TSTP Solution File: DAT133^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : DAT133^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 19:48:05 EDT 2024
% Result : Theorem 23.88s 13.30s
% Output : Refutation 24.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 330
% Syntax : Number of formulae : 612 ( 217 unt; 50 typ; 0 def)
% Number of atoms : 1481 ( 424 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 7052 ( 184 ~; 22 |; 108 &;6144 @)
% ( 0 <=>; 594 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 349 ( 349 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 8 con; 0-4 aty)
% Number of variables : 1924 ( 164 ^1646 !; 72 ?;1924 :)
% ( 42 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_add_type,type,
semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semilattice_inf_type,type,
semilattice_inf:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(strict2144017051up_add_type,type,
strict2144017051up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu493225792length_type,type,
coindu493225792length:
!>[TA: $tType] : ( nat > ( coindu1593790203_llist @ TA ) > extended_enat ) ).
thf(coindu191418589_ldrop_type,type,
coindu191418589_ldrop:
!>[TA: $tType] : ( extended_enat > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu438612276pWhile_type,type,
coindu438612276pWhile:
!>[TA: $tType] : ( ( TA > $o ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu531130065ldropn_type,type,
coindu531130065ldropn:
!>[TA: $tType] : ( nat > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1889960678filter_type,type,
coindu1889960678filter:
!>[TA: $tType] : ( ( TA > $o ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1213758845finite_type,type,
coindu1213758845finite:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu2000965700_llast_type,type,
coindu2000965700_llast:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > TA ) ).
thf(coindu1018505716length_type,type,
coindu1018505716length:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > extended_enat ) ).
thf(coindu1046438764le_lhd_type,type,
coindu1046438764le_lhd:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > TA ) ).
thf(coindu335574135_lnull_type,type,
coindu335574135_lnull:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1112613586e_lset_type,type,
coindu1112613586e_lset:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( set @ TA ) ) ).
thf(coindu1047225960le_ltl_type,type,
coindu1047225960le_ltl:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu749330388e_lnth_type,type,
coindu749330388e_lnth:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > nat > TA ) ).
thf(coindu721411036eWhile_type,type,
coindu721411036eWhile:
!>[TA: $tType] : ( ( TA > $o ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1491768222unfold_type,type,
coindu1491768222unfold:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > TA ) > TA > extended_enat ) ).
thf(extended_enat2_type,type,
extended_enat2: nat > extended_enat ).
thf(extended_rec_enat_type,type,
extended_rec_enat:
!>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).
thf(extended_the_enat_type,type,
extended_the_enat: extended_enat > nat ).
thf(finite_finite2_type,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ 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(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: a > $o ).
thf(n_type,type,
n: nat ).
thf(xs_type,type,
xs: coindu1593790203_llist @ a ).
thf(xsa_type,type,
xsa: coindu1593790203_llist @ a ).
thf(214,axiom,
! [TA: $tType] :
( ( coindu493225792length @ TA )
= ( ^ [A: nat,B: coindu1593790203_llist @ TA] : ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_gen__llength__def) ).
thf(893,plain,
! [TA: $tType] :
( ( coindu493225792length @ TA )
= ( ^ [A: nat,B: coindu1593790203_llist @ TA] : ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(82,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_is__num__normalize_I1_J) ).
thf(518,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_nat__neq__iff) ).
thf(555,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(219,axiom,
lattice @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_2) ).
thf(909,plain,
lattice @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(260,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( coindu1018505716length @ TA @ B ) )
= ( ( coindu721411036eWhile @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_llength__ltakeWhile__all) ).
thf(1031,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( coindu1018505716length @ TA @ B ) )
= ( ( coindu721411036eWhile @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(20,axiom,
semilattice_inf @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_6) ).
thf(333,plain,
semilattice_inf @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(125,axiom,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( ord_less @ extended_enat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_enat__add__mono) ).
thf(628,plain,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( ord_less @ extended_enat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(281,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_3) ).
thf(1083,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(238,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) )
=> ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_llist_Oset__sel_I2_J) ).
thf(962,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) )
=> ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(170,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_inf_OorderI) ).
thf(762,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(251,axiom,
coindu1213758845finite @ a @ ( coindu1889960678filter @ a @ p @ xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__092_060open_062lfinite_A_Ilfilter_AP_Axs_J_092_060close_062) ).
thf(1005,plain,
coindu1213758845finite @ a @ ( coindu1889960678filter @ a @ p @ xs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(275,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] : ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ ( coindu1018505716length @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_llength__ltakeWhile__le) ).
thf(1068,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] : ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ ( coindu1018505716length @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(11,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_lnull__imp__lfinite) ).
thf(308,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(277,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_IntE) ).
thf(1073,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(264,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
=> ( ! [D: set @ TA] :
( ( ord_less @ ( set @ TA ) @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite__psubset__induct) ).
thf(1041,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
=> ( ! [D: set @ TA] :
( ( ord_less @ ( set @ TA ) @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(208,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_5) ).
thf(878,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_less__not__refl3) ).
thf(440,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(279,axiom,
! [A: nat] :
( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__Collect__less__nat) ).
thf(1078,plain,
! [A: nat] :
( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(37,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ( B @ ( coindu1047225960le_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_lfinite__induct) ).
thf(385,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ( B @ ( coindu1047225960le_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(89,axiom,
! [A: nat,B: set @ nat] :
( ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ C @ D )
& ( member @ nat @ D @ B ) ) )
=> ~ ( finite_finite2 @ nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_unbounded__k__infinite) ).
thf(533,plain,
! [A: nat,B: set @ nat] :
( ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ C @ D )
& ( member @ nat @ D @ B ) ) )
=> ~ ( finite_finite2 @ nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(95,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_inf__sup__aci_I3_J) ).
thf(550,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(179,axiom,
! [TA: $tType,A: extended_enat,B: nat,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ A @ ( extended_enat2 @ B ) ) @ ( coindu1018505716length @ TA @ C ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu191418589_ldrop @ TA @ A @ C ) @ B )
= ( coindu749330388e_lnth @ TA @ C @ ( plus_plus @ nat @ B @ ( extended_the_enat @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_lnth__ldrop) ).
thf(797,plain,
! [TA: $tType,A: extended_enat,B: nat,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ A @ ( extended_enat2 @ B ) ) @ ( coindu1018505716length @ TA @ C ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu191418589_ldrop @ TA @ A @ C ) @ B )
= ( coindu749330388e_lnth @ TA @ C @ ( plus_plus @ nat @ B @ ( extended_the_enat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(185,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ TA @ B ) @ ( extended_enat2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_lnull__ldropn) ).
thf(814,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ TA @ B ) @ ( extended_enat2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(148,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ 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 @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_inf__mono) ).
thf(698,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ 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 @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(23,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1889960678filter @ TA
@ ^ [B: TA] : $true
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_lfilter__K__True) ).
thf(340,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1889960678filter @ TA
@ ^ [B: TA] : $true
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(191,axiom,
ordere223160158up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(829,plain,
ordere223160158up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(153,axiom,
~ ! [A: nat] :
( ( coindu1018505716length @ a
@ ( coindu721411036eWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) )
!= ( extended_enat2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_A_IltakeWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(709,plain,
~ ! [A: nat] :
( ( coindu1018505716length @ a
@ ( coindu721411036eWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) )
!= ( extended_enat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(10,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu721411036eWhile @ TA @ C @ A )
= ( coindu721411036eWhile @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_ltakeWhile__cong) ).
thf(301,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu721411036eWhile @ TA @ C @ A )
= ( coindu721411036eWhile @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1889960678filter @ TA @ A @ ( coindu1889960678filter @ TA @ A @ B ) )
= ( coindu1889960678filter @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_lfilter__idem) ).
thf(320,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1889960678filter @ TA @ A @ ( coindu1889960678filter @ TA @ A @ B ) )
= ( coindu1889960678filter @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(211,axiom,
! [A: extended_enat,B: extended_enat] :
( ! [C: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ C ) )
=> ( ord_less @ extended_enat @ B @ ( extended_enat2 @ C ) ) )
=> ( ord_less_eq @ extended_enat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_enat__less__imp__le) ).
thf(885,plain,
! [A: extended_enat,B: extended_enat] :
( ! [C: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ C ) )
=> ( ord_less @ extended_enat @ B @ ( extended_enat2 @ C ) ) )
=> ( ord_less_eq @ extended_enat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(266,axiom,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lfinite__conv__llength__enat) ).
thf(1046,plain,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(158,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu438612276pWhile @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_in__lset__ldropWhileD) ).
thf(724,plain,
! [TA: $tType,A: TA,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu438612276pWhile @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(156,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_inf1D1) ).
thf(719,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(150,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_inf__le1) ).
thf(702,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(227,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Collect__conj__eq) ).
thf(934,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(233,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_inf_Obounded__iff) ).
thf(949,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(92,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_inf_Ocommute) ).
thf(542,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_plus__enat__simps_I1_J) ).
thf(817,plain,
! [A: nat,B: nat] :
( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(128,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
= ( ? [C: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ C ) @ ( coindu1018505716length @ TA @ B ) )
& ( ( coindu749330388e_lnth @ TA @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_in__lset__conv__lnth) ).
thf(638,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
= ( ? [C: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ C ) @ ( coindu1018505716length @ TA @ B ) )
& ( ( coindu749330388e_lnth @ TA @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(255,axiom,
! [TA: $tType] :
( ( coindu1112613586e_lset @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( collect @ TA
@ ^ [B: TA] :
? [C: nat] :
( ( B
= ( coindu749330388e_lnth @ TA @ A @ C ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ C ) @ ( coindu1018505716length @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_lset__conv__lnth) ).
thf(1013,plain,
! [TA: $tType] :
( ( coindu1112613586e_lset @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( collect @ TA
@ ^ [B: TA] :
? [C: nat] :
( ( B
= ( coindu749330388e_lnth @ TA @ A @ C ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ C ) @ ( coindu1018505716length @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(47,axiom,
! [TA: $tType,A: ( nat > TA > TA ) > nat > nat > TA > $o,B: nat > TA > TA,C: nat,D: nat,E: TA] :
( ! [F: nat > TA > TA,G: nat,H: nat,I: TA] :
( ( ~ ( ord_less @ nat @ H @ G )
=> ( A @ F @ ( plus_plus @ nat @ G @ ( one_one @ nat ) ) @ H @ ( F @ G @ I ) ) )
=> ( A @ F @ G @ H @ I ) )
=> ( A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_fold__atLeastAtMost__nat_Oinduct) ).
thf(416,plain,
! [TA: $tType,A: ( nat > TA > TA ) > nat > nat > TA > $o,B: nat > TA > TA,C: nat,D: nat,E: TA] :
( ! [F: nat > TA > TA,G: nat,H: nat,I: TA] :
( ( ~ ( ord_less @ nat @ H @ G )
=> ( A @ F @ ( plus_plus @ nat @ G @ ( one_one @ nat ) ) @ H @ ( F @ G @ I ) ) )
=> ( A @ F @ G @ H @ I ) )
=> ( A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_ltakeWhile_Odisc__iff_I1_J) ).
thf(289,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(168,axiom,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_enat_Osimps_I6_J) ).
thf(756,plain,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_image__image) ).
thf(789,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(228,axiom,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(937,plain,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(26,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_ltakeWhile_Odisc_I2_J) ).
thf(348,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_nat__add__left__cancel) ).
thf(480,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(115,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_le__infI1) ).
thf(602,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(146,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_inf__sup__aci_I4_J) ).
thf(692,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(161,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_inf_Oabsorb2) ).
thf(734,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(204,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Int__Collect) ).
thf(866,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(58,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( finite_finite2 @ TA @ A )
| ( finite_finite2 @ TA @ B ) )
=> ( finite_finite2 @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_finite__Int) ).
thf(453,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( finite_finite2 @ TA @ A )
| ( finite_finite2 @ TA @ B ) )
=> ( finite_finite2 @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(39,axiom,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_less__set__def) ).
thf(396,plain,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(45,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ A @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu2000965700_llast @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( coindu2000965700_llast @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_llast__ldrop) ).
thf(411,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ A @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu2000965700_llast @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( coindu2000965700_llast @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(13,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu1889960678filter @ TA @ C @ A )
= ( coindu1889960678filter @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_lfilter__cong) ).
thf(312,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu1889960678filter @ TA @ C @ A )
= ( coindu1889960678filter @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ~ ( coindu335574135_lnull @ TA @ B )
=> ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_lnull__ltakeWhile) ).
thf(292,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ~ ( coindu335574135_lnull @ TA @ B )
=> ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(80,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_inf_Oidem) ).
thf(512,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(140,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_inf_Ostrict__coboundedI1) ).
thf(678,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(134,axiom,
! [A: nat] :
( ( extended_the_enat @ ( extended_enat2 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_the__enat_Osimps) ).
thf(661,plain,
! [A: nat] :
( ( extended_the_enat @ ( extended_enat2 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(225,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_inf__unique) ).
thf(925,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(183,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_infinite__descent__measure) ).
thf(810,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(31,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( member @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_llist_Oset__sel_I1_J) ).
thf(366,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( member @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(154,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ ( coindu1018505716length @ TA @ B ) )
=> ~ ( A @ ( coindu749330388e_lnth @ TA @ B @ ( extended_the_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_lnth__llength__ltakeWhile) ).
thf(714,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ ( coindu1018505716length @ TA @ B ) )
=> ~ ( A @ ( coindu749330388e_lnth @ TA @ B @ ( extended_the_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(271,axiom,
! [TA: $tType,A: nat,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ B @ C ) ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu721411036eWhile @ TA @ B @ C ) @ A )
= ( coindu749330388e_lnth @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_ltakeWhile__nth) ).
thf(1057,plain,
! [TA: $tType,A: nat,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ B @ C ) ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu721411036eWhile @ TA @ B @ C ) @ A )
= ( coindu749330388e_lnth @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(21,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_ltakeWhile_Odisc_I1_J) ).
thf(334,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(220,axiom,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_enat__less__induct) ).
thf(910,plain,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(165,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_inf_OorderE) ).
thf(746,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(258,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu438612276pWhile @ TA @ C @ A )
= ( coindu438612276pWhile @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_ldropWhile__cong) ).
thf(1021,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu438612276pWhile @ TA @ C @ A )
= ( coindu438612276pWhile @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA] :
( ( finite_finite2 @ TB @ ( collect @ TB @ A ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
? [D: TB] :
( ( C
= ( B @ D ) )
& ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_finite__image__set) ).
thf(952,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA] :
( ( finite_finite2 @ TB @ ( collect @ TB @ A ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
? [D: TB] :
( ( C
= ( B @ D ) )
& ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(187,axiom,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_one__reorient) ).
thf(820,plain,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(99,axiom,
~ ( coindu335574135_lnull @ a @ ( coindu1889960678filter @ a @ p @ xsa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_LCons_Ohyps_I2_J) ).
thf(561,plain,
~ ( coindu335574135_lnull @ a @ ( coindu1889960678filter @ a @ p @ xsa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(297,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_add__mono__thms__linordered__semiring_I4_J) ).
thf(407,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(101,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_4_finite__imageI) ).
thf(566,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)],[101]) ).
thf(29,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ B )
& ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_ltakeWhile_Odisc__iff_I2_J) ).
thf(361,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ B )
& ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(123,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_inf_Ostrict__coboundedI2) ).
thf(625,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(51,axiom,
( ( one_one @ extended_enat )
= ( extended_enat2 @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_one__enat__def) ).
thf(435,plain,
( ( one_one @ extended_enat )
= ( extended_enat2 @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(17,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ( coindu1213758845finite @ TA @ B )
| ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_lfinite__ltakeWhile) ).
thf(324,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ( coindu1213758845finite @ TA @ B )
| ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(107,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: nat] :
( ( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_llength__eq__enat__lfiniteD) ).
thf(583,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: nat] :
( ( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(84,axiom,
! [A: extended_enat,B: nat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ A @ ( extended_enat2 @ B ) )
= ( plus_plus @ extended_enat @ C @ ( extended_enat2 @ B ) ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_enat__add2__eq) ).
thf(522,plain,
! [A: extended_enat,B: nat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ A @ ( extended_enat2 @ B ) )
= ( plus_plus @ extended_enat @ C @ ( extended_enat2 @ B ) ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_inf__apply) ).
thf(830,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(59,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_inf1D2) ).
thf(456,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(196,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_add__less__mono) ).
thf(842,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(105,axiom,
! [TA: $tType,A: TA > extended_enat,B: nat] :
( ! [C: TA] :
? [D: TA] : ( ord_less @ extended_enat @ ( A @ C ) @ ( A @ D ) )
=> ? [C: TA] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_chain__incr) ).
thf(578,plain,
! [TA: $tType,A: TA > extended_enat,B: nat] :
( ! [C: TA] :
? [D: TA] : ( ord_less @ extended_enat @ ( A @ C ) @ ( A @ D ) )
=> ? [C: TA] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(42,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__Collect__disjI) ).
thf(403,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(252,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(1006,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(28,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
=> ( B @ C ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_ltakeWhile__all) ).
thf(356,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
=> ( B @ C ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(205,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_inf__right__idem) ).
thf(869,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(118,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Int__left__commute) ).
thf(610,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(174,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__iff__inf) ).
thf(783,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ B @ A ) )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( B @ D )
= ( B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_pigeonhole__infinite) ).
thf(857,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ B @ A ) )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( B @ D )
= ( B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(259,axiom,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) @ ( coindu1018505716length @ TA @ C ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu531130065ldropn @ TA @ A @ C ) @ B )
= ( coindu749330388e_lnth @ TA @ C @ ( plus_plus @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_lnth__ldropn) ).
thf(1028,plain,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) @ ( coindu1018505716length @ TA @ C ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu531130065ldropn @ TA @ A @ C ) @ B )
= ( coindu749330388e_lnth @ TA @ C @ ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(71,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu749330388e_lnth @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_lhd__ldropn) ).
thf(488,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu749330388e_lnth @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(167,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_not__add__less1) ).
thf(753,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(137,axiom,
! [A: coindu1593790203_llist @ a] :
( ( ( coindu1047225960le_ltl @ a @ ( coindu1889960678filter @ a @ p @ xsa ) )
= ( coindu1889960678filter @ a @ p @ A ) )
=> ( ~ ( coindu1213758845finite @ a @ A )
=> ( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ a @ A ) )
& ( p @ ( coindu749330388e_lnth @ a @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_LCons_Ohyps_I3_J) ).
thf(669,plain,
! [A: coindu1593790203_llist @ a] :
( ( ( coindu1047225960le_ltl @ a @ ( coindu1889960678filter @ a @ p @ xsa ) )
= ( coindu1889960678filter @ a @ p @ A ) )
=> ( ~ ( coindu1213758845finite @ a @ A )
=> ( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ a @ A ) )
& ( p @ ( coindu749330388e_lnth @ a @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(143,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_inf__sup__ord_I2_J) ).
thf(686,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_IntD1) ).
thf(526,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(256,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_less__infI2) ).
thf(1016,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(241,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ D ) )
=> ( ! [D: coindu1593790203_llist @ TA,E: TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( ( C @ E @ ( coindu1047225960le_ltl @ TA @ D ) )
=> ( C @ E @ D ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_llist__set__induct) ).
thf(970,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ D ) )
=> ( ! [D: coindu1593790203_llist @ TA,E: TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( ( C @ E @ ( coindu1047225960le_ltl @ TA @ D ) )
=> ( C @ E @ D ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(122,axiom,
! [A: nat,B: nat,C: extended_enat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_enat__less__enat__plusI) ).
thf(622,plain,
! [A: nat,B: nat,C: extended_enat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(81,axiom,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( one_one @ extended_enat ) )
= ( A
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_enat__1__iff_I1_J) ).
thf(515,plain,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( one_one @ extended_enat ) )
= ( A
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(131,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_psubset__trans) ).
thf(654,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > TA > $o] :
( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ( ( finite_finite2 @ TB
@ ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( A @ D )
& ( B @ C @ D ) ) ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( finite_finite2 @ TB
@ ( collect @ TB
@ ^ [D: TB] : ( B @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_finite__Collect__bounded__ex) ).
thf(984,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > TA > $o] :
( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ( ( finite_finite2 @ TB
@ ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( A @ D )
& ( B @ C @ D ) ) ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( finite_finite2 @ TB
@ ( collect @ TB
@ ^ [D: TB] : ( B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(157,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1047225960le_ltl @ TA @ A ) )
= ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_lfinite__ltl) ).
thf(721,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1047225960le_ltl @ TA @ A ) )
= ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(250,axiom,
? [A: a] :
( ( member @ a @ A @ ( coindu1112613586e_lset @ a @ xsa ) )
& ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_exP) ).
thf(1002,plain,
? [A: a] :
( ( member @ a @ A @ ( coindu1112613586e_lset @ a @ xsa ) )
& ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(33,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_lfinite__ldropn) ).
thf(371,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(272,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inf__sup__ord_I1_J) ).
thf(1060,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(268,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu191418589_ldrop @ TA @ ( extended_enat2 @ A ) @ B )
= ( coindu531130065ldropn @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_ldrop__enat) ).
thf(1050,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu191418589_ldrop @ TA @ ( extended_enat2 @ A ) @ B )
= ( coindu531130065ldropn @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(24,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_lhd__ltakeWhile) ).
thf(343,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(177,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add__right__cancel) ).
thf(792,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(229,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__numeral__extra_I4_J) ).
thf(938,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(182,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_infinite__descent) ).
thf(805,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(78,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_less__infI1) ).
thf(508,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(223,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_add__lessD1) ).
thf(921,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(171,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_enat__iless) ).
thf(765,plain,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Compr__image__eq) ).
thf(558,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(108,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add__strict__mono) ).
thf(586,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(212,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_add__left__cancel) ).
thf(888,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(218,axiom,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ A @ ( coindu531130065ldropn @ TA @ B @ C ) )
= ( coindu531130065ldropn @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_ldropn__ldropn) ).
thf(906,plain,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ A @ ( coindu531130065ldropn @ TA @ B @ C ) )
= ( coindu531130065ldropn @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(189,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_le__infI) ).
thf(824,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(54,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_inf_Oabsorb1) ).
thf(444,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(41,axiom,
one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(402,plain,
one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( coindu1889960678filter @ TA @ A @ ( coindu1889960678filter @ TA @ B @ C ) )
= ( coindu1889960678filter @ TA
@ ^ [D: TA] :
( ( A @ D )
& ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lfilter__lfilter) ).
thf(286,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( coindu1889960678filter @ TA @ A @ ( coindu1889960678filter @ TA @ B @ C ) )
= ( coindu1889960678filter @ TA
@ ^ [D: TA] :
( ( A @ D )
& ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(164,axiom,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B )
= ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_enat__add1__eq) ).
thf(743,plain,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B )
= ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(236,axiom,
semilattice_inf @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Osemilattice__inf_11) ).
thf(958,plain,
semilattice_inf @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(93,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ TA @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_lnull__ldrop) ).
thf(545,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ TA @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_image__ident) ).
thf(875,plain,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_linorder__neqE__nat) ).
thf(826,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(129,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( ( coindu1047225960le_ltl @ TA @ D )
= ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_llist_Ocoinduct__strong) ).
thf(641,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( ( coindu1047225960le_ltl @ TA @ D )
= ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(36,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_inf__sup__aci_I1_J) ).
thf(382,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(103,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_linorder__neqE__linordered__idom) ).
thf(572,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(75,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_add__mono__thms__linordered__field_I1_J) ).
thf(498,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(63,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__le__cancel__left) ).
thf(466,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(151,axiom,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coindu1593790203_llist @ TA] :
( ( coindu191418589_ldrop @ TA @ A @ ( coindu191418589_ldrop @ TA @ B @ C ) )
= ( coindu191418589_ldrop @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_ldrop__ldrop) ).
thf(704,plain,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coindu1593790203_llist @ TA] :
( ( coindu191418589_ldrop @ TA @ A @ ( coindu191418589_ldrop @ TA @ B @ C ) )
= ( coindu191418589_ldrop @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(27,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ~ ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_ltakeWhile_Oexhaust) ).
thf(350,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ~ ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ball__imageD) ).
thf(672,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(43,axiom,
ordere779506340up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(406,plain,
ordere779506340up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(57,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_add__less__imp__less__right) ).
thf(451,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(162,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_measure__induct__rule) ).
thf(737,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(209,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_inf__le2) ).
thf(880,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(120,axiom,
! [TA: $tType,A: set @ TA,B: nat > TA,C: nat] :
( ( A
= ( image @ nat @ TA @ B
@ ( collect @ nat
@ ^ [D: nat] : ( ord_less @ nat @ D @ C ) ) ) )
=> ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__seg__image__imp__finite) ).
thf(616,plain,
! [TA: $tType,A: set @ TA,B: nat > TA,C: nat] :
( ( A
= ( image @ nat @ TA @ B
@ ( collect @ nat
@ ^ [D: nat] : ( ord_less @ nat @ D @ C ) ) ) )
=> ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(114,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_inf_Oleft__commute) ).
thf(599,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(203,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add_Oassoc) ).
thf(863,plain,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(242,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_inf__sup__aci_I2_J) ).
thf(979,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(116,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_add_Oright__cancel) ).
thf(604,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(254,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_less__add__one) ).
thf(1011,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(48,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_46_Collect__cong) ).
thf(419,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)],[48]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_pigeonhole__infinite__rel) ).
thf(377,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(246,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_add__right__imp__eq) ).
thf(990,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(248,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inf__set__def) ).
thf(996,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__less__cancel__left) ).
thf(477,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_imageE) ).
thf(631,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(16,axiom,
lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_8) ).
thf(323,plain,
lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(112,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_lfinite__finite__index) ).
thf(594,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(159,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_nat__less__induct) ).
thf(726,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(69,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
& ~ ( B @ C ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu438612276pWhile @ TA @ B @ A ) )
= ( coindu749330388e_lnth @ TA @ A @ ( extended_the_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_lhd__ldropWhile__conv__lnth) ).
thf(483,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
& ~ ( B @ C ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu438612276pWhile @ TA @ B @ A ) )
= ( coindu749330388e_lnth @ TA @ A @ ( extended_the_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(239,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Int__absorb) ).
thf(964,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(221,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_add__le__cancel__right) ).
thf(915,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(172,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
= ( coindu335574135_lnull @ TA @ B ) )
=> ( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( ( coindu1047225960le_ltl @ TA @ A )
= ( coindu1047225960le_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_llist_Oexpand) ).
thf(769,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
= ( coindu335574135_lnull @ TA @ B ) )
=> ( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( ( coindu1047225960le_ltl @ TA @ A )
= ( coindu1047225960le_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(231,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ A @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( coindu749330388e_lnth @ TA @ B @ ( extended_the_enat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_lhd__ldrop) ).
thf(943,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ A @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( coindu749330388e_lnth @ TA @ B @ ( extended_the_enat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(19,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu721411036eWhile @ TA
@ ^ [B: TA] : $true
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_ltakeWhile__K__True) ).
thf(330,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu721411036eWhile @ TA
@ ^ [B: TA] : $true
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(73,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_inf__Int__eq) ).
thf(494,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(280,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( member @ TA @ D @ B ) ) )
= ( image @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Setcompr__eq__image) ).
thf(1080,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( member @ TA @ D @ B ) ) )
= ( image @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(198,axiom,
! [TA: $tType] :
( ( coindu1018505716length @ TA )
= ( coindu1491768222unfold @ ( coindu1593790203_llist @ TA ) @ ( coindu335574135_lnull @ TA ) @ ( coindu1047225960le_ltl @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_llength__def) ).
thf(848,plain,
! [TA: $tType] :
( ( coindu1018505716length @ TA )
= ( coindu1491768222unfold @ ( coindu1593790203_llist @ TA ) @ ( coindu335574135_lnull @ TA ) @ ( coindu1047225960le_ltl @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(149,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_in__lset__ltlD) ).
thf(700,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(61,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
& ~ ( B @ C ) )
=> ( member @ TA @ ( coindu1046438764le_lhd @ TA @ ( coindu438612276pWhile @ TA @ B @ A ) ) @ ( coindu1112613586e_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_lhd__ldropWhile__in__lset) ).
thf(462,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
& ~ ( B @ C ) )
=> ( member @ TA @ ( coindu1046438764le_lhd @ TA @ ( coindu438612276pWhile @ TA @ B @ A ) ) @ ( coindu1112613586e_lset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(226,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IntI) ).
thf(932,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(83,axiom,
semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_13) ).
thf(521,plain,
semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(40,axiom,
! [A: nat,B: extended_enat,C: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ C @ A ) ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_enat__less__enat__plusI2) ).
thf(399,plain,
! [A: nat,B: extended_enat,C: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ C @ A ) ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(237,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_le__infE) ).
thf(959,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(147,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_less__irrefl__nat) ).
thf(695,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_IntD2) ).
thf(394,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(100,axiom,
! [TA: $tType] :
( ( coindu438612276pWhile @ TA )
= ( ^ [A: TA > $o,B: coindu1593790203_llist @ TA] : ( coindu191418589_ldrop @ TA @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_ldropWhile__eq__ldrop) ).
thf(563,plain,
! [TA: $tType] :
( ( coindu438612276pWhile @ TA )
= ( ^ [A: TA > $o,B: coindu1593790203_llist @ TA] : ( coindu191418589_ldrop @ TA @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(9,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1889960678filter @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_lfinite__lfilterI) ).
thf(299,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1889960678filter @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(199,axiom,
! [TA: $tType] :
( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] :
? [B: nat,C: nat > TA] :
( A
= ( image @ nat @ TA @ C
@ ( collect @ nat
@ ^ [D: nat] : ( ord_less @ nat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_finite__conv__nat__seg__image) ).
thf(851,plain,
! [TA: $tType] :
( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] :
? [B: nat,C: nat > TA] :
( A
= ( image @ nat @ TA @ C
@ ( collect @ nat
@ ^ [D: nat] : ( ord_less @ nat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(77,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__conjI) ).
thf(505,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(133,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_ltakeWhile_Osimps_I4_J) ).
thf(658,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(278,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_add__strict__right__mono) ).
thf(1076,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(261,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu438612276pWhile @ TA @ A @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ~ ( A @ C ) )
=> ( coindu1213758845finite @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_lfinite__ldropWhile) ).
thf(1034,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu438612276pWhile @ TA @ A @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ~ ( A @ C ) )
=> ( coindu1213758845finite @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(139,axiom,
! [A: set @ nat] :
( ( ~ ( finite_finite2 @ nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less @ nat @ B @ C )
& ( member @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_infinite__nat__iff__unbounded) ).
thf(675,plain,
! [A: set @ nat] :
( ( ~ ( finite_finite2 @ nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less @ nat @ B @ C )
& ( member @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(50,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_llist_Ocoinduct) ).
thf(426,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(110,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_le__inf__iff) ).
thf(589,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(88,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add__mono__thms__linordered__field_I5_J) ).
thf(531,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(94,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_psubsetD) ).
thf(548,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_inf__left__idem) ).
thf(374,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(166,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ~ ! [C: nat] :
( ( A
= ( extended_enat2 @ C ) )
=> ~ ( ord_less @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__enatE) ).
thf(749,plain,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ~ ! [C: nat] :
( ( A
= ( extended_enat2 @ C ) )
=> ~ ( ord_less @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(257,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_inf__left__commute) ).
thf(1018,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(96,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__less__imp__less__left) ).
thf(553,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(194,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_add__left__imp__eq) ).
thf(836,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(267,axiom,
linordered_semidom @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom) ).
thf(1049,plain,
linordered_semidom @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(178,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( finite_finite2 @ TA @ ( coindu1112613586e_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_lfinite__imp__finite__lset) ).
thf(795,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( finite_finite2 @ TA @ ( coindu1112613586e_lset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(141,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_less__add__eq__less) ).
thf(680,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rev__image__eqI) ).
thf(458,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(188,axiom,
coindu1213758845finite @ a @ ( coindu1889960678filter @ a @ p @ xsa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_LCons_Ohyps_I1_J) ).
thf(823,plain,
coindu1213758845finite @ a @ ( coindu1889960678filter @ a @ p @ xsa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(173,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_image__cong) ).
thf(776,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(85,axiom,
lattice @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Olattice_14) ).
thf(525,plain,
lattice @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(106,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu438612276pWhile @ TA @ A @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_lnull__ldropWhile) ).
thf(580,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu438612276pWhile @ TA @ A @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: extended_enat,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu191418589_ldrop @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_in__lset__ldropD) ).
thf(295,plain,
! [TA: $tType,A: TA,B: extended_enat,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu191418589_ldrop @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
( finite_finite2 @ nat
@ ( image @ nat @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) )
@ ( inf_inf @ ( set @ nat )
@ ( collect @ nat
@ ^ [A: nat] :
( ord_less @ extended_enat @ ( extended_enat2 @ A )
@ ( coindu1018505716length @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) ) ) ) )
@ ( collect @ nat
@ ^ [A: nat] :
( p
@ ( coindu749330388e_lnth @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) )
@ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite_finite2 @ nat
@ ( image @ nat @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) )
@ ( inf_inf @ ( set @ nat )
@ ( collect @ nat
@ ^ [A: nat] :
( ord_less @ extended_enat @ ( extended_enat2 @ A )
@ ( coindu1018505716length @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) ) ) ) )
@ ( collect @ nat
@ ^ [A: nat] :
( p
@ ( coindu749330388e_lnth @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) )
@ A ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(282,plain,
~ ( finite_finite2 @ nat
@ ( image @ nat @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) )
@ ( inf_inf @ ( set @ nat )
@ ( collect @ nat
@ ^ [A: nat] :
( ord_less @ extended_enat @ ( extended_enat2 @ A )
@ ( coindu1018505716length @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) ) ) ) )
@ ( collect @ nat
@ ^ [A: nat] :
( p
@ ( coindu749330388e_lnth @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) )
@ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(152,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_inf1I) ).
thf(707,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(46,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_le__infI2) ).
thf(414,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(18,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_lappend_Oexhaust) ).
thf(327,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(235,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_add__mono__thms__linordered__field_I2_J) ).
thf(954,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(310,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(247,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_lfinite__llength__enat) ).
thf(993,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_bex__imageD) ).
thf(1070,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(206,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ ( coindu1018505716length @ TA @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_llength__ltakeWhile__lt__iff) ).
thf(872,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( coindu1018505716length @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) @ ( coindu1018505716length @ TA @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(269,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_trans__less__add1) ).
thf(1053,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(263,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_inf__idem) ).
thf(1038,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(76,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_inf__assoc) ).
thf(502,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__not__refl2) ).
thf(470,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(132,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
& ~ ( B @ C ) )
=> ~ ( B @ ( coindu1046438764le_lhd @ TA @ ( coindu438612276pWhile @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_lhd__ldropWhile) ).
thf(656,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
& ~ ( B @ C ) )
=> ~ ( B @ ( coindu1046438764le_lhd @ TA @ ( coindu438612276pWhile @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_inf_Oright__idem) ).
thf(613,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(74,axiom,
( finite_finite2 @ nat
@ ( inf_inf @ ( set @ nat )
@ ( collect @ nat
@ ^ [A: nat] :
( ord_less @ extended_enat @ ( extended_enat2 @ A )
@ ( coindu1018505716length @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) ) ) ) )
@ ( collect @ nat
@ ^ [A: nat] :
( p
@ ( coindu749330388e_lnth @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) )
@ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062finite_A_I_123n_O_Aenat_An_A_060_Allength_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_125_A_092_060inter_062_A_123n_O_AP_A_Ilnth_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_An_J_125_J_092_060close_062) ).
thf(497,plain,
( finite_finite2 @ nat
@ ( inf_inf @ ( set @ nat )
@ ( collect @ nat
@ ^ [A: nat] :
( ord_less @ extended_enat @ ( extended_enat2 @ A )
@ ( coindu1018505716length @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) ) ) ) )
@ ( collect @ nat
@ ^ [A: nat] :
( p
@ ( coindu749330388e_lnth @ a
@ ( coindu1047225960le_ltl @ a
@ ( coindu438612276pWhile @ a
@ ^ [B: a] :
~ ( p @ B )
@ xsa ) )
@ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(197,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_add_Ocommute) ).
thf(845,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(124,axiom,
semilattice_inf @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_1) ).
thf(627,plain,
semilattice_inf @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(56,axiom,
ab_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(450,plain,
ab_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(91,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_trans__less__add2) ).
thf(539,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(759,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(213,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_4) ).
thf(891,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu721411036eWhile @ TA @ B @ C ) ) )
=> ( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) )
& ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_lset__ltakeWhileD) ).
thf(368,plain,
! [TA: $tType,A: TA,B: TA > $o,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu721411036eWhile @ TA @ B @ C ) ) )
=> ( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) )
& ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(144,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu2000965700_llast @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu2000965700_llast @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_llast__ldropn) ).
thf(688,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu2000965700_llast @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu2000965700_llast @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(217,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_add_Oleft__commute) ).
thf(903,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(109,axiom,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(588,plain,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(184,axiom,
semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).
thf(813,plain,
semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(14,axiom,
finite_finite @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_7) ).
thf(319,plain,
finite_finite @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(215,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_inf_Oleft__idem) ).
thf(896,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(273,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_measure__induct) ).
thf(1062,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(232,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_nat__add__left__cancel__less) ).
thf(946,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(130,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add__strict__left__mono) ).
thf(652,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Int__left__absorb) ).
thf(731,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(175,axiom,
! [A: nat] :
( ( ( one_one @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_enat__1__iff_I2_J) ).
thf(786,plain,
! [A: nat] :
( ( ( one_one @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(102,axiom,
! [A: set @ nat,B: nat] :
( ! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less @ nat @ C @ B ) )
=> ( finite_finite2 @ nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_bounded__nat__set__is__finite) ).
thf(568,plain,
! [A: set @ nat,B: nat] :
( ! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less @ nat @ C @ B ) )
=> ( finite_finite2 @ nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(79,axiom,
( ( finite_finite2 @ nat )
= ( ^ [A: set @ nat] :
? [B: nat] :
! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_finite__nat__set__iff__bounded) ).
thf(510,plain,
( ( finite_finite2 @ nat )
= ( ^ [A: set @ nat] :
? [B: nat] :
! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(136,axiom,
( ( coindu1018505716length @ a
@ ( coindu721411036eWhile @ a
@ ^ [A: a] :
~ ( p @ A )
@ xsa ) )
= ( extended_enat2 @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_n) ).
thf(667,plain,
( ( coindu1018505716length @ a
@ ( coindu721411036eWhile @ a
@ ^ [A: a] :
~ ( p @ A )
@ xsa ) )
= ( extended_enat2 @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(216,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_20_image__eqI) ).
thf(899,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)],[216]) ).
thf(142,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_le__numeral__extra_I4_J) ).
thf(684,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: nat,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu531130065ldropn @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_in__lset__ldropnD) ).
thf(346,plain,
! [TA: $tType,A: TA,B: nat,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu531130065ldropn @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_nat__add__right__cancel) ).
thf(536,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(265,axiom,
strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_9) ).
thf(1045,plain,
strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(155,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1112613586e_lset @ TA @ ( coindu1889960678filter @ TA @ A @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_lset__lfilter) ).
thf(716,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu1112613586e_lset @ TA @ ( coindu1889960678filter @ TA @ A @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(180,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(800,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_enat_Oinject) ).
thf(447,plain,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(200,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Int__iff) ).
thf(854,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(49,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_79_finite__set__choice) ).
thf(422,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)],[49]) ).
thf(249,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_inf_Oassoc) ).
thf(999,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(121,axiom,
! [A: nat > $o,B: nat] :
( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [C: nat] :
( ( A @ C )
& ( ord_less @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_finite__M__bounded__by__nat) ).
thf(620,plain,
! [A: nat > $o,B: nat] :
( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [C: nat] :
( ( A @ C )
& ( ord_less @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(193,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu531130065ldropn @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ltl__ldropn) ).
thf(833,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu531130065ldropn @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(240,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_less__not__refl) ).
thf(967,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_inf__fun__def) ).
thf(918,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(52,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_add_Oleft__cancel) ).
thf(437,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_enat__ord__simps_I2_J) ).
thf(474,plain,
! [A: nat,B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(127,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__code) ).
thf(635,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(274,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Int__assoc) ).
thf(1065,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ~ ( coindu335574135_lnull @ TB @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_lzip_Oexhaust) ).
thf(283,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ~ ( coindu335574135_lnull @ TB @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(270,axiom,
ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_12) ).
thf(1056,plain,
ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(135,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_inf_Ostrict__boundedE) ).
thf(664,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(195,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( coindu191418589_ldrop @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ltl__ldrop) ).
thf(839,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu191418589_ldrop @ TA @ A @ B ) )
= ( coindu191418589_ldrop @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(163,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_inf1E) ).
thf(740,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(245,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_inf_Ostrict__order__iff) ).
thf(987,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(62,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_finite) ).
thf(464,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(104,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_not__add__less2) ).
thf(575,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(202,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_image__iff) ).
thf(860,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(113,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Int__def) ).
thf(596,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_add__less__mono1) ).
thf(528,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: TB > $o,C: TC > TB > TA] :
( ( finite_finite2 @ TC @ ( collect @ TC @ A ) )
=> ( ( finite_finite2 @ TB @ ( collect @ TB @ B ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [D: TA] :
? [E: TC,F: TB] :
( ( D
= ( C @ E @ F ) )
& ( A @ E )
& ( B @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_finite__image__set2) ).
thf(982,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: TB > $o,C: TC > TB > TA] :
( ( finite_finite2 @ TC @ ( collect @ TC @ A ) )
=> ( ( finite_finite2 @ TB @ ( collect @ TB @ B ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [D: TA] :
? [E: TC,F: TB] :
( ( D
= ( C @ E @ F ) )
& ( A @ E )
& ( B @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(145,axiom,
strict2144017051up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(691,plain,
strict2144017051up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA > $o] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( B @ D ) ) )
= ( image @ TA @ TB @ A @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_setcompr__eq__image) ).
thf(607,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA > $o] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( B @ D ) ) )
= ( image @ TA @ TB @ A @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(70,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_lnull__ltlI) ).
thf(486,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(181,axiom,
~ ( coindu1213758845finite @ a @ xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__092_060open_062_092_060not_062_Alfinite_Axs_092_060close_062) ).
thf(803,plain,
~ ( coindu1213758845finite @ a @ xs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(22,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu1889960678filter @ TA @ A @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
=> ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_lnull__lfilter) ).
thf(337,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu1889960678filter @ TA @ A @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ B ) )
=> ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(253,axiom,
~ ( coindu1213758845finite @ a @ xsa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_LCons_Oprems) ).
thf(1009,plain,
~ ( coindu1213758845finite @ a @ xsa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_imageI) ).
thf(923,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(262,axiom,
one @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oone_15) ).
thf(1037,plain,
one @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(72,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Int__commute) ).
thf(491,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(111,axiom,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_not__finite__existsD) ).
thf(592,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(364,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(210,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_inf__commute) ).
thf(882,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(64,axiom,
ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_10) ).
thf(469,plain,
ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(230,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__less__cancel__right) ).
thf(940,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1085,plain,
$false,
inference(e,[status(thm)],[893,518,555,909,1031,333,628,1083,962,762,1005,1068,308,1073,1041,878,440,1078,385,533,550,797,814,698,340,829,709,301,320,885,1046,724,719,702,934,949,542,817,638,1013,416,289,756,789,937,348,480,602,692,734,866,453,396,411,312,292,512,678,661,925,810,366,714,1057,334,910,746,1021,952,820,561,297,407,566,361,625,435,324,583,522,830,456,842,578,403,1006,356,869,610,783,857,1028,488,753,669,686,526,1016,970,622,515,654,984,721,1002,371,1060,1050,343,792,938,805,508,921,765,558,586,888,906,824,444,402,286,743,958,545,875,826,641,382,572,498,466,704,350,672,406,451,737,880,616,599,863,979,604,1011,419,377,990,996,477,631,323,594,726,483,964,915,769,943,330,494,1080,848,700,462,932,521,399,959,695,394,563,299,851,505,658,1076,1034,675,426,589,531,548,374,749,1018,553,836,1049,795,680,458,823,776,525,580,295,282,707,414,327,954,310,993,1070,872,1053,1038,502,470,656,613,497,845,627,450,539,759,891,368,688,903,588,813,319,896,1062,946,652,731,786,568,510,667,899,684,346,536,1045,716,800,447,854,422,999,620,833,967,918,437,474,635,1065,283,1056,664,839,740,987,464,575,860,596,528,982,691,607,486,803,337,1009,923,1037,491,592,364,882,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : DAT133^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.10 % Command : run_Leo-III %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun May 19 23:17:39 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.69/0.69 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.92 % [INFO] Parsing done (224ms).
% 1.51/0.93 % [INFO] Running in sequential loop mode.
% 2.07/1.14 % [INFO] eprover registered as external prover.
% 2.07/1.14 % [INFO] cvc4 registered as external prover.
% 2.07/1.15 % [INFO] Scanning for conjecture ...
% 2.39/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 280 axioms. Running axiom selection ...
% 2.73/1.33 % [INFO] Axiom selection finished. Selected 279 axioms (removed 1 axioms).
% 3.27/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 3.27/1.50 % [INFO] Type checking passed.
% 3.27/1.50 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 23.88/13.30 % External prover 'e' found a proof!
% 23.88/13.30 % [INFO] Killing All external provers ...
% 23.88/13.30 % Time passed: 12902ms (effective reasoning time: 12371ms)
% 23.88/13.30 % 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)>
% 23.88/13.30 % Axioms used in derivation (279): fact_74_image__cong, fact_137_measure__induct__rule, fact_199_is__num__normalize_I1_J, fact_139_lappend_Oexhaust, fact_123_lnull__lfilter, fact_58_lfinite__conv__llength__enat, fact_213_lhd__ltakeWhile, fact_98_Int__Collect, fact_83_Int__absorb, fact_66_add_Oright__cancel, fact_6_add__less__cancel__right, fact_104_add__strict__mono, fact_96_not__finite__existsD, fact_151_inf_Oassoc, tcon_fun___Finite__Set_Ofinite, fact_207_llist_Oset__sel_I1_J, tcon_Extended__Nat_Oenat___Lattices_Olattice_14, fact_206_ltakeWhile_Oexhaust, fact_95_pigeonhole__infinite__rel, fact_158_nat__add__right__cancel, fact_82_Int__commute, fact_179_inf1E, fact_164_trans__less__add1, fact_65_add_Ocommute, fact_9_finite__Collect__disjI, fact_232_inf_Obounded__iff, fact_31_lset__lfilter, fact_8_finite__Collect__conjI, fact_48_in__lset__ltlD, fact_84_Int__assoc, fact_15__092_060open_062_092_060not_062_Alfinite_Axs_092_060close_062, fact_1_LCons_Oprems, fact_51_ldropWhile__cong, fact_57_nat__seg__image__imp__finite, fact_105_add__mono__thms__linordered__field_I1_J, fact_241_inf__le2, fact_43_llength__ltakeWhile__lt__iff, fact_106_add__mono__thms__linordered__field_I2_J, fact_138_infinite__descent__measure, fact_182_finite__nat__set__iff__bounded, fact_16_LCons_Ohyps_I1_J, fact_195_ldrop__ldrop, fact_127_less__set__def, fact_109_chain__incr, fact_248_inf_OorderI, fact_175_finite__M__bounded__by__nat, fact_242_le__infE, fact_203_lnull__ltakeWhile, fact_172_inf_Ostrict__coboundedI2, fact_64_add_Oleft__commute, fact_201_lhd__ldropWhile__conv__lnth, fact_34_ltakeWhile__all, fact_55_less__enatE, fact_191_ltl__ldropn, fact_219_lhd__ldropn, tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_10, fact_23_IntI, fact_120_inf__idem, fact_3_finite__Int, fact_236_enat__less__imp__le, fact_71_one__reorient, fact_247_inf_OorderE, fact_21_finite__code, fact_160_add__less__mono, fact_249_inf__unique, fact_5_add__less__cancel__left, tcon_Set_Oset___Lattices_Olattice_5, fact_208_llist_Ocoinduct__strong, fact_140_lzip_Oexhaust, fact_67_add_Oleft__cancel, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_35_ltakeWhile__cong, fact_70_ab__semigroup__add__class_Oadd__ac_I1_J, fact_99_Int__def, fact_41_finite__psubset__induct, fact_153_inf_Ocommute, fact_131_less__not__refl3, fact_12_exP, fact_133_less__irrefl__nat, fact_60_lfinite__llength__enat, fact_230_add__le__cancel__right, fact_200_ldropWhile__eq__ldrop, fact_223_finite__Collect__bounded__ex, fact_87_IntE, fact_85_IntD2, fact_54_enat__1__iff_I2_J, fact_161_not__add__less1, fact_231_add__le__cancel__left, tcon_Nat_Onat___Groups_Oone, fact_38_lfinite__ltakeWhile, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, fact_178_inf1I, tcon_Nat_Onat___Rings_Olinordered__semidom, fact_63_add__left__imp__eq, fact_108_enat__iless, fact_92_Compr__image__eq, fact_165_trans__less__add2, fact_146_inf__sup__aci_I4_J, fact_239_inf__sup__ord_I1_J, fact_121_inf__apply, tcon_HOL_Obool___Lattices_Olattice_8, fact_154_inf__commute, fact_246_le__infI2, fact_183_infinite__nat__iff__unbounded, fact_216_llist__set__induct, fact_185_inf__Int__eq, fact_209_llist_Ocoinduct, fact_107_add__mono__thms__linordered__field_I5_J, fact_93_image__image, fact_214_lhd__ldropWhile__in__lset, fact_244_inf__mono, fact_252_inf_Oabsorb2, fact_30_enat__ord__simps_I2_J, fact_126_nat__neq__iff, fact_237_llength__ltakeWhile__le, fact_170_inf_Ostrict__order__iff, fact_72_rev__image__eqI, fact_215_lhd__ldropWhile, fact_204_ltakeWhile_Odisc__iff_I1_J, fact_234_lnull__ldrop, fact_61_linorder__neqE__linordered__idom, fact_141_lnull__ltlI, fact_226_Setcompr__eq__image, fact_116_inf__right__idem, fact_56_finite__conv__nat__seg__image, fact_243_le__infI, fact_81_Int__left__absorb, tcon_Nat_Onat___Lattices_Osemilattice__inf_1, fact_189_lfinite__ldropn, fact_210_llist_Oexpand, fact_250_le__iff__inf, fact_79_finite__set__choice, fact_19_add__left__cancel, fact_147_inf__sup__aci_I3_J, fact_14_LCons_Ohyps_I3_J, fact_76_image__iff, fact_143_inf__set__def, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_218_llast__ldrop, tcon_fun___Lattices_Osemilattice__inf, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_12, fact_22_Int__iff, tcon_HOL_Obool___Lattices_Osemilattice__inf_6, fact_245_le__infI1, fact_184_bounded__nat__set__is__finite, fact_2_n, fact_186_lnth__llength__ltakeWhile, fact_32_LCons_Ohyps_I2_J, fact_33_lfilter__cong, fact_59_llength__eq__enat__lfiniteD, tcon_HOL_Obool___Finite__Set_Ofinite_7, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_9, fact_111_enat__add__mono, fact_75_bex__imageD, fact_202_llast__ldropn, tcon_Extended__Nat_Oenat___Groups_Oone_15, fact_29_lfinite__ltl, fact_188_ldropn__ldropn, fact_228_lnull__ldropn, fact_176_gen__llength__def, fact_4_finite__imageI, fact_103_add__strict__left__mono, fact_90_ltakeWhile__nth, fact_135_infinite__descent, fact_117_inf_Oright__idem, fact_94_imageE, fact_114_enat__add1__eq, fact_163_add__less__mono1, fact_136_linorder__neqE__nat, fact_13_enat_Oinject, fact_180_inf1D1, fact_115_nat__add__left__cancel__less, fact_50_in__lset__ldropWhileD, fact_238_inf__sup__ord_I2_J, fact_17__092_060open_062lfinite_A_Ilfilter_AP_Axs_J_092_060close_062, fact_91_lfinite__finite__index, fact_88_enat__less__induct, fact_149_inf__sup__aci_I1_J, fact_205_ltakeWhile_Odisc__iff_I2_J, fact_169_inf_Ostrict__boundedE, fact_42_lfilter__lfilter, fact_37_lset__ltakeWhileD, fact_159_add__lessD1, fact_192_in__lset__ldropnD, fact_77_imageI, fact_101_add__less__imp__less__left, fact_173_enat__less__enat__plusI, fact_220_lhd__ldrop, fact_100_add__less__imp__less__right, fact_89_in__lset__conv__lnth, fact_212_ltakeWhile_Odisc_I1_J, tcon_Extended__Nat_Oenat___Lattices_Osemilattice__inf_11, fact_174_fold__atLeastAtMost__nat_Oinduct, fact_196_in__lset__ldropD, fact_168_less__infI2, fact_28_plus__enat__simps_I1_J, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_45_Collect__mem__eq, fact_112_enat__less__enat__plusI2, fact_0__092_060open_062finite_A_I_123n_O_Aenat_An_A_060_Allength_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_125_A_092_060inter_062_A_123n_O_AP_A_Ilnth_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_An_J_125_J_092_060close_062, fact_152_inf__assoc, tcon_Set_Oset___Lattices_Osemilattice__inf_3, fact_240_inf__le1, tcon_Nat_Onat___Lattices_Olattice_2, fact_181_inf1D2, fact_27_lfilter__K__True, fact_162_not__add__less2, fact_227_setcompr__eq__image, fact_49_llength__ltakeWhile__all, fact_39_lfinite__imp__finite__lset, fact_40_lfinite__ldropWhile, fact_134_nat__less__induct, fact_97_Collect__conj__eq, fact_194_less__numeral__extra_I4_J, fact_26_finite__Collect__less__nat, fact_24_lfilter__idem, fact_198_ldrop__enat, fact_20_image__eqI, fact_251_inf_Oabsorb1, fact_167_less__infI1, fact_102_add__strict__right__mono, fact_148_inf__sup__aci_I2_J, fact_150_inf__fun__def, fact_233_le__inf__iff, fact_171_inf_Ostrict__coboundedI1, fact_110_pigeonhole__infinite, fact_11_less__add__one, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, fact_78_finite, fact_156_inf__left__commute, fact_222_lset__conv__lnth, tcon_Nat_Onat___Groups_Osemigroup__add, fact_129_psubset__trans, fact_113_enat__add2__eq, fact_187_lnth__ldropn, fact_36_lfinite__lfilterI, fact_128_less__not__refl, fact_118_inf__left__idem, fact_119_inf_Oleft__idem, fact_132_measure__induct, fact_177_unbounded__k__infinite, fact_69_add__mono__thms__linordered__semiring_I4_J, fact_62_add__right__imp__eq, fact_124_lnull__ldropWhile, fact_221_enat_Osimps_I6_J, fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_A_IltakeWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_122_inf_Oidem, fact_144_llist_Oset__sel_I2_J, fact_224_finite__image__set, fact_155_inf_Oleft__commute, fact_225_finite__image__set2, fact_125_psubsetD, fact_80_Int__left__commute, fact_68_add_Oassoc, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_229_llength__def, fact_18_add__right__cancel, tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_13, fact_217_ltakeWhile_Osimps_I4_J, fact_86_IntD1, fact_211_ltakeWhile_Odisc_I2_J, fact_25_ltakeWhile__K__True, fact_73_ball__imageD, fact_157_nat__add__left__cancel, fact_142_lnull__imp__lfinite, fact_235_le__numeral__extra_I4_J, fact_52_one__enat__def, fact_190_the__enat_Osimps, fact_46_Collect__cong, fact_10_image__ident, fact_44_mem__Collect__eq, fact_53_enat__1__iff_I1_J, fact_145_lfinite__induct, fact_193_lnth__ldrop, tcon_Set_Oset___Finite__Set_Ofinite_4, fact_130_less__not__refl2, fact_197_ltl__ldrop, tcon_fun___Lattices_Olattice, fact_166_less__add__eq__less
% 23.88/13.30 % No. of inferences in proof: 562
% 23.88/13.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12902 ms resp. 12371 ms w/o parsing
% 24.53/13.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.53/13.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------