TSTP Solution File: ITP072^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP072^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 07:47:36 EDT 2024
% Result : Theorem 74.28s 53.93s
% Output : Refutation 74.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 307
% Syntax : Number of formulae : 572 ( 188 unt; 44 typ; 0 def)
% Number of atoms : 1982 ( 495 equ; 10 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 6654 ( 175 ~; 18 |; 88 &;5627 @)
% ( 0 <=>; 746 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 206 ( 206 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 43 usr; 5 con; 0-4 aty)
% Number of variables : 1754 ( 60 ^1609 !; 46 ?;1754 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(hF_Mirabelle_hf_type,type,
hF_Mirabelle_hf: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(order_bot_type,type,
order_bot:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_type,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(semiring_bit_shifts_type,type,
semiring_bit_shifts:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(unique788075200shifts_type,type,
unique788075200shifts:
!>[TA: $tType] : $o ).
thf(finite_card_type,type,
finite_card:
!>[TA: $tType] : ( ( set @ TA ) > nat ) ).
thf(finite_finite2_type,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(inj_on_type,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(hF_Mirabelle_HF_type,type,
hF_Mirabelle_HF: ( set @ hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_Abs_hf_type,type,
hF_Mirabelle_Abs_hf: nat > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hfset_type,type,
hF_Mirabelle_hfset: hF_Mirabelle_hf > ( set @ hF_Mirabelle_hf ) ).
thf(hF_Mirabelle_hinsert_type,type,
hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hmem_type,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(lattic1704895705min_on_type,type,
lattic1704895705min_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TB ) ).
thf(semiring_1_Nats_type,type,
semiring_1_Nats:
!>[TA: $tType] : ( set @ TA ) ).
thf(semiri532925092at_aux_type,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( TA > TA ) > nat > TA > TA ) ).
thf(neg_numeral_dbl_type,type,
neg_numeral_dbl:
!>[TA: $tType] : ( TA > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(semiri2097166173op_bit_type,type,
semiri2097166173op_bit:
!>[TA: $tType] : ( nat > TA > TA ) ).
thf(semiri1924326578sh_bit_type,type,
semiri1924326578sh_bit:
!>[TA: $tType] : ( nat > TA > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_type,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_type,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(z_type,type,
z: hF_Mirabelle_hf ).
thf(124,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_bot__empty__eq) ).
thf(645,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(117,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_finite__subset) ).
thf(629,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(40,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_rev__finite__subset) ).
thf(365,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(249,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__zero__eq) ).
thf(1105,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(33,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order_Otrans) ).
thf(347,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_linorder__wlog) ).
thf(333,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(241,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_dbl__simps_I2_J) ).
thf(1083,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(207,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insertE) ).
thf(941,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic1704895705min_on @ TA @ TB @ B @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_arg__min__if__finite_I1_J) ).
thf(481,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic1704895705min_on @ TA @ TB @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(102,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Diff__insert0) ).
thf(582,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(235,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_less__eq__nat_Osimps_I1_J) ).
thf(1068,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(237,axiom,
! [TA: $tType] :
( ( semiring_bit_shifts @ TA )
=> ! [A: nat] :
( ( semiri1924326578sh_bit @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_push__bit__of__0) ).
thf(1073,plain,
! [TA: $tType] :
( ( semiring_bit_shifts @ TA )
=> ! [A: nat] :
( ( semiri1924326578sh_bit @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(80,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1) ).
thf(511,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(107,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_bounded__Max__nat) ).
thf(597,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(189,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_insertCI) ).
thf(861,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ( finite_card @ TA @ B )
= ( finite_card @ TA @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_card__subset__eq) ).
thf(533,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ( finite_card @ TA @ B )
= ( finite_card @ TA @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(168,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ~ ! [B: set @ TA,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( finite_finite2 @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite__cases) ).
thf(797,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ~ ! [B: set @ TA,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( finite_finite2 @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( finite_card @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( finite_card @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_card__image) ).
thf(472,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( finite_card @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( finite_card @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(172,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) @ ( finite_card @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_card__Diff1__le) ).
thf(814,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) @ ( finite_card @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(139,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_Diff__eq__empty__iff) ).
thf(698,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_image__is__empty) ).
thf(747,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(209,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Collect__empty__eq) ).
thf(945,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_inj__on__eq__iff) ).
thf(829,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(218,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_mem__Collect__eq) ).
thf(1001,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(257,axiom,
( ( zero_zero @ nat )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zero__natural_Orsp) ).
thf(1127,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( ( image @ TA @ TB @ A @ C )
= ( image @ TA @ TB @ A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_inj__on__image__eq__iff) ).
thf(709,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( ( image @ TA @ TB @ A @ C )
= ( image @ TA @ TB @ A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(12,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_eq__iff) ).
thf(288,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_order__class_Oorder_Oeq__iff) ).
thf(301,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(98,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TA @ ( insert @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_finite_OinsertI) ).
thf(565,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TA @ ( insert @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ~ ! [B: set @ TA] :
( ? [C: TA] :
( A
= ( insert @ TA @ C @ B ) )
=> ~ ( finite_finite2 @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_finite_Ocases) ).
thf(436,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ~ ! [B: set @ TA] :
( ? [C: TA] :
( A
= ( insert @ TA @ C @ B ) )
=> ~ ( finite_finite2 @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: TA,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TB @ ( C @ ( lattic1704895705min_on @ TA @ TB @ C @ A ) ) @ ( C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_arg__min__least) ).
thf(651,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: TA,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TB @ ( C @ ( lattic1704895705min_on @ TA @ TB @ C @ A ) ) @ ( C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_subset__emptyI) ).
thf(719,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ C @ D ) @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ C @ D ) )
= ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_inj__on__image__set__diff) ).
thf(372,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ C @ D ) @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ C @ D ) )
= ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(231,axiom,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hmem__def) ).
thf(1059,plain,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(91,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__cong) ).
thf(542,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)],[91]) ).
thf(229,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_le__iff__diff__le__0) ).
thf(1055,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(149,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_bot_Oextremum__uniqueI) ).
thf(724,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_all__subset__image) ).
thf(559,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_le__numeral__extra_I3_J) ).
thf(1147,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(9,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(284,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(253,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_le__0__eq) ).
thf(1115,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(25,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_linear) ).
thf(316,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_singleton__inject) ).
thf(475,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(73,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_finite) ).
thf(492,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(158,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_finite__has__minimal) ).
thf(756,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(223,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_diff__0__right) ).
thf(1040,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_singleton__insert__inj__eq_H) ).
thf(574,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(196,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_doubleton__eq__iff) ).
thf(905,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(261,axiom,
! [A: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hinsert @ B @ C ) )
=> ( hF_Mirabelle_hmem @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hf__cases) ).
thf(1136,plain,
! [A: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hinsert @ B @ C ) )
=> ( hF_Mirabelle_hmem @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_subset__trans) ).
thf(834,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( ( inj_on @ TA @ TB @ A @ C )
& ~ ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_inj__on__insert) ).
thf(981,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( ( inj_on @ TA @ TB @ A @ C )
& ~ ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_inj__on__contraD) ).
thf(634,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(190,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_all__not__in__conv) ).
thf(866,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1,conjecture,
( ( z
= ( zero_zero @ hF_Mirabelle_hf ) )
= ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( z
= ( zero_zero @ hF_Mirabelle_hf ) )
!= ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(265,plain,
( ( z
= ( zero_zero @ hF_Mirabelle_hf ) )
!= ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_le__trans) ).
thf(527,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(60,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_empty__Diff) ).
thf(452,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(200,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_set__eq__subset) ).
thf(920,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(81,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Collect__empty__eq__bot) ).
thf(512,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(4,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_le__cases) ).
thf(270,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_double__diff) ).
thf(761,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(46,axiom,
! [TA: $tType,A: ( set @ TA ) > $o,B: set @ TA] :
( ! [C: set @ TA] :
( ~ ( finite_finite2 @ TA @ C )
=> ( A @ C ) )
=> ( ( A @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_infinite__finite__induct) ).
thf(381,plain,
! [TA: $tType,A: ( set @ TA ) > $o,B: set @ TA] :
( ! [C: set @ TA] :
( ~ ( finite_finite2 @ TA @ C )
=> ( A @ C ) )
=> ( ( A @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(145,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_emptyE) ).
thf(714,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(198,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_finite__has__maximal) ).
thf(910,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_finite__Diff2) ).
thf(825,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(349,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(137,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_empty__subsetI) ).
thf(693,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(213,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( C @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ( member @ TA @ D @ B )
=> ( ~ ( member @ TA @ D @ E )
=> ( ( C @ E )
=> ( C @ ( insert @ TA @ D @ E ) ) ) ) ) )
=> ( C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_finite__subset__induct) ).
thf(957,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( C @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ( member @ TA @ D @ B )
=> ( ~ ( member @ TA @ D @ E )
=> ( ( C @ E )
=> ( C @ ( insert @ TA @ D @ E ) ) ) ) ) )
=> ( C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(192,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
& ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_subset__Diff__insert) ).
thf(894,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
& ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(71,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_ex__in__conv) ).
thf(484,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TB @ B ) )
=> ? [C: TA > TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ B )
& ( inj_on @ TA @ TB @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_card__le__inj) ).
thf(852,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TB @ B ) )
=> ? [C: TA > TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ B )
& ( inj_on @ TA @ TB @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(85,axiom,
! [TA: $tType,A: set @ TA,B: nat] :
( ~ ( finite_finite2 @ TA @ A )
=> ? [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
& ( ( finite_card @ TA @ C )
= B )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_infinite__arbitrarily__large) ).
thf(522,plain,
! [TA: $tType,A: set @ TA,B: nat] :
( ~ ( finite_finite2 @ TA @ A )
=> ? [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
& ( ( finite_card @ TA @ C )
= B )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(63,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Diff__empty) ).
thf(461,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(239,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_le0) ).
thf(1079,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(133,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_the__elem__eq) ).
thf(682,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(285,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(94,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_card__seteq) ).
thf(551,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(258,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ( finite_card @ TA @ A )
= ( zero_zero @ nat ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_card__0__eq) ).
thf(1128,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ( finite_card @ TA @ A )
= ( zero_zero @ nat ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_insert__mono) ).
thf(742,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(210,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_bot_Oextremum) ).
thf(948,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(112,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(615,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(255,axiom,
! [TA: $tType] :
( ( semiring_bit_shifts @ TA )
=> ! [A: nat] :
( ( semiri2097166173op_bit @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_drop__bit__of__0) ).
thf(1121,plain,
! [TA: $tType] :
( ( semiring_bit_shifts @ TA )
=> ! [A: nat] :
( ( semiri2097166173op_bit @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(233,axiom,
zero @ hF_Mirabelle_hf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HF__Mirabelle__fsbjehakzm_Ohf___Groups_Ozero_19) ).
thf(1064,plain,
zero @ hF_Mirabelle_hf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(251,axiom,
( ( zero_zero @ hF_Mirabelle_hf )
= ( hF_Mirabelle_HF @ ( bot_bot @ ( set @ hF_Mirabelle_hf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Zero__hf__def) ).
thf(1111,plain,
( ( zero_zero @ hF_Mirabelle_hf )
= ( hF_Mirabelle_HF @ ( bot_bot @ ( set @ hF_Mirabelle_hf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(246,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_bot__nat__0_Oextremum__unique) ).
thf(1096,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] : ( ord_less_eq @ ( set @ TB ) @ ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_image__diff__subset) ).
thf(356,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] : ( ord_less_eq @ ( set @ TB ) @ ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_finite__set__choice) ).
thf(593,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(191,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( C @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ( member @ TA @ D @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ E @ B )
=> ( ~ ( member @ TA @ D @ E )
=> ( ( C @ E )
=> ( C @ ( insert @ TA @ D @ E ) ) ) ) ) ) )
=> ( C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_finite__subset__induct_H) ).
thf(869,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( C @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ( member @ TA @ D @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ E @ B )
=> ( ~ ( member @ TA @ D @ E )
=> ( ( C @ E )
=> ( C @ ( insert @ TA @ D @ E ) ) ) ) ) ) )
=> ( C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(76,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_equalityD2) ).
thf(499,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_subsetD) ).
thf(857,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(48,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_singletonI) ).
thf(420,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(254,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_bot__nat__0_Oextremum__uniqueI) ).
thf(1118,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_inj__on__def) ).
thf(637,plain,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(132,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_insert__Diff1) ).
thf(679,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(93,axiom,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_infinite__imp__nonempty) ).
thf(547,plain,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(142,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_finite__code) ).
thf(706,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(95,axiom,
! [TA: $tType,A: nat,B: set @ TA] :
( ( ord_less_eq @ nat @ A @ ( finite_card @ TA @ B ) )
=> ~ ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ( finite_card @ TA @ C )
= A )
=> ~ ( finite_finite2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_obtain__subset__with__card__n) ).
thf(554,plain,
! [TA: $tType,A: nat,B: set @ TA] :
( ( ord_less_eq @ nat @ A @ ( finite_card @ TA @ B ) )
=> ~ ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ( finite_card @ TA @ C )
= A )
=> ~ ( finite_finite2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(157,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subset__antisym) ).
thf(753,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(221,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_is__singletonI_H) ).
thf(1016,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(105,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Diff__cancel) ).
thf(590,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(116,axiom,
! [TA: $tType,A: set @ TA,B: nat] :
( ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ( ( finite_finite2 @ TA @ C )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ C ) @ B ) ) )
=> ( ( finite_finite2 @ TA @ A )
& ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_finite__if__finite__subsets__card__bdd) ).
thf(622,plain,
! [TA: $tType,A: set @ TA,B: nat] :
( ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ( ( finite_finite2 @ TA @ C )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ C ) @ B ) ) )
=> ( ( finite_finite2 @ TA @ A )
& ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(247,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( ( A = B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_hmem__hinsert) ).
thf(1099,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( ( A = B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(140,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_in__mono) ).
thf(701,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(82,axiom,
( ( finite_finite2 @ nat )
= ( ^ [A: set @ nat] :
? [B: nat] :
! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_finite__nat__set__iff__bounded__le) ).
thf(515,plain,
( ( finite_finite2 @ nat )
= ( ^ [A: set @ nat] :
? [B: nat] :
! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(227,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_zero__diff) ).
thf(1050,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(217,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_finite__induct) ).
thf(984,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_insert__commute) ).
thf(721,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(165,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: set @ TA,D: TA] :
( ( finite_finite2 @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( insert @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_finite_Oinducts) ).
thf(779,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: set @ TA,D: TA] :
( ( finite_finite2 @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( insert @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_subset__eq) ).
thf(503,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(259,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( member @ TA @ ( zero_zero @ TA ) @ ( semiring_1_Nats @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Nats__0) ).
thf(1131,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( member @ TA @ ( zero_zero @ TA ) @ ( semiring_1_Nats @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( finite_finite2 @ TA @ D )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_finite__subset__image) ).
thf(654,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( finite_finite2 @ TA @ D )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(31,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_antisym__conv) ).
thf(343,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( member @ TB @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_image__subset__iff) ).
thf(792,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( member @ TB @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(119,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).
thf(633,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(22,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_6) ).
thf(311,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_finite__image__iff) ).
thf(530,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(129,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] : ( B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ( D
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) ) )
=> ( B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_finite__ne__induct) ).
thf(662,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] : ( B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ( D
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) ) )
=> ( B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(202,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( member @ TB @ ( A @ C ) @ ( image @ TA @ TB @ A @ D ) )
= ( member @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_inj__on__image__mem__iff) ).
thf(926,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( member @ TB @ ( A @ C ) @ ( image @ TA @ TB @ A @ D ) )
= ( member @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(242,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_bot__nat__0_Oextremum) ).
thf(1086,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(206,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
= ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_finite__Diff__insert) ).
thf(938,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
= ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(156,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_singleton__insert__inj__eq) ).
thf(750,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(114,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ ( insert @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_card__insert__le) ).
thf(618,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ ( insert @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_image__empty) ).
thf(430,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_order__subst2) ).
thf(296,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_subset__refl) ).
thf(444,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_DiffE) ).
thf(375,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(174,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_bot__set__def) ).
thf(819,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(97,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__Diff__single) ).
thf(562,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_subset__inj__on) ).
thf(843,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_equalityD1) ).
thf(772,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(101,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_finite__has__maximal2) ).
thf(577,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(13,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_dual__order_Oantisym) ).
thf(291,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_insertI1) ).
thf(545,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(256,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hmem__hempty) ).
thf(1124,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_image__insert) ).
thf(281,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_14) ).
thf(313,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(230,axiom,
inj_on @ ( set @ hF_Mirabelle_hf ) @ hF_Mirabelle_hf @ hF_Mirabelle_HF @ ( collect @ ( set @ hF_Mirabelle_hf ) @ ( finite_finite2 @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_inj__on__HF) ).
thf(1058,plain,
inj_on @ ( set @ hF_Mirabelle_hf ) @ hF_Mirabelle_hf @ hF_Mirabelle_HF @ ( collect @ ( set @ hF_Mirabelle_hf ) @ ( finite_finite2 @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(244,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_diff__ge__0__iff__ge) ).
thf(1090,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(169,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_subset__singletonD) ).
thf(804,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_subsetI) ).
thf(900,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_image__eqI) ).
thf(274,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(263,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: TA > TA,B: TA] :
( ( semiri532925092at_aux @ TA @ A @ ( zero_zero @ nat ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_of__nat__aux_Osimps_I1_J) ).
thf(1144,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: TA > TA,B: TA] :
( ( semiri532925092at_aux @ TA @ A @ ( zero_zero @ nat ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(26,axiom,
order_bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_12) ).
thf(318,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(113,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_infinite__super) ).
thf(616,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(160,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_subset__iff) ).
thf(764,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(215,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_inj__on__subset) ).
thf(979,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ? [D: set @ TB] :
( ( finite_finite2 @ TB @ D )
& ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: set @ TA] :
( ( finite_finite2 @ TA @ D )
& ( ord_less_eq @ ( set @ TA ) @ D @ B )
& ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_ex__finite__subset__image) ).
thf(604,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ? [D: set @ TB] :
( ( finite_finite2 @ TB @ D )
& ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: set @ TA] :
( ( finite_finite2 @ TA @ D )
& ( ord_less_eq @ ( set @ TA ) @ D @ B )
& ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(226,axiom,
! [A: hF_Mirabelle_hf] : ( finite_finite2 @ hF_Mirabelle_hf @ ( hF_Mirabelle_hfset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_finite__hfset) ).
thf(1048,plain,
! [A: hF_Mirabelle_hf] : ( finite_finite2 @ hF_Mirabelle_hf @ ( hF_Mirabelle_hfset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(151,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_bot_Oextremum__unique) ).
thf(736,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(39,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_diff__right__commute) ).
thf(362,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(99,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_equalityE) ).
thf(567,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(79,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Diff__subset) ).
thf(509,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(224,axiom,
( hF_Mirabelle_hinsert
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_hinsert__def) ).
thf(1043,plain,
( hF_Mirabelle_hinsert
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(171,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_image__subsetI) ).
thf(811,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_subset__image__iff) ).
thf(494,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(118,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_diff__right__mono) ).
thf(631,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ B ) @ C )
=> ( ( finite_finite2 @ TA @ C )
=> ( ord_less_eq @ nat @ ( finite_card @ TB @ B ) @ ( finite_card @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_card__inj__on__le) ).
thf(367,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ B ) @ C )
=> ( ( finite_finite2 @ TA @ C )
=> ( ord_less_eq @ nat @ ( finite_card @ TB @ B ) @ ( finite_card @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(173,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_insert__iff) ).
thf(816,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ( finite_finite2 @ TB @ D )
& ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ( finite_finite2 @ TA @ D )
& ( ord_less_eq @ ( set @ TA ) @ D @ B ) )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_all__finite__subset__image) ).
thf(609,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ( finite_finite2 @ TB @ D )
& ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ( finite_finite2 @ TA @ D )
& ( ord_less_eq @ ( set @ TA ) @ D @ B ) )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(199,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__has__minimal2) ).
thf(915,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) )
= ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_insert__image) ).
thf(769,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) )
= ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(232,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_diff__zero) ).
thf(1061,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_eq__imp__le) ).
thf(848,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
=> ( ( inj_on @ TA @ TB @ A @ B )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_finite__imageD) ).
thf(520,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
=> ( ( inj_on @ TA @ TB @ A @ B )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_singleton__iff) ).
thf(685,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(138,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Collect__mono__iff) ).
thf(695,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(7,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_order__class_Oorder_Oantisym) ).
thf(278,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_Diff__idemp) ).
thf(455,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order__subst1) ).
thf(306,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(252,axiom,
( ( (=) @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hf__ext) ).
thf(1113,plain,
( ( (=) @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(16,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_3) ).
thf(299,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_dual__order_Oeq__iff) ).
thf(267,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(248,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_hemptyE) ).
thf(1102,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(238,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(1076,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(50,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(426,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(208,axiom,
unique788075200shifts @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Parity_Ounique__euclidean__semiring__with__bit__shifts) ).
thf(944,plain,
unique788075200shifts @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_nat__le__linear) ).
thf(795,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(240,axiom,
( ( bot_bot @ nat )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_bot__nat__def) ).
thf(1081,plain,
( ( bot_bot @ nat )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(62,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_is__singleton__the__elem) ).
thf(458,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_inj__onI) ).
thf(836,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(125,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_empty__Collect__eq) ).
thf(648,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(72,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: TA,C: set @ TA] :
( ! [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ A )
=> ~ ( member @ TA @ B @ D ) )
=> ( ( member @ ( set @ TA ) @ C @ ( image @ ( set @ TA ) @ ( set @ TA ) @ ( insert @ TA @ B ) @ A ) )
= ( ( member @ TA @ B @ C )
& ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_in__image__insert__iff) ).
thf(487,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: TA,C: set @ TA] :
( ! [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ A )
=> ~ ( member @ TA @ B @ D ) )
=> ( ( member @ ( set @ TA ) @ C @ ( image @ ( set @ TA ) @ ( set @ TA ) @ ( insert @ TA @ B ) @ A ) )
= ( ( member @ TA @ B @ C )
& ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(164,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Diff__insert) ).
thf(776,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(144,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_finite__Diff) ).
thf(712,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TA @ ( minus_minus @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(186,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_le__refl) ).
thf(855,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(136,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_insert__absorb2) ).
thf(690,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(122,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( insert @ TA @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_finite__insert) ).
thf(640,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( insert @ TA @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(236,axiom,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_card @ TA @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_card_Oinfinite) ).
thf(1070,plain,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_card @ TA @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(47,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Nat_Oex__has__greatest__nat) ).
thf(414,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(212,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insert__subset) ).
thf(954,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(152,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Diff__iff) ).
thf(739,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(228,axiom,
( ( hF_Mirabelle_Abs_hf @ ( zero_zero @ nat ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Abs__hf__0) ).
thf(1053,plain,
( ( hF_Mirabelle_Abs_hf @ ( zero_zero @ nat ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(130,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Diff__insert2) ).
thf(673,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(55,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Collect__mem__eq) ).
thf(441,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(103,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_ex__has__least__nat) ).
thf(585,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(29,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_antisym) ).
thf(338,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] : ( inj_on @ TA @ TB @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_inj__on__empty) ).
thf(470,plain,
! [TA: $tType,TB: $tType,A: TA > TB] : ( inj_on @ TA @ TB @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(123,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_diff__left__mono) ).
thf(643,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(154,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Collect__mono) ).
thf(744,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(141,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_subset__insert) ).
thf(703,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(262,axiom,
! [TA: $tType,A: set @ TA] :
( ( ( finite_card @ TA @ A )
= ( zero_zero @ nat ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ~ ( finite_finite2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_card__eq__0__iff) ).
thf(1141,plain,
! [TA: $tType,A: set @ TA] :
( ( ( finite_card @ TA @ A )
= ( zero_zero @ nat ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ~ ( finite_finite2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: ( set @ TA ) > $o,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ! [F: TA] :
( ( member @ TA @ F @ E )
=> ( ord_less_eq @ TB @ ( C @ F ) @ ( C @ D ) ) )
=> ( ( B @ E )
=> ( B @ ( insert @ TA @ D @ E ) ) ) ) )
=> ( B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_finite__ranking__induct) ).
thf(1023,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: ( set @ TA ) > $o,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ! [F: TA] :
( ( member @ TA @ F @ E )
=> ( ord_less_eq @ TB @ ( C @ F ) @ ( C @ D ) ) )
=> ( ( B @ E )
=> ( B @ ( insert @ TA @ D @ E ) ) ) ) )
=> ( B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ~ ( member @ TB @ C @ D )
=> ( ( ( insert @ TB @ C @ D )
= ( image @ TA @ TB @ A @ B ) )
=> ~ ! [E: TA,F: set @ TA] :
( ~ ( member @ TA @ E @ F )
=> ( ( B
= ( insert @ TA @ E @ F ) )
=> ( ( C
= ( A @ E ) )
=> ( D
!= ( image @ TA @ TB @ A @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_inj__img__insertE) ).
thf(727,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ~ ( member @ TB @ C @ D )
=> ( ( ( insert @ TB @ C @ D )
= ( image @ TA @ TB @ A @ B ) )
=> ~ ! [E: TA,F: set @ TA] :
( ~ ( member @ TA @ E @ F )
=> ( ( B
= ( insert @ TA @ E @ F ) )
=> ( ( C
= ( A @ E ) )
=> ( D
!= ( image @ TA @ TB @ A @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(214,axiom,
semiring_bit_shifts @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Parity_Osemiring__bit__shifts) ).
thf(978,plain,
semiring_bit_shifts @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(24,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_dual__order_Orefl) ).
thf(314,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(57,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(446,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(111,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_subset__singleton__iff) ).
thf(612,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(75,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_subset__insertI2) ).
thf(497,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_image__mono) ).
thf(859,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(183,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_le__antisym) ).
thf(845,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_inj__on__cong) ).
thf(465,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_DiffD1) ).
thf(450,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(250,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_diff__self) ).
thf(1108,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(204,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_mk__disjoint__insert) ).
thf(931,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_insert__Diff) ).
thf(539,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(135,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_insert__subsetI) ).
thf(688,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(195,axiom,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_finite_OemptyI) ).
thf(903,plain,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(104,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_subset__insertI) ).
thf(588,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_inj__onD) ).
thf(517,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(27,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_le__cases3) ).
thf(319,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(304,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_empty__is__image) ).
thf(351,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_insert__not__empty) ).
thf(378,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(53,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_diff__eq__diff__less__eq) ).
thf(433,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(203,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insertI2) ).
thf(929,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(69,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Diff__insert__absorb) ).
thf(478,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(5,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_9) ).
thf(272,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: TB > TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( image @ TB @ TA @ C @ A ) )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_finite__surj) ).
thf(832,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: TB > TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( image @ TB @ TA @ C @ A ) )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(32,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_16) ).
thf(346,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(89,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_subset__empty) ).
thf(536,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(225,axiom,
! [TA: $tType] :
( ( finite_card @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_card_Oempty) ).
thf(1045,plain,
! [TA: $tType] :
( ( finite_card @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(146,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_singletonD) ).
thf(716,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(11,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_15) ).
thf(287,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(260,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_zero__reorient) ).
thf(1133,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(17,axiom,
order_bot @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder__bot_1) ).
thf(300,plain,
order_bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Diff__mono) ).
thf(620,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(58,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insert__absorb) ).
thf(447,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(211,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
=> ( A
!= ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subset__imageE) ).
thf(950,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
=> ( A
!= ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_equals0D) ).
thf(422,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TB @ ( image @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_finite__imageI) ).
thf(294,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TB @ ( image @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_8) ).
thf(341,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(78,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_diff__eq__diff__eq) ).
thf(506,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(177,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(828,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(234,axiom,
! [TA: $tType] :
( ( unique788075200shifts @ TA )
=> ! [A: nat,B: TA] :
( ( ( semiri1924326578sh_bit @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_push__bit__eq__0__iff) ).
thf(1065,plain,
! [TA: $tType] :
( ( unique788075200shifts @ TA )
=> ! [A: nat,B: TA] :
( ( ( semiri1924326578sh_bit @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_inj__on__inverseI) ).
thf(358,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(170,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Set_Oset__insert) ).
thf(807,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(193,axiom,
! [TA: $tType] :
( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ? [B: set @ TA,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
& ( finite_finite2 @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_finite_Osimps) ).
thf(897,plain,
! [TA: $tType] :
( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ? [B: set @ TA,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
& ( finite_finite2 @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(161,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_card__mono) ).
thf(767,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(245,axiom,
! [A: set @ hF_Mirabelle_hf] :
( ( finite_finite2 @ hF_Mirabelle_hf @ A )
=> ( ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_hfset__HF) ).
thf(1093,plain,
! [A: set @ hF_Mirabelle_hf] :
( ( finite_finite2 @ hF_Mirabelle_hf @ A )
=> ( ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(64,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(464,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(51,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_insert__ident) ).
thf(427,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(197,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_DiffI) ).
thf(908,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(175,axiom,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_HF__hfset) ).
thf(822,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TB > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [D: TB] :
( ( member @ TB @ D @ B )
=> ? [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: TB,E: TB,F: TA] :
( ( member @ TB @ D @ B )
=> ( ( member @ TB @ E @ B )
=> ( ( member @ TA @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq @ nat @ ( finite_card @ TB @ B ) @ ( finite_card @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_card__le__if__inj__on__rel) ).
thf(1004,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TB > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [D: TB] :
( ( member @ TB @ D @ B )
=> ? [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: TB,E: TB,F: TA] :
( ( member @ TB @ D @ B )
=> ( ( member @ TB @ E @ B )
=> ( ( member @ TA @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq @ nat @ ( finite_card @ TB @ B ) @ ( finite_card @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(42,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Set_Ois__empty__def) ).
thf(369,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(109,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_diff__mono) ).
thf(607,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(36,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_is__singletonI) ).
thf(354,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(205,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_insert__eq__iff) ).
thf(935,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_equals0I) ).
thf(923,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(131,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_is__singleton__def) ).
thf(676,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(243,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_zero__le) ).
thf(1088,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(220,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_empty__iff) ).
thf(1014,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(21,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_dual__order_Otrans) ).
thf(309,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(128,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_is__singletonE) ).
thf(659,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1149,plain,
$false,
inference(e,[status(thm)],[645,629,365,1105,347,333,1083,941,481,582,1068,1073,511,597,861,533,797,472,814,698,747,945,829,1001,1127,709,288,301,565,436,651,719,372,1059,542,1055,724,559,1147,284,1115,316,475,492,756,1040,574,905,1136,834,981,634,866,265,527,452,920,512,270,761,381,714,910,825,349,693,957,894,484,852,522,461,1079,682,285,551,1128,742,948,615,1121,1064,1111,1096,356,593,869,499,857,420,1118,637,679,547,706,554,753,1016,590,622,1099,701,515,1050,984,721,779,503,1131,654,343,792,633,311,530,662,926,1086,938,750,618,430,296,444,375,819,562,843,772,577,291,545,1124,281,313,1058,1090,804,900,274,1144,318,616,764,979,604,1048,736,362,567,509,1043,811,494,631,367,816,609,915,769,1061,848,520,685,695,278,455,306,1113,299,267,1102,1076,426,944,795,1081,458,836,648,487,776,712,855,690,640,1070,414,954,739,1053,673,441,585,338,470,643,744,703,1141,1023,727,978,314,446,612,497,859,845,465,450,1108,931,539,688,903,588,517,319,304,351,378,433,929,478,272,832,346,536,1045,716,287,1133,300,620,447,950,422,294,341,506,828,1065,358,807,897,767,1093,464,427,908,822,1004,369,607,354,935,923,676,1088,1014,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP072^2 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n020.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 6 14:40:09 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.57/1.14 % [INFO] Parsing done (257ms).
% 1.57/1.15 % [INFO] Running in sequential loop mode.
% 2.63/1.38 % [INFO] eprover registered as external prover.
% 2.63/1.38 % [INFO] cvc4 registered as external prover.
% 2.63/1.39 % [INFO] Scanning for conjecture ...
% 2.93/1.48 % [INFO] Found a conjecture and 289 axioms. Running axiom selection ...
% 3.12/1.59 % [INFO] Axiom selection finished. Selected 262 axioms (removed 27 axioms).
% 4.03/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 4.11/1.81 % [INFO] Type checking passed.
% 4.19/1.82 % [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 ...
% 74.10/53.93 % External prover 'e' found a proof!
% 74.28/53.93 % [INFO] Killing All external provers ...
% 74.28/53.93 % Time passed: 53392ms (effective reasoning time: 52771ms)
% 74.28/53.93 % 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)>
% 74.28/53.93 % Axioms used in derivation (262): fact_128_equalityE, fact_136_bot_Oextremum__unique, fact_9_Zero__hf__def, fact_219_inj__on__image__set__diff, fact_220_diff__mono, fact_132_infinite__arbitrarily__large, fact_147_finite__has__minimal, fact_32_insert__absorb, fact_193_Diff__iff, fact_247_Diff__insert, fact_91_card_Oempty, tcon_HOL_Obool___Orderings_Olinorder_14, fact_41_insert__not__empty, fact_164_finite__if__finite__subsets__card__bdd, fact_90_singleton__insert__inj__eq, tcon_Nat_Onat___Rings_Osemiring__1, fact_78_finite__subset__induct_H, tcon_fun___Finite__Set_Ofinite, fact_110_eq__iff, fact_14_HF__hfset, fact_96_linorder__wlog, fact_75_is__singletonI_H, fact_31_insert__eq__iff, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_174_inj__onD, tcon_Nat_Onat___Orderings_Olinorder, fact_20_hinsert__def, fact_29_mk__disjoint__insert, fact_33_insert__ident, fact_87_empty__subsetI, fact_155_subset__inj__on, fact_44_Collect__mem__eq, fact_54_finite__insert, fact_192_DiffI, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_242_inj__img__insertE, fact_239_finite__image__iff, fact_64_finite, fact_183_eq__imp__le, fact_34_Set_Oset__insert, fact_175_obtain__subset__with__card__n, fact_127_subset__eq, fact_2_hmem__hempty, fact_113_order__subst2, fact_168_inj__on__inverseI, fact_176_card__le__if__inj__on__rel, fact_25_insert__absorb2, fact_94_dual__order_Oeq__iff, fact_28_singletonI, fact_124_subset__iff, tcon_Set_Oset___Finite__Set_Ofinite_8, fact_215_insert__Diff__single, fact_228_image__subset__iff, fact_224_all__subset__image, fact_201_empty__is__image, fact_238_finite__imageD, fact_40_singleton__inject, fact_152_inj__on__empty, fact_73_is__singleton__def, fact_67_finite_OinsertI, fact_37_insertE, fact_172_inj__on__def, fact_210_finite__Diff2, fact_69_Collect__empty__eq__bot, fact_221_diff__left__mono, fact_250_diff__eq__diff__eq, fact_18_empty__Collect__eq, fact_151_card__eq__0__iff, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_223_diff__eq__diff__less__eq, fact_245_Diff__insert2, tcon_HOL_Obool___Finite__Set_Ofinite_15, fact_233_le__iff__diff__le__0, fact_161_bot__nat__0_Oextremum__unique, fact_7_Abs__hf__0, fact_109_antisym, fact_218_image__diff__subset, fact_234_finite__surj, fact_195_cancel__comm__monoid__add__class_Odiff__cancel, fact_181_nat__le__linear, fact_200_image__empty, fact_15_empty__iff, fact_156_insert__subsetI, fact_135_bot_Oextremum, fact_43_mem__Collect__eq, fact_3_hf__cases, fact_57_finite__induct, fact_50_finite__hfset, fact_170_inj__on__eq__iff, fact_194_Diff__idemp, fact_125_equalityD2, fact_49_bot__nat__def, fact_240_inj__on__image__eq__iff, fact_121_subset__trans, fact_99_order__class_Oorder_Oantisym, fact_52_ex__in__conv, fact_53_equals0I, fact_149_subset__singleton__iff, fact_0_hf__ext, fact_196_diff__zero, fact_55_finite_Ocases, fact_211_Diff__insert0, fact_216_finite__Diff__insert, fact_226_image__subsetI, fact_70_is__singleton__the__elem, fact_77_finite__subset__induct, fact_146_subset__insertI2, fact_60_infinite__finite__induct, fact_16_all__not__in__conv, fact_61_the__elem__eq, fact_83_subset__antisym, fact_13_Nats__0, fact_179_ex__has__least__nat, fact_186_finite__nat__set__iff__bounded__le, fact_177_arg__min__least, fact_180_Nat_Oex__has__greatest__nat, fact_93_dual__order_Oantisym, fact_129_subsetD, fact_5_hmem__def, fact_30_insert__commute, fact_225_image__mono, tcon_HF__Mirabelle__fsbjehakzm_Ohf___Groups_Ozero_19, fact_241_inj__on__image__mem__iff, fact_249_in__image__insert__iff, fact_202_image__is__empty, fact_138_finite__has__maximal2, fact_21_hfset__HF, fact_102_order__class_Oorder_Oeq__iff, fact_191_image__eqI, fact_154_inj__on__subset, tcon_Nat_Onat___Groups_Ozero, fact_162_le__0__eq, fact_204_image__insert, fact_68_bot__empty__eq, fact_167_card__insert__le, fact_222_diff__right__mono, tcon_HOL_Obool___Orderings_Oorder_16, fact_81_of__nat__aux_Osimps_I1_J, fact_115_Collect__mono__iff, fact_207_empty__Diff, fact_144_subset__insert, fact_190_card__inj__on__le, fact_157_subset__emptyI, fact_209_finite__Diff, fact_230_Diff__mono, fact_88_insert__subset, fact_66_infinite__imp__nonempty, fact_134_le__numeral__extra_I3_J, fact_65_finite_OemptyI, fact_42_doubleton__eq__iff, fact_4_hmem__hinsert, fact_246_insert__Diff, fact_203_finite__imageI, fact_141_infinite__super, fact_117_set__eq__subset, tcon_Nat_Onat___Parity_Osemiring__bit__shifts, fact_39_bot__set__def, fact_103_antisym__conv, fact_173_inj__onI, fact_114_order__subst1, fact_160_bot__nat__0_Oextremum__uniqueI, fact_244_Diff__insert__absorb, tcon_Nat_Onat___Orderings_Oorder__bot_1, fact_232_double__diff, fact_95_dual__order_Otrans, fact_62_finite__code, fact_171_inj__on__cong, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_178_bounded__Max__nat, fact_248_subset__Diff__insert, fact_227_subset__imageE, fact_17_Collect__empty__eq, tcon_fun___Orderings_Oorder__bot, fact_251_diff__right__commute, fact_137_bot_Oextremum__uniqueI, fact_143_insert__mono, fact_185_le__refl, fact_97_dual__order_Orefl, fact_27_insertCI, fact_213_diff__ge__0__iff__ge, tcon_Set_Oset___Orderings_Oorder_9, fact_253_DiffD1, fact_126_equalityD1, fact_85_le__zero__eq, tcon_Nat_Onat___Orderings_Oorder_3, fact_74_is__singletonE, fact_38_finite__cases, fact_22_zero__natural_Orsp, fact_189_card__le__inj, fact_26_insert__iff, fact_80_inj__on__HF, fact_197_zero__diff, fact_165_card__seteq, fact_188_card__Diff1__le, fact_11_push__bit__eq__0__iff, fact_235_finite__subset__image, fact_122_Collect__mono, fact_24_equals0D, fact_23_emptyE, fact_231_Diff__subset, fact_208_Diff__cancel, fact_108_linear, fact_205_insert__image, fact_217_inj__on__insert, fact_139_finite__has__minimal2, fact_45_Collect__cong, fact_63_finite__set__choice, fact_106_le__cases, fact_89_singleton__insert__inj__eq_H, fact_59_finite__ne__induct, fact_105_order_Otrans, fact_159_le0, fact_35_insertI2, fact_84_subsetI, fact_182_le__antisym, tcon_fun___Orderings_Oorder, fact_163_less__eq__nat_Osimps_I1_J, fact_47_singleton__iff, fact_1_hemptyE, fact_104_le__cases3, fact_130_in__mono, fact_206_Diff__empty, fact_123_subset__refl, fact_198_diff__0__right, fact_199_diff__self, fact_140_finite__subset, fact_236_ex__finite__subset__image, fact_252_DiffE, fact_58_finite_Oinducts, fact_237_all__finite__subset__image, fact_72_Set_Ois__empty__def, fact_145_subset__insertI, fact_153_finite__ranking__induct, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_142_rev__finite__subset, fact_212_insert__Diff1, tcon_Set_Oset___Orderings_Oorder__bot_6, fact_6_zero__reorient, fact_36_insertI1, fact_243_card__image, fact_92_card_Oinfinite, fact_86_subset__empty, fact_56_finite_Osimps, fact_10_push__bit__of__0, fact_8_dbl__simps_I2_J, tcon_Nat_Onat___Parity_Ounique__euclidean__semiring__with__bit__shifts, fact_148_finite__has__maximal, fact_131_card__subset__eq, fact_184_le__trans, fact_187_arg__min__if__finite_I1_J, fact_229_subset__image__iff, fact_76_card__0__eq, fact_150_subset__singletonD, fact_12_drop__bit__of__0, fact_133_zero__le, fact_214_Diff__eq__empty__iff, tcon_HOL_Obool___Orderings_Oorder__bot_12, fact_71_is__singletonI, fact_158_bot__nat__0_Oextremum, fact_169_inj__on__contraD, fact_166_card__mono, fact_48_singletonD
% 74.28/53.93 % No. of inferences in proof: 528
% 74.28/53.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 53392 ms resp. 52771 ms w/o parsing
% 74.72/54.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 74.72/54.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------