__nat__0__eq__iff) ).
thf(855,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1,conjecture,
( ( ord_less @ extended_enat @ ( extended_enat2 @ ( zero_zero @ nat ) ) @ ( coindu76177514sfirst @ a @ p @ omega ) )
= ( ~ ( p @ ( sdrop @ a @ ( zero_zero @ nat ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ord_less @ extended_enat @ ( extended_enat2 @ ( zero_zero @ nat ) ) @ ( coindu76177514sfirst @ a @ p @ omega ) )
!= ( ~ ( p @ ( sdrop @ a @ ( zero_zero @ nat ) @ omega ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(295,plain,
( ( ord_less @ extended_enat @ ( extended_enat2 @ ( zero_zero @ nat ) ) @ ( coindu76177514sfirst @ a @ p @ omega ) )
!= ( ~ ( p @ ( sdrop @ a @ ( zero_zero @ nat ) @ omega ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(208,axiom,
! [A: int] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_zero__less__nat__eq) ).
thf(872,plain,
! [A: int] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(51,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(414,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(162,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_mult__less__mono2) ).
thf(739,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(139,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_infinite__descent) ).
thf(673,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(63,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA,D: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A @ B @ C )
=> ( ! [E: stream @ TA] :
( ( B @ E )
=> ( D @ E ) )
=> ( linear1341015445_UNTIL @ TA @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_until__monoR) ).
thf(441,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA,D: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A @ B @ C )
=> ( ! [E: stream @ TA] :
( ( B @ E )
=> ( D @ E ) )
=> ( linear1341015445_UNTIL @ TA @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(154,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_of__nat__0__less__iff) ).
thf(717,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(28,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ ( linear505997466_on_ev @ TA @ A ) )
= ( linear505997466_on_ev @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ev__ev) ).
thf(359,plain,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ ( linear505997466_on_ev @ TA @ A ) )
= ( linear505997466_on_ev @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(101,axiom,
( ( times_times @ extended_enat )
= ( ^ [A: extended_enat,B: extended_enat] :
( extended_case_enat @ extended_enat
@ ^ [C: nat] :
( extended_case_enat @ extended_enat
@ ^ [D: nat] : ( extended_enat2 @ ( times_times @ nat @ C @ D ) )
@ ( if @ extended_enat
@ ( C
= ( zero_zero @ nat ) )
@ ( zero_zero @ extended_enat )
@ ( extend1396239628finity @ extended_enat ) )
@ B )
@ ( if @ extended_enat
@ ( B
= ( zero_zero @ extended_enat ) )
@ ( zero_zero @ extended_enat )
@ ( extend1396239628finity @ extended_enat ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_times__enat__def) ).
thf(544,plain,
( ( times_times @ extended_enat )
= ( ^ [A: extended_enat,B: extended_enat] :
( extended_case_enat @ extended_enat
@ ^ [C: nat] :
( extended_case_enat @ extended_enat
@ ^ [D: nat] : ( extended_enat2 @ ( times_times @ nat @ C @ D ) )
@ ( if @ extended_enat
@ ( C
= ( zero_zero @ nat ) )
@ ( zero_zero @ extended_enat )
@ ( extend1396239628finity @ extended_enat ) )
@ B )
@ ( if @ extended_enat
@ ( B
= ( zero_zero @ extended_enat ) )
@ ( zero_zero @ extended_enat )
@ ( extend1396239628finity @ extended_enat ) )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(19,axiom,
linord893533164strict @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__comm__semiring__strict) ).
thf(336,plain,
linord893533164strict @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(243,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_mult__cancel__right) ).
thf(1023,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(122,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ( ( archimedean_ceiling @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_ceiling__zero) ).
thf(613,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ( ( archimedean_ceiling @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(254,axiom,
( ( semiring_1_of_nat @ extended_enat )
= extended_enat2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_of__nat__eq__enat) ).
thf(1052,plain,
( ( semiring_1_of_nat @ extended_enat )
= extended_enat2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(205,axiom,
( ( extended_size_enat @ ( extend1396239628finity @ extended_enat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_enat_Osize_I2_J) ).
thf(864,plain,
( ( extended_size_enat @ ( extend1396239628finity @ extended_enat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(158,axiom,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ int @ ( archimedean_ceiling @ TA @ A ) @ ( archimedean_ceiling @ TA @ B ) )
=> ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_ceiling__less__cancel) ).
thf(727,plain,
! [TA: $tType] :
( ( archim1727834104eiling @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ int @ ( archimedean_ceiling @ TA @ A ) @ ( archimedean_ceiling @ TA @ B ) )
=> ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(11,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_semiring__normalization__rules_I17_J) ).
thf(314,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(121,axiom,
semiring_1 @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__1_19) ).
thf(612,plain,
semiring_1 @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(286,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_mult__cancel__left) ).
thf(1140,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(39,axiom,
comm_semiring_1 @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(386,plain,
comm_semiring_1 @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(106,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mult__less__mono1) ).
thf(556,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(77,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( A @ B )
=> ( linear505997466_on_ev @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_ev_Obase) ).
thf(482,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( A @ B )
=> ( linear505997466_on_ev @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(138,axiom,
( ( size_size @ extended_enat @ ( extend1396239628finity @ extended_enat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_enat_Osize_I4_J) ).
thf(671,plain,
( ( size_size @ extended_enat @ ( extend1396239628finity @ extended_enat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_transfer__int__nat__relations_I2_J) ).
thf(581,plain,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(83,axiom,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_mult__0) ).
thf(495,plain,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(169,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_linordered__field__class_Osign__simps_I45_J) ).
thf(759,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(238,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zero__less__iff__neq__zero) ).
thf(1010,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_int__int__eq) ).
thf(368,plain,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(66,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_alwD) ).
thf(450,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(267,axiom,
! [A: extended_enat] :
( ( A
!= ( extend1396239628finity @ extended_enat ) )
=> ( ( extended_enat2 @ ( extended_the_enat @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_enat__the__enat) ).
thf(1084,plain,
! [A: extended_enat] :
( ( A
!= ( extend1396239628finity @ extended_enat ) )
=> ( ( extended_enat2 @ ( extended_the_enat @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(225,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ C ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_mult__less__cancel__right__disj) ).
thf(976,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ C ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(144,axiom,
! [A: extended_enat] :
~ ( ord_less @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_enat__ord__simps_I6_J) ).
thf(688,plain,
! [A: extended_enat] :
~ ( ord_less @ extended_enat @ ( extend1396239628finity @ extended_enat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(111,axiom,
canoni770627133id_add @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_13) ).
thf(588,plain,
canoni770627133id_add @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(189,axiom,
! [TA: $tType] :
( ( mult_zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_mult__zero__right) ).
thf(813,plain,
! [TA: $tType] :
( ( mult_zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(90,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: nat] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( linear1386806755on_alw @ TA @ A @ ( sdrop @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_alw__sdrop) ).
thf(517,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: nat] :
( ( linear1386806755on_alw @ TA @ A @ B )
=> ( linear1386806755on_alw @ TA @ A @ ( sdrop @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(256,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_mult__eq__0__iff) ).
thf(1062,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(274,axiom,
! [TA: $tType] :
( ( linear1386806755on_alw @ TA )
= ( ^ [A: ( stream @ TA ) > $o,B: stream @ TA] :
! [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_alw__iff__sdrop) ).
thf(1101,plain,
! [TA: $tType] :
( ( linear1386806755on_alw @ TA )
= ( ^ [A: ( stream @ TA ) > $o,B: stream @ TA] :
! [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(24,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA] :
( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( linear505997466_on_ev @ TA @ B @ D ) )
@ C )
=> ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( linear505997466_on_ev @ TA @ A @ D )
=> ( linear505997466_on_ev @ TA @ B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_alw__impl__ev__alw) ).
thf(351,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA] :
( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( linear505997466_on_ev @ TA @ B @ D ) )
@ C )
=> ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( linear505997466_on_ev @ TA @ A @ D )
=> ( linear505997466_on_ev @ TA @ B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(41,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( linear505997466_on_ev @ TA @ C @ D ) )
@ B )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_ev__alw__impl__ev) ).
thf(390,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( linear505997466_on_ev @ TA @ C @ D ) )
@ B )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(45,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_semiring__normalization__rules_I14_J) ).
thf(401,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(232,axiom,
! [A: int,B: int] :
( ( ord_less @ nat @ ( nat2 @ A ) @ ( nat2 @ B ) )
= ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_zless__nat__conj) ).
thf(995,plain,
! [A: int,B: int] :
( ( ord_less @ nat @ ( nat2 @ A ) @ ( nat2 @ B ) )
= ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(245,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_gr__implies__not__zero) ).
thf(1030,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(59,axiom,
! [TA: $tType,A: stream @ TA] :
~ ( linear505997466_on_ev @ TA
@ ^ [B: stream @ TA] : $false
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_ev__False) ).
thf(433,plain,
! [TA: $tType,A: stream @ TA] :
~ ( linear505997466_on_ev @ TA
@ ^ [B: stream @ TA] : $false
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(36,axiom,
linordered_idom @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(383,plain,
linordered_idom @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(195,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_zero__less__mult__pos2) ).
thf(832,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(98,axiom,
zero @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_12) ).
thf(536,plain,
zero @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(294,axiom,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_case_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_enat_Osimps_I4_J) ).
thf(1161,plain,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_case_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(183,axiom,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_case_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= ( A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_case__enat__0) ).
thf(800,plain,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_case_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= ( A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(65,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_semiring__normalization__rules_I18_J) ).
thf(447,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(58,axiom,
semiring_char_0 @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0) ).
thf(432,plain,
semiring_char_0 @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(216,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_infinite__descent0__measure) ).
thf(950,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(47,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B )
=> ( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ C ) @ B )
=> ( linear505997466_on_ev @ TA
@ ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
& ( C @ D ) ) )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_ev__alw__aand) ).
thf(405,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B )
=> ( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ C ) @ B )
=> ( linear505997466_on_ev @ TA
@ ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
& ( C @ D ) ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(289,axiom,
( linear1341015445_UNTIL @ a
@ ^ [A: stream @ a] :
~ ( p @ A )
@ ( linear1386806755on_alw @ a @ p )
@ omega ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__C0_Oprems_C) ).
thf(1148,plain,
( linear1341015445_UNTIL @ a
@ ^ [A: stream @ a] :
~ ( p @ A )
@ ( linear1386806755on_alw @ a @ p )
@ omega ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(180,axiom,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: nat] : ( A @ ( extended_enat2 @ C ) )
=> ( ( A @ ( extend1396239628finity @ extended_enat ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_enat_Oinducts) ).
thf(790,plain,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: nat] : ( A @ ( extended_enat2 @ C ) )
=> ( ( A @ ( extend1396239628finity @ extended_enat ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_linorder__neqE__nat) ).
thf(603,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(161,axiom,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ A @ ( extend1396239628finity @ extended_enat ) )
=> ~ ! [B: nat] :
( A
!= ( extended_enat2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_less__infinityE) ).
thf(735,plain,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ A @ ( extend1396239628finity @ extended_enat ) )
=> ~ ! [B: nat] :
( A
!= ( extended_enat2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(49,axiom,
linord20386208strict @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semiring__strict) ).
thf(410,plain,
linord20386208strict @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(221,axiom,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_case_enat @ TA @ A @ B @ ( extend1396239628finity @ extended_enat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_enat_Osimps_I5_J) ).
thf(967,plain,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_case_enat @ TA @ A @ B @ ( extend1396239628finity @ extended_enat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(15,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ ( linear1386806755on_alw @ TA @ A ) )
= ( linear1386806755on_alw @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_alw__alw) ).
thf(326,plain,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( linear1386806755on_alw @ TA @ ( linear1386806755on_alw @ TA @ A ) )
= ( linear1386806755on_alw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(187,axiom,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_rec_enat @ TA @ A @ B @ ( extend1396239628finity @ extended_enat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_enat_Osimps_I7_J) ).
thf(807,plain,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_rec_enat @ TA @ A @ B @ ( extend1396239628finity @ extended_enat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(257,axiom,
linord893533164strict @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict_2) ).
thf(1065,plain,
linord893533164strict @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(155,axiom,
! [A: int,B: int,C: nat] :
( ( ord_less @ int @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ int @ ( times_times @ int @ ( semiring_1_of_nat @ int @ C ) @ A ) @ ( times_times @ int @ ( semiring_1_of_nat @ int @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_zmult__zless__mono2__lemma) ).
thf(720,plain,
! [A: int,B: int,C: nat] :
( ( ord_less @ int @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ int @ ( times_times @ int @ ( semiring_1_of_nat @ int @ C ) @ A ) @ ( times_times @ int @ ( semiring_1_of_nat @ int @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(181,axiom,
semiring_char_0 @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_9) ).
thf(796,plain,
semiring_char_0 @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(71,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
@ B )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_ev__alw__impl) ).
thf(464,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ A @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( A @ D )
=> ( C @ D ) )
@ B )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(17,axiom,
semiring_1 @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(332,plain,
semiring_1 @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(95,axiom,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
=> ( ( times_times @ extended_enat @ A @ ( extend1396239628finity @ extended_enat ) )
= ( extend1396239628finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_imult__infinity__right) ).
thf(528,plain,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
=> ( ( times_times @ extended_enat @ A @ ( extend1396239628finity @ extended_enat ) )
= ( extend1396239628finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(70,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA,D: ( stream @ TA ) > $o,E: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A @ B @ C )
=> ( ! [F: stream @ TA] :
( ( A @ F )
=> ( D @ F ) )
=> ( ! [F: stream @ TA] :
( ( B @ F )
=> ( E @ F ) )
=> ( linear1341015445_UNTIL @ TA @ D @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_until__mono) ).
thf(459,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o,C: stream @ TA,D: ( stream @ TA ) > $o,E: ( stream @ TA ) > $o] :
( ( linear1341015445_UNTIL @ TA @ A @ B @ C )
=> ( ! [F: stream @ TA] :
( ( A @ F )
=> ( D @ F ) )
=> ( ! [F: stream @ TA] :
( ( B @ F )
=> ( E @ F ) )
=> ( linear1341015445_UNTIL @ TA @ D @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(231,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_linordered__field__class_Osign__simps_I44_J) ).
thf(992,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(156,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ( times_times @ extended_enat @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( ( A
= ( zero_zero @ extended_enat ) )
| ( B
= ( zero_zero @ extended_enat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_imult__is__0) ).
thf(723,plain,
! [A: extended_enat,B: extended_enat] :
( ( ( times_times @ extended_enat @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( ( A
= ( zero_zero @ extended_enat ) )
| ( B
= ( zero_zero @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(236,axiom,
! [TA: $tType] :
( ( linear505997466_on_ev @ TA )
= ( ^ [A: ( stream @ TA ) > $o,B: stream @ TA] :
? [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ev__iff__sdrop) ).
thf(1004,plain,
! [TA: $tType] :
( ( linear505997466_on_ev @ TA )
= ( ^ [A: ( stream @ TA ) > $o,B: stream @ TA] :
? [C: nat] : ( A @ ( sdrop @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(145,axiom,
! [TA: $tType] :
( ( linord893533164strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(691,plain,
! [TA: $tType] :
( ( linord893533164strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(278,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_mult__strict__left__mono) ).
thf(1120,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(85,axiom,
! [A: nat,B: int] :
( ( ord_less @ nat @ A @ ( nat2 @ B ) )
= ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_zless__nat__eq__int__zless) ).
thf(501,plain,
! [A: nat,B: int] :
( ( ord_less @ nat @ A @ ( nat2 @ B ) )
= ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(271,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu1365464361scount @ TA @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_scount__eq__0__iff) ).
thf(1093,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu1365464361scount @ TA @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(43,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_mult_Ocommute) ).
thf(395,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(198,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_of__nat__less__imp__less) ).
thf(839,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(291,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_no__zero__divisors) ).
thf(1152,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(56,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: stream @ TA] :
( ( linear505997466_on_ev @ TA @ A @ C )
| ( linear505997466_on_ev @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_ev__or) ).
thf(427,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA
@ ^ [C: stream @ TA] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: stream @ TA] :
( ( linear505997466_on_ev @ TA @ A @ C )
| ( linear505997466_on_ev @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(184,axiom,
mult_zero @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Omult__zero_20) ).
thf(803,plain,
mult_zero @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(20,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) )
= ( linear505997466_on_ev @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_not__alw__not) ).
thf(337,plain,
! [TA: $tType,A: ( stream @ TA ) > $o] :
( ( ^ [B: stream @ TA] :
~ ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) )
= ( linear505997466_on_ev @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__not__refl3) ).
thf(940,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(26,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_linordered__field__class_Osign__simps_I23_J) ).
thf(354,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(9,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ D )
=> ( linear505997466_on_ev @ TA @ C @ D ) )
@ B )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_ev__alw__alw__impl) ).
thf(309,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA,C: ( stream @ TA ) > $o] :
( ( linear505997466_on_ev @ TA @ ( linear1386806755on_alw @ TA @ A ) @ B )
=> ( ( linear1386806755on_alw @ TA
@ ^ [D: stream @ TA] :
( ( linear1386806755on_alw @ TA @ A @ D )
=> ( linear505997466_on_ev @ TA @ C @ D ) )
@ B )
=> ( linear505997466_on_ev @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(247,axiom,
! [A: extended_enat] :
( ( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) ) )
= ( A
= ( extend1396239628finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_not__enat__eq) ).
thf(1037,plain,
! [A: extended_enat] :
( ( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) ) )
= ( A
= ( extend1396239628finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(168,axiom,
! [A: nat] :
( ( extended_enat2 @ A )
!= ( extend1396239628finity @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_enat_Odistinct_I1_J) ).
thf(755,plain,
! [A: nat] :
( ( extended_enat2 @ A )
!= ( extend1396239628finity @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(113,axiom,
! [TA: $tType] :
( ( linordered_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( times_times @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_not__square__less__zero) ).
thf(592,plain,
! [TA: $tType] :
( ( linordered_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( times_times @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(260,axiom,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu1365464361scount @ TA @ A @ B )
= ( zero_zero @ extended_enat ) )
=> ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_scount__eq__0D) ).
thf(1069,plain,
! [TA: $tType,A: ( stream @ TA ) > $o,B: stream @ TA] :
( ( ( coindu1365464361scount @ TA @ A @ B )
= ( zero_zero @ extended_enat ) )
=> ( linear1386806755on_alw @ TA
@ ^ [C: stream @ TA] :
~ ( A @ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(151,axiom,
( ( extend1396239628finity @ extended_enat )
!= ( zero_zero @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_infinity__ne__i0) ).
thf(708,plain,
( ( extend1396239628finity @ extended_enat )
!= ( zero_zero @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1164,plain,
$false,
inference(e,[status(thm)],[645,365,333,777,666,479,1105,962,468,683,597,861,1158,762,878,655,511,1078,385,384,1137,533,797,698,340,1001,782,973,320,436,651,829,404,841,417,785,504,751,934,357,559,638,1087,606,1013,770,492,789,1040,514,937,806,353,1136,834,1020,348,866,1072,774,660,998,411,1104,507,307,452,380,678,546,810,1067,714,1047,957,825,1042,302,598,820,392,297,729,407,693,484,329,522,456,852,435,551,1128,1143,317,1017,980,1096,869,420,989,519,742,1082,488,753,537,642,637,970,1155,686,1075,476,1099,701,1131,1050,779,371,311,398,1026,765,1054,618,430,745,444,601,584,423,1007,732,562,975,843,1125,875,826,711,787,498,1090,804,704,947,540,466,1092,979,377,362,616,303,1122,387,816,609,323,594,726,621,520,668,345,858,1149,964,983,959,1066,455,1015,1113,1000,299,438,658,1044,695,986,306,1034,490,426,589,680,374,1145,553,836,1049,473,1076,531,944,663,548,1134,648,487,1081,749,525,855,295,872,414,739,673,441,717,359,544,336,1023,613,1052,864,727,314,612,1140,386,556,482,671,581,495,759,1010,368,450,1084,976,688,588,813,517,1062,1101,351,390,401,995,1030,433,383,832,536,1161,800,447,432,950,405,1148,790,603,735,410,967,326,807,1065,720,796,464,332,528,459,992,723,1004,691,1120,501,1093,395,839,1152,427,803,337,940,354,309,1037,755,592,1069,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT153^1 : TPTP v8.1.2. Released v7.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n025.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 : Mon May 6 11:32:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.78/1.10 % [INFO] Parsing done (239ms).
% 1.78/1.11 % [INFO] Running in sequential loop mode.
% 2.60/1.32 % [INFO] eprover registered as external prover.
% 2.60/1.33 % [INFO] cvc4 registered as external prover.
% 2.60/1.33 % [INFO] Scanning for conjecture ...
% 2.77/1.42 % [INFO] Found a conjecture and 293 axioms. Running axiom selection ...
% 3.18/1.52 % [INFO] Axiom selection finished. Selected 292 axioms (removed 1 axioms).
% 3.88/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 3.88/1.70 % [INFO] Type checking passed.
% 3.88/1.70 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 15.77/4.92 % External prover 'e' found a proof!
% 15.77/4.92 % [INFO] Killing All external provers ...
% 15.77/4.92 % Time passed: 4389ms (effective reasoning time: 3808ms)
% 15.77/4.92 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 15.77/4.92 % Axioms used in derivation (292): fact_54_not__less0, fact_238_nat__int, fact_27_neq0__conv, fact_152_enat__the__enat, fact_249_inverse__negative__imp__negative, fact_164_times__enat__simps_I1_J, fact_251_inverse__less__imp__less__neg, fact_22_zero__reorient, fact_239_inverse__positive__iff__positive, tcon_Nat_Onat___Nat_Osemiring__char__0_9, fact_130_imult__is__0, fact_176_no__zero__divisors, tcon_Int_Oint___Rings_Olinordered__semidom, fact_91_enat__ex__split, fact_221_semiring__normalization__rules_I17_J, fact_6_enat__iless, fact_125_less__int__code_I1_J, fact_39_measure__induct, fact_66_until__monoL, fact_203_nat__mult__eq__cancel__disj, fact_25_until__false, tcon_Int_Oint___Rings_Olinordered__semiring__strict, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_4, fact_1_less__sfirstD, fact_72_enat_Osimps_I4_J, fact_228_transfer__morphism__int__nat, fact_172_zmult__zless__mono2__lemma, tcon_Extended__Nat_Oenat___Rings_Osemiring__no__zero__divisors_14, fact_219_semiring__normalization__rules_I15_J, fact_143_alw__ev__sdrop, fact_207_linordered__field__class_Osign__simps_I45_J, fact_122_ev_Obase, fact_194_mult__neg__pos, fact_170_zmult__zless__mono2, tcon_Int_Oint___Rings_Omult__zero, fact_105_zero__less__imp__eq__int, tcon_Int_Oint___Groups_Ozero, fact_220_semiring__normalization__rules_I16_J, fact_173_times__enat__def, fact_129_mult__of__nat__commute, fact_73_scount__eq__0__iff, fact_118_mult_Oassoc, fact_4_sdrop_Osimps_I1_J, fact_139_not__ev__iff, fact_210_linordered__field__no__lb, fact_84_of__nat__eq__0__iff, fact_230_ceiling__zero, fact_28_alw__iff__sdrop, fact_42_infinite__descent, fact_109_the__enat__0, fact_242_inverse__less__iff__less, fact_68_UNTIL_Obase, fact_92_enat_Oinducts, fact_80_enat__ord__simps_I4_J, fact_70_less__enat__def, tcon_Nat_Onat___Rings_Olinordered__semiring__strict_3, fact_31_enat_Osimps_I6_J, fact_74_scount__eq__0I, fact_2_not__gr__zero, fact_134_alw__alw__impl__ev, tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict_2, fact_171_linorder__neqE__linordered__idom, tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_17, fact_98_infinity__ne__i0, fact_112_of__nat__mult, fact_83_enat_Osimps_I7_J, fact_94_enat3__cases, fact_165_times__int__code_I1_J, fact_55_less__zeroE, fact_126_ev__alw__imp__alw__ev, fact_215_semiring__normalization__rules_I10_J, fact_236_inverse__nonzero__iff__nonzero, fact_132_ev__alw__alw__impl, fact_123_ev__mono, tcon_Int_Oint___Groups_Oab__semigroup__mult, fact_41_nat__less__induct, fact_209_linordered__field__no__ub, fact_38_less__not__refl3, fact_234_ex__inverse__of__nat__less, fact_107_times__enat__simps_I3_J, fact_52_gr0I, fact_103_less__infinityE, fact_99_of__nat__less__0__iff, fact_160_mult__0__right, tcon_Int_Oint___Rings_Olinordered__comm__semiring__strict, fact_62_alw__cong, fact_250_less__imp__inverse__less__neg, fact_101_less__imp__of__nat__less, fact_23_enat__less__induct, fact_235_inverse__zero, fact_13_i0__less, tcon_Int_Oint___Rings_Olinordered__ring, fact_223_semiring__normalization__rules_I19_J, fact_212_linordered__field__class_Osign__simps_I24_J, fact_151_imult__infinity, fact_227_sdrop__wait, fact_186_mult__less__cancel__left__pos, fact_202_int__if__cong, fact_166_times__int__code_I2_J, fact_61_alw__mono, fact_197_mult__neg__neg, fact_40_less__irrefl__nat, fact_200_transfer__int__nat__numerals_I1_J, fact_65_until__monoR, fact_198_nat__mult__less__cancel__disj, fact_71_case__enat__def, fact_100_of__nat__less__imp__less, fact_241_inverse__less__iff__less__neg, fact_232_ceiling__less__cancel, fact_252_less__imp__inverse__less, fact_33_alw__aand, fact_3_enat_Oinject, fact_153_mult__cancel__right, help_If_1_1_T, fact_187_mult__less__cancel__left__neg, fact_95_enat2__cases, fact_174_mult__not__zero, fact_154_mult__cancel__left, fact_168_mult__less__mono1, fact_182_mult__strict__right__mono__neg, fact_34_alw__mp, fact_77_of__nat__eq__iff, fact_110_scount__finite, fact_17_zero__enat__def, fact_222_semiring__normalization__rules_I18_J, tcon_Nat_Onat___Rings_Omult__zero_11, fact_8_gr__zeroI, tcon_Int_Oint___Groups_Osemigroup__mult, tcon_Int_Oint___Rings_Olinordered__idom, tcon_Int_Oint___Rings_Ocomm__semiring__1, fact_206_nat__mult__eq__cancel1, fact_43_linorder__neqE__nat, fact_208_linordered__field__class_Osign__simps_I44_J, fact_119_mult_Ocommute, fact_97_enat_Odistinct_I2_J, fact_82_enat_Osimps_I5_J, fact_14_sfirst__0, fact_231_ceiling__of__nat, fact_11_zero__less__iff__neq__zero, fact_162_mult__less__cancel2, fact_53_not__gr0, fact_213_linordered__field__class_Osign__simps_I23_J, fact_78_not__infinity__eq, fact_36_less__not__refl, fact_245_zless__nat__eq__int__zless, fact_75_scount__eq__0D, fact_150_imult__infinity__right, fact_196_not__square__less__zero, fact_135_ev__alw__impl__ev, fact_15_enat__ord__simps_I2_J, fact_64_alwD, fact_211_linordered__field__class_Osign__simps_I25_J, fact_191_mult__pos__neg2, fact_141_not__ev, fact_51_size__enat__def, fact_19_enat__0__iff_I2_J, tcon_Int_Oint___Rings_Osemiring__1, fact_224_scount__eq__card, fact_138_ev__alw__aand, fact_159_mult__cancel1, fact_147_scount__infinite__iff, fact_201_transfer__int__nat__relations_I1_J, fact_199_transfer__int__nat__relations_I2_J, fact_161_mult__is__0, fact_185_mult__strict__left__mono__neg, fact_37_less__not__refl2, tcon_Nat_Onat___Groups_Oab__semigroup__mult_6, fact_16_not__iless0, fact_195_mult__less__0__iff, fact_104_enat__ord__code_I4_J, fact_216_semiring__normalization__rules_I7_J, fact_90_of__nat__eq__enat, fact_179_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_93_enat_Oexhaust, fact_12_fun__cong__unused__0, fact_237_inverse__mult__distrib, fact_59_infinite__descent0__measure, help_If_3_1_T, fact_69_of__nat__0__less__iff, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_16, help_If_2_1_T, fact_177_mult__left__cancel, fact_115_not__ev__not, tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_13, tcon_Nat_Onat___Groups_Ozero_12, fact_79_not__enat__eq, fact_193_mult__pos__neg, fact_192_mult__pos__pos, fact_205_nat__mult__less__cancel1, fact_9_not__less__zero, fact_180_mult__less__cancel__right__disj, fact_35_nat__neq__iff, fact_63_alw__alwD, fact_29_alw__sdrop, fact_158_mult__cancel2, fact_116_int__int__eq, tcon_Int_Oint___Rings_Osemiring__no__zero__divisors, fact_137_ev__alw__impl, fact_136_not__alw__iff, fact_124_ev__False, fact_49_infinite__descent__measure, fact_246_positive__imp__inverse__positive, fact_240_inverse__negative__iff__negative, tcon_Extended__Nat_Oenat___Rings_Osemiring__1_19, fact_20_less__enatE, fact_145_imult__is__infinity, fact_247_negative__imp__inverse__negative, fact_45_Collect__mem__eq, fact_121_ev__or, tcon_Nat_Onat___Groups_Osemigroup__mult_8, fact_85_of__nat__0__eq__iff, fact_248_inverse__positive__imp__positive, fact_225_semiring__normalization__rules_I9_J, fact_76_enat_Osize_I4_J, fact_217_semiring__normalization__rules_I13_J, fact_21_sfirst__eq__0, fact_144_ex__less__of__nat__mult, fact_155_mult__eq__0__iff, fact_146_enat__0__less__mult__iff, fact_26_alw__alw, fact_149_sfirst__finite, fact_229_zero__less__ceiling, fact_163_nat__0__less__mult__iff, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel_1, fact_120_mult_Oleft__commute, fact_243_nat__0, tcon_Int_Oint___Nat_Osemiring__char__0, fact_190_zero__less__mult__iff, fact_127_ev__cong, fact_18_enat__0__iff_I1_J, fact_117_ab__semigroup__mult__class_Omult__ac_I1_J, fact_188_zero__less__mult__pos2, fact_131_alw__ev__imp__ev__alw, fact_142_the__enat_Osimps, tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_18, fact_175_divisors__zero, fact_48_measure__induct__rule, tcon_Extended__Nat_Oenat___Groups_Ozero_21, tcon_Int_Oint___Rings_Olinordered__ring__strict, fact_167_mult__0, tcon_Nat_Onat___Rings_Osemiring__1_10, fact_189_zero__less__mult__pos, fact_7_less__numeral__extra_I3_J, fact_181_mult__strict__right__mono, tcon_Extended__Nat_Oenat___Rings_Omult__zero_20, fact_156_mult__zero__right, tcon_Nat_Onat___Rings_Ocomm__semiring__1_7, fact_86_of__nat__0, fact_24_enat_Osize_I1_J, fact_60_all__imp__alw, fact_0__C0_Oprems_C, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_148_scount__infinite, fact_226_card__Collect__less__nat, tcon_Nat_Onat___Rings_Olinordered__semidom_5, fact_32_alw__False, fact_57_infinite__descent0, fact_89_enat_Osize_I2_J, fact_214_scount__eq, fact_106_reals__Archimedean2, fact_108_times__enat__simps_I4_J, fact_204_Nat__Transfer_Otransfer__int__nat__functions_I2_J, fact_10_gr__implies__not__zero, fact_5_chain__incr, fact_183_mult__less__cancel__left__disj, fact_56_gr__implies__not0, fact_88_case__enat__0, fact_114_not__alw__not, fact_133_alw__impl__ev__alw, fact_169_mult__less__mono2, tcon_Int_Oint___Rings_Osemiring__no__zero__divisors__cancel, fact_81_enat__ord__simps_I6_J, fact_178_mult__right__cancel, fact_140_not__alw, fact_157_mult__zero__left, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_15, fact_58_less__nat__zero__code, fact_113_times__enat__simps_I2_J, fact_96_enat_Odistinct_I1_J, fact_46_Collect__cong, fact_184_mult__strict__left__mono, fact_111_ev__ev, fact_87_of__nat__less__iff, fact_44_mem__Collect__eq, fact_50_size__enat__overloaded__def, fact_218_semiring__normalization__rules_I14_J, fact_128_ev__iff__sdrop, fact_244_zless__nat__conj, fact_67_until__mono, fact_30_enat_Osize_I3_J, fact_102_infinity__ilessE, fact_233_zero__less__nat__eq
% 15.77/4.92 % No. of inferences in proof: 588
% 15.77/4.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4389 ms resp. 3808 ms w/o parsing
% 16.70/5.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.70/5.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------