TSTP Solution File: DAT130^1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT130^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:33 EDT 2024
% Result : Theorem 28.85s 13.19s
% Output : Refutation 29.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 276
% Syntax : Number of formulae : 517 ( 231 unt; 37 typ; 0 def)
% Number of atoms : 1537 ( 460 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 7151 ( 276 ~; 81 |; 152 &;6040 @)
% ( 0 <=>; 602 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 400 ( 400 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 6 con; 0-7 aty)
% Number of variables : 1719 ( 70 ^1497 !; 116 ?;1719 :)
% ( 36 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(coindu1571841457prefix_type,type,
coindu1571841457prefix:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu526335360e_lSup_type,type,
coindu526335360e_lSup:
!>[TA: $tType] : ( ( set @ ( coindu1593790203_llist @ TA ) ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu268472904append_type,type,
coindu268472904append:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu6345450stinct_type,type,
coindu6345450stinct:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
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(coindu300403952lexord_type,type,
coindu300403952lexord:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1121789889_LCons_type,type,
coindu1121789889_LCons:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1598213697e_LNil_type,type,
coindu1598213697e_LNil:
!>[TA: $tType] : ( coindu1593790203_llist @ TA ) ).
thf(coindu882539134_llist_type,type,
coindu882539134_llist:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coindu1593790203_llist @ TA ) > TB ) > ( coindu1593790203_llist @ TA ) > TB ) ).
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(coindu1696667936prefix_type,type,
coindu1696667936prefix:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu574146665prefix_type,type,
coindu574146665prefix:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu721411036eWhile_type,type,
coindu721411036eWhile:
!>[TA: $tType] : ( ( TA > $o ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu543932918sorted_type,type,
coindu543932918sorted:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1599971794_llist_type,type,
coindu1599971794_llist:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > TB ) > TB > ( coindu1593790203_llist @ TA ) ) ).
thf(comple2143767107ompact_type,type,
comple2143767107ompact:
!>[TA: $tType] : ( ( ( set @ TA ) > TA ) > ( TA > TA > $o ) > TA > $o ) ).
thf(comple1412571634l_cont_type,type,
comple1412571634l_cont:
!>[TA: $tType,TB: $tType] : ( ( ( set @ TB ) > TB ) > ( TB > TB > $o ) > ( ( set @ TA ) > TA ) > ( TA > TA > $o ) > ( TB > TA ) > $o ) ).
thf(comple1986059218ssible_type,type,
comple1986059218ssible:
!>[TA: $tType] : ( ( ( set @ TA ) > TA ) > ( TA > TA > $o ) > ( TA > $o ) > $o ) ).
thf(comple1193779247_chain_type,type,
comple1193779247_chain:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(max_type,type,
max:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > TA ) ).
thf(min_type,type,
min:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(set_atLeast_type,type,
set_atLeast:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_atLeastAtMost_type,type,
set_atLeastAtMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_atMost_type,type,
set_atMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(ya_type,type,
ya: set @ ( coindu1593790203_llist @ a ) ).
thf(less_eq_type,type,
less_eq: a > a > $o ).
thf(xs_type,type,
xs: coindu1593790203_llist @ a ).
thf(120,axiom,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_lfinite__LNil) ).
thf(645,plain,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(231,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_lhd__LCons__ltl) ).
thf(1036,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(168,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( coindu1213758845finite @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( ( finite_finite @ ( coindu1593790203_llist @ TA ) @ A )
& ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1213758845finite @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_lfinite__lSup__chain) ).
thf(809,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( coindu1213758845finite @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( ( finite_finite @ ( coindu1593790203_llist @ TA ) @ A )
& ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1213758845finite @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(227,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_lSup_Odisc__iff_I2_J) ).
thf(1024,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(37,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_not__lfinite__lprefix__conv__eq) ).
thf(347,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__cong) ).
thf(249,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)],[6]) ).
thf(93,axiom,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: coindu1593790203_llist @ TA,C: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
& ( coindu1213758845finite @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_lfinite_Osimps) ).
thf(555,plain,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: coindu1593790203_llist @ TA,C: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
& ( coindu1213758845finite @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_unfold__llist_Odisc__iff_I2_J) ).
thf(666,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(352,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_unfold__llist_Osimps_I4_J) ).
thf(977,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(188,axiom,
less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062) ).
thf(878,plain,
less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ A @ D ) )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_LCons__lprefix__conv) ).
thf(614,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ A @ D ) )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_compact__LCons__iff) ).
thf(741,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(239,axiom,
coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_lsorted__code_I1_J) ).
thf(1073,plain,
coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_214_ltakeWhile__all) ).
thf(384,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)],[50]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mem__Collect__eq) ).
thf(472,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_58_llist_Ocoinduct__strong) ).
thf(747,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)],[152]) ).
thf(207,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_local_OatLeastAtMost__iff) ).
thf(945,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(125,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Int__absorb) ).
thf(670,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_133_Int__iff) ).
thf(320,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)],[32]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',fact_153_IntE) ).
thf(436,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)],[60]) ).
thf(9,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] : ( coindu300403952lexord @ TA @ A @ ( coindu1598213697e_LNil @ TA ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_llexord__LNil) ).
thf(257,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] : ( coindu300403952lexord @ TA @ A @ ( coindu1598213697e_LNil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu882539134_llist @ TA @ TB )
= ( ^ [A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA,C: coindu1593790203_llist @ TB] : ( if @ TA @ ( coindu335574135_lnull @ TB @ C ) @ A @ ( B @ ( coindu1046438764le_lhd @ TB @ C ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_llist_Ocase__eq__if) ).
thf(841,plain,
! [TA: $tType,TB: $tType] :
( ( coindu882539134_llist @ TA @ TB )
= ( ^ [A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA,C: coindu1593790203_llist @ TB] : ( if @ TA @ ( coindu335574135_lnull @ TB @ C ) @ A @ ( B @ ( coindu1046438764le_lhd @ TB @ C ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(57,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( A @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ D )
=> ( ( A @ D )
=> ( A @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) )
=> ( ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ C @ B )
=> ( A @ C ) )
=> ( A @ B ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_llimit__induct) ).
thf(417,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( A @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ D )
=> ( ( A @ D )
=> ( A @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) )
=> ( ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ C @ B )
=> ( A @ C ) )
=> ( A @ B ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(51,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
& ( coindu6345450stinct @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_ldistinct__LCons) ).
thf(389,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
& ( coindu6345450stinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(98,axiom,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) )
= ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_llast__LCons2) ).
thf(570,plain,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) )
= ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(144,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
& ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lprefix__expand) ).
thf(719,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
& ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(47,axiom,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_llist_Odisc_I1_J) ).
thf(372,plain,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu1599971794_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ D ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ D ) @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_unfold__llist_Ocode) ).
thf(619,plain,
! [TA: $tType,TB: $tType] :
( ( coindu1599971794_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ D ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ D ) @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(36,axiom,
! [TA: $tType,A: TA > $o] :
( ( coindu721411036eWhile @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_ltakeWhile__LNil) ).
thf(344,plain,
! [TA: $tType,A: TA > $o] :
( ( coindu721411036eWhile @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(204,axiom,
! [A: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1598213697e_LNil @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Singleton) ).
thf(934,plain,
! [A: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1598213697e_LNil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(41,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_lprefix__not__lnullD) ).
thf(357,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(170,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( coindu6345450stinct @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ldistinct__ltlI) ).
thf(817,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( coindu6345450stinct @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(157,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1121789889_LCons @ TA @ A @ B ) )
=> ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_compact__LConsD) ).
thf(770,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1121789889_LCons @ TA @ A @ B ) )
=> ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(20,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_lprefix__lnullD) ).
thf(289,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(261,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(212,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_compact__lfiniteI) ).
thf(969,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(106,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_lprefix__trans) ).
thf(606,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA,D: TA] :
( ( member @ TA @ A @ ( set_atLeastAtMost @ TA @ B @ C @ D ) )
= ( ( B @ C @ A )
& ( B @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_ord_OatLeastAtMost__iff) ).
thf(475,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA,D: TA] :
( ( member @ TA @ A @ ( set_atLeastAtMost @ TA @ B @ C @ D ) )
= ( ( B @ C @ A )
& ( B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(162,axiom,
! [A: coindu1593790203_llist @ a] :
( ( member @ ( coindu1593790203_llist @ a ) @ A @ ya )
=> ( coindu543932918sorted @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_lsorted_I2_J) ).
thf(789,plain,
! [A: coindu1593790203_llist @ a] :
( ( member @ ( coindu1593790203_llist @ a ) @ A @ ya )
=> ( coindu543932918sorted @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(62,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_ord_OLCons__LCons) ).
thf(443,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(175,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_ltakeWhile_Octr_I1_J) ).
thf(834,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',fact_160_Int__left__commute) ).
thf(514,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)],[83]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(687,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(211,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( comple1986059218ssible @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( A @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ D )
=> ( ( A @ D )
=> ( A @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_llist__induct) ).
thf(956,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( comple1986059218ssible @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( A @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ D )
=> ( ( A @ D )
=> ( A @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_lfinite__LCons) ).
thf(396,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(13,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ord_Olsorted__code_I2_J) ).
thf(265,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_lprefix__LNil) ).
thf(312,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',fact_178_lhd__ltakeWhile) ).
thf(1074,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)],[240]) ).
thf(66,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_llist_Oexhaust) ).
thf(452,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(128,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ~ ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ C ) )
=> ~ ( coindu6345450stinct @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_ldistinct_Ocases) ).
thf(678,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ~ ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ C ) )
=> ~ ( coindu6345450stinct @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_llist_Oset__intros_I2_J) ).
thf(270,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(200,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1696667936prefix @ TA @ B @ ( coindu526335360e_lSup @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_llist_Olub__upper) ).
thf(925,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1696667936prefix @ TA @ B @ ( coindu526335360e_lSup @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(154,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) )
=> ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_lSup_Odisc_I1_J) ).
thf(761,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) )
=> ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',fact_55_ltakeWhile_Oexhaust) ).
thf(1067,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)],[238]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_170_ltakeWhile_Odisc__iff_I1_J) ).
thf(714,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)],[142]) ).
thf(82,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_llist_Oleq__trans) ).
thf(512,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(206,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1599971794_llist @ ( coindu1593790203_llist @ TA ) @ TA @ ( coindu335574135_lnull @ TA ) @ ( coindu1046438764le_lhd @ TA ) @ ( coindu1047225960le_ltl @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_unfold__llist__id) ).
thf(942,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1599971794_llist @ ( coindu1593790203_llist @ TA ) @ TA @ ( coindu335574135_lnull @ TA ) @ ( coindu1046438764le_lhd @ TA ) @ ( coindu1047225960le_ltl @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(61,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_llist_OdiscI_I2_J) ).
thf(439,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(90,axiom,
! [TA: $tType] :
( ( min @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( if @ TA @ ( A @ B @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ord_Omin__def) ).
thf(546,plain,
! [TA: $tType] :
( ( min @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( if @ TA @ ( A @ B @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(164,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_lhd__LCons) ).
thf(793,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',fact_59_llist_Ocoinduct) ).
thf(894,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)],[195]) ).
thf(160,axiom,
! [A: coindu1593790203_llist @ a] :
( ( member @ ( coindu1593790203_llist @ a ) @ A @ ya )
=> ( coindu543932918sorted @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_sorted) ).
thf(778,plain,
! [A: coindu1593790203_llist @ a] :
( ( member @ ( coindu1593790203_llist @ a ) @ A @ ya )
=> ( coindu543932918sorted @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(233,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( coindu1213758845finite @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
=> ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1213758845finite @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_lfinite__lSupD) ).
thf(1042,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( coindu1213758845finite @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
=> ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1213758845finite @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_lset__intros_I2_J) ).
thf(302,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(185,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_local_Omin__def) ).
thf(862,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(103,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_not__lnull__conv) ).
thf(598,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(95,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_llist_Odistinct_I1_J) ).
thf(561,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(52,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( coindu6345450stinct @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_ldistinct__lprefix) ).
thf(392,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( coindu6345450stinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu574146665prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_lstrict__prefix__code_I3_J) ).
thf(297,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu574146665prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(58,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( coindu2000965700_llast @ TA @ ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) )
= ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_llast__lappend__LCons) ).
thf(429,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( coindu2000965700_llast @ TA @ ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) )
= ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(17,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( A @ C )
=> ( ( C
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: TA,E: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ D @ E ) )
& ~ ( member @ TA @ D @ ( coindu1112613586e_lset @ TA @ E ) )
& ( ( A @ E )
| ( coindu6345450stinct @ TA @ E ) ) ) ) )
=> ( coindu6345450stinct @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ldistinct_Ocoinduct) ).
thf(275,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( A @ C )
=> ( ( C
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: TA,E: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ D @ E ) )
& ~ ( member @ TA @ D @ ( coindu1112613586e_lset @ TA @ E ) )
& ( ( A @ E )
| ( coindu6345450stinct @ TA @ E ) ) ) ) )
=> ( coindu6345450stinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_unfold__llist_Odisc_I1_J) ).
thf(693,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(115,axiom,
! [TA: $tType,A: TA > TA > $o] : ( coindu543932918sorted @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_ord_Olsorted__code_I1_J) ).
thf(630,plain,
! [TA: $tType,A: TA > TA > $o] : ( coindu543932918sorted @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(71,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( coindu6345450stinct @ TA @ B )
=> ( coindu6345450stinct @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ldistinct_OLCons) ).
thf(467,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ( coindu6345450stinct @ TA @ B )
=> ( coindu6345450stinct @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(97,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_lset__induct_H) ).
thf(566,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(7,axiom,
! [TA: $tType] :
~ ( coindu574146665prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_lstrict__prefix__code_I1_J) ).
thf(252,plain,
! [TA: $tType] :
~ ( coindu574146665prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(43,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_ord_Olsorted__LCons__LCons) ).
thf(361,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(113,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ C @ B )
=> ( ( coindu1696667936prefix @ TA @ A @ C )
| ( coindu1696667936prefix @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_lprefix__down__linear) ).
thf(625,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ C @ B )
=> ( ( coindu1696667936prefix @ TA @ A @ C )
| ( coindu1696667936prefix @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(189,axiom,
coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_LNil) ).
thf(879,plain,
coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(86,axiom,
! [TA: $tType] :
( ( max @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( if @ TA @ ( A @ B @ C ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_ord_Omax__def) ).
thf(522,plain,
! [TA: $tType] :
( ( max @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( if @ TA @ ( A @ B @ C ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(69,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_lprefix__antisym) ).
thf(461,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(228,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1047225960le_ltl @ TA @ A ) )
= ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_lfinite__ltl) ).
thf(1027,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1047225960le_ltl @ TA @ A ) )
= ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(140,axiom,
~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lsorted_I4_J) ).
thf(710,plain,
~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_llist_Oset__intros_I1_J) ).
thf(697,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(208,axiom,
! [A: a,B: a,C: coindu1593790203_llist @ a] :
( ( less_eq @ A @ B )
=> ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ B @ C ) )
=> ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1121789889_LCons @ a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_LCons__LCons) ).
thf(948,plain,
! [A: a,B: a,C: coindu1593790203_llist @ a] :
( ( less_eq @ A @ B )
=> ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ B @ C ) )
=> ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1121789889_LCons @ a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fact_177_ltakeWhile_Odisc_I1_J) ).
thf(1064,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)],[237]) ).
thf(217,axiom,
~ ! [A: coindu1593790203_llist @ a] :
( ( member @ ( coindu1593790203_llist @ a ) @ A @ ya )
=> ( ~ ( coindu335574135_lnull @ a @ A )
=> ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062xs_A_092_060in_062_AY_059_A_092_060not_062_Alnull_Axs_059_A_092_060not_062_Alnull_A_Iltl_Axs_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(980,plain,
~ ! [A: coindu1593790203_llist @ a] :
( ( member @ ( coindu1593790203_llist @ a ) @ A @ ya )
=> ( ~ ( coindu335574135_lnull @ a @ A )
=> ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(186,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_local_Omax__def) ).
thf(869,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(78,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_llist_OdiscI_I1_J) ).
thf(499,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(183,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( member @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_ldistinct__lhdD) ).
thf(857,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu6345450stinct @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( member @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(85,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1571841457prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1571841457prefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(519,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1571841457prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1571841457prefix @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(101,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
=> ( ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
=> ~ ( coindu300403952lexord @ TA @ A @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: coindu1593790203_llist @ TA] :
( B
= ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: coindu1593790203_llist @ TA] :
( C
= ( coindu1121789889_LCons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ( ( B
= ( coindu1598213697e_LNil @ TA ) )
=> ! [D: coindu1593790203_llist @ TA] : ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_llexord_Ocases) ).
thf(578,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
=> ( ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
=> ~ ( coindu300403952lexord @ TA @ A @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: coindu1593790203_llist @ TA] :
( B
= ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: coindu1593790203_llist @ TA] :
( C
= ( coindu1121789889_LCons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ( ( B
= ( coindu1598213697e_LNil @ TA ) )
=> ! [D: coindu1593790203_llist @ TA] : ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(35,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_llist_Oset__cases) ).
thf(339,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(225,axiom,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
= ( ( A
= ( coindu1598213697e_LNil @ a ) )
| ? [B: a] :
( A
= ( coindu1121789889_LCons @ a @ B @ ( coindu1598213697e_LNil @ a ) ) )
| ? [B: a,C: a,D: coindu1593790203_llist @ a] :
( ( A
= ( coindu1121789889_LCons @ a @ B @ ( coindu1121789889_LCons @ a @ C @ D ) ) )
& ( less_eq @ B @ C )
& ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_lsorted_Osimps) ).
thf(1016,plain,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
= ( ( A
= ( coindu1598213697e_LNil @ a ) )
| ? [B: a] :
( A
= ( coindu1121789889_LCons @ a @ B @ ( coindu1598213697e_LNil @ a ) ) )
| ? [B: a,C: a,D: coindu1593790203_llist @ a] :
( ( A
= ( coindu1121789889_LCons @ a @ B @ ( coindu1121789889_LCons @ a @ C @ D ) ) )
& ( less_eq @ B @ C )
& ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_llist_Osplit__sel__asm) ).
thf(1039,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coindu1593790203_llist @ TB] :
( ( ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D )
= ( coindu1121789889_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_unfold__llist__eq__LCons) ).
thf(622,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coindu1593790203_llist @ TB] :
( ( ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D )
= ( coindu1121789889_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(121,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) )
= ( coindu2000965700_llast @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_llast__LCons) ).
thf(647,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) )
= ( coindu2000965700_llast @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_213_in__lset__ltlD) ).
thf(985,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)],[218]) ).
thf(136,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_lprefix__refl) ).
thf(701,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(123,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coindu1593790203_llist @ TA,F: coindu1593790203_llist @ TA] :
( ( A @ E @ F )
=> ( ? [G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA,I: TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ I @ G ) )
& ( F
= ( coindu1121789889_LCons @ TA @ I @ H ) )
& ( ( A @ G @ H )
| ( coindu300403952lexord @ TA @ D @ G @ H ) ) )
| ? [G: TA,H: TA,I: coindu1593790203_llist @ TA,J: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ G @ I ) )
& ( F
= ( coindu1121789889_LCons @ TA @ H @ J ) )
& ( D @ G @ H ) )
| ? [G: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1598213697e_LNil @ TA ) )
& ( F = G ) ) ) )
=> ( coindu300403952lexord @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_llexord_Ocoinduct) ).
thf(654,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coindu1593790203_llist @ TA,F: coindu1593790203_llist @ TA] :
( ( A @ E @ F )
=> ( ? [G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA,I: TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ I @ G ) )
& ( F
= ( coindu1121789889_LCons @ TA @ I @ H ) )
& ( ( A @ G @ H )
| ( coindu300403952lexord @ TA @ D @ G @ H ) ) )
| ? [G: TA,H: TA,I: coindu1593790203_llist @ TA,J: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ G @ I ) )
& ( F
= ( coindu1121789889_LCons @ TA @ H @ J ) )
& ( D @ G @ H ) )
| ? [G: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1598213697e_LNil @ TA ) )
& ( F = G ) ) ) )
=> ( coindu300403952lexord @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(79,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
( ( ( A @ B )
=> ( ( coindu721411036eWhile @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1121789889_LCons @ TA @ B @ ( coindu721411036eWhile @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coindu721411036eWhile @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_ltakeWhile__LCons) ).
thf(503,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
( ( ( A @ B )
=> ( ( coindu721411036eWhile @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1121789889_LCons @ TA @ B @ ( coindu721411036eWhile @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coindu721411036eWhile @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(4,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_llexord__LCons__less) ).
thf(244,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(80,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_lfinite__LConsI) ).
thf(508,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(94,axiom,
! [TA: $tType] :
( ( coindu300403952lexord @ TA )
= ( ^ [A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ? [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
& ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
& ( coindu300403952lexord @ TA @ A @ D @ E ) )
| ? [D: TA,E: TA,F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ D @ F ) )
& ( C
= ( coindu1121789889_LCons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1598213697e_LNil @ TA ) )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_llexord_Osimps) ).
thf(558,plain,
! [TA: $tType] :
( ( coindu300403952lexord @ TA )
= ( ^ [A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ? [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
& ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
& ( coindu300403952lexord @ TA @ A @ D @ E ) )
| ? [D: TA,E: TA,F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ D @ F ) )
& ( C
= ( coindu1121789889_LCons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1598213697e_LNil @ TA ) )
& ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(193,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_local_OatMost__iff) ).
thf(888,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(197,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ( A @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ D ) )
=> ( ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1046438764le_lhd @ TA @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) )
| ( coindu543932918sorted @ TA @ C @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) )
=> ( coindu543932918sorted @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ord_Olsorted__coinduct_H) ).
thf(906,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ( A @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ D ) )
=> ( ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1046438764le_lhd @ TA @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) )
| ( coindu543932918sorted @ TA @ C @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) )
=> ( coindu543932918sorted @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(173,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ( A @ B @ ( coindu1046438764le_lhd @ TA @ C ) )
& ( coindu543932918sorted @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_ord_Olsorted__LCons_H) ).
thf(824,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ( A @ B @ ( coindu1046438764le_lhd @ TA @ C ) )
& ( coindu543932918sorted @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_156_Int__assoc) ).
thf(573,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)],[99]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_176_ltakeWhile_Odisc_I2_J) ).
thf(733,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)],[146]) ).
thf(104,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_lnull__lprefix) ).
thf(601,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(171,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu6345450stinct @ TA @ B ) )
=> ( coindu6345450stinct @ TA @ ( coindu526335360e_lSup @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_ldistinct__lSup) ).
thf(819,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu6345450stinct @ TA @ B ) )
=> ( coindu6345450stinct @ TA @ ( coindu526335360e_lSup @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(215,axiom,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
=> ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_lsorted__ltlI) ).
thf(975,plain,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
=> ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(158,axiom,
! [TA: $tType] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_ltl__simps_I1_J) ).
thf(772,plain,
! [TA: $tType] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(19,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atMost @ TA @ B @ C ) )
= ( B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_ord_OatMost__iff) ).
thf(286,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atMost @ TA @ B @ C ) )
= ( B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1571841457prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(291,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1571841457prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ B ) @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_llexord__LCons__eq) ).
thf(259,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ B ) @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_227_lfinite__ltakeWhile) ).
thf(611,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)],[108]) ).
thf(167,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ( A @ ( coindu1046438764le_lhd @ TA @ B ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( coindu721411036eWhile @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
& ( ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_ltl__ltakeWhile) ).
thf(804,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ( A @ ( coindu1046438764le_lhd @ TA @ B ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( coindu721411036eWhile @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
& ( ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_unfold__llist_Odisc_I2_J) ).
thf(350,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(89,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_lset__induct) ).
thf(540,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(63,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1571841457prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(445,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1571841457prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(205,axiom,
! [A: ( coindu1593790203_llist @ a ) > $o,B: coindu1593790203_llist @ a] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ a] :
( ( A @ C )
=> ( ~ ( coindu335574135_lnull @ a @ C )
=> ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ C ) )
=> ( ( less_eq @ ( coindu1046438764le_lhd @ a @ C ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ C ) ) )
& ( ( A @ ( coindu1047225960le_ltl @ a @ C ) )
| ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ C ) ) ) ) ) ) )
=> ( coindu543932918sorted @ a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_lsorted__coinduct_H) ).
thf(936,plain,
! [A: ( coindu1593790203_llist @ a ) > $o,B: coindu1593790203_llist @ a] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ a] :
( ( A @ C )
=> ( ~ ( coindu335574135_lnull @ a @ C )
=> ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ C ) )
=> ( ( less_eq @ ( coindu1046438764le_lhd @ a @ C ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ C ) ) )
& ( ( A @ ( coindu1047225960le_ltl @ a @ C ) )
| ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ C ) ) ) ) ) ) )
=> ( coindu543932918sorted @ a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(155,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_lprefix__lhdD) ).
thf(764,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_184_ltakeWhile_Osimps_I4_J) ).
thf(880,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)],[190]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fact_215_ltakeWhile__cong) ).
thf(377,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)],[49]) ).
thf(220,axiom,
~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__092_060open_062_092_060not_062_Alnull_A_Iltl_Axs_J_092_060close_062) ).
thf(990,plain,
~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(148,axiom,
~ ( coindu335574135_lnull @ a @ xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__092_060open_062_092_060not_062_Alnull_Axs_092_060close_062) ).
thf(737,plain,
~ ( coindu335574135_lnull @ a @ xs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(31,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_lprefix__ltakeWhile) ).
thf(318,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(153,axiom,
! [A: a,B: a] :
( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ A ) @ ( set_atMost @ a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_local_OatLeastAtMost__def) ).
thf(758,plain,
! [A: a,B: a] :
( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ A ) @ ( set_atMost @ a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(33,axiom,
! [TA: $tType] :
( ( set_atLeastAtMost @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_atLeast @ TA @ A @ B ) @ ( set_atMost @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_ord_OatLeastAtMost__def) ).
thf(323,plain,
! [TA: $tType] :
( ( set_atLeastAtMost @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_atLeast @ TA @ A @ B ) @ ( set_atMost @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(76,axiom,
! [TA: $tType] :
( ( coindu1571841457prefix @ TA )
= ( coindu1696667936prefix @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def) ).
thf(483,plain,
! [TA: $tType] :
( ( coindu1571841457prefix @ TA )
= ( coindu1696667936prefix @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(180,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_compact__LConsI) ).
thf(848,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(199,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
& ( ( coindu1046438764le_lhd @ TA @ A )
= B )
& ( ( coindu1047225960le_ltl @ TA @ A )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_eq__LConsD) ).
thf(915,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
& ( ( coindu1046438764le_lhd @ TA @ A )
= B )
& ( ( coindu1047225960le_ltl @ TA @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_llist_Odisc_I2_J) ).
thf(367,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA] :
( ( coindu882539134_llist @ TA @ TB @ A @ B @ ( coindu1598213697e_LNil @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_llist_Osimps_I4_J) ).
thf(552,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA] :
( ( coindu882539134_llist @ TA @ TB @ A @ B @ ( coindu1598213697e_LNil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(55,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 )
=> ( ? [F: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ( E = F ) )
| ? [F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA,H: TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ H @ F ) )
& ( E
= ( coindu1121789889_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coindu1696667936prefix @ TA @ F @ G ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_lprefix_Ocoinduct) ).
thf(399,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 )
=> ( ? [F: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ( E = F ) )
| ? [F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA,H: TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ H @ F ) )
& ( E
= ( coindu1121789889_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coindu1696667936prefix @ TA @ F @ G ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',fact_22_llist_Oexpand) ).
thf(827,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)],[174]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',fact_239_lfinite__induct) ).
thf(780,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)],[161]) ).
thf(107,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( finite_finite @ TA @ A )
| ( finite_finite @ TA @ B ) )
=> ( finite_finite @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_finite__Int) ).
thf(608,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( finite_finite @ TA @ A )
| ( finite_finite @ TA @ B ) )
=> ( finite_finite @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(24,axiom,
! [TA: $tType,A: TA] :
( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_llast__singleton) ).
thf(299,plain,
! [TA: $tType,A: TA] :
( ( coindu2000965700_llast @ TA @ ( coindu1121789889_LCons @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_lfinite__code_I2_J) ).
thf(267,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(241,plain,
~ ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_llist_Osplit__sel) ).
thf(912,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(129,axiom,
! [TA: $tType] : ( coindu6345450stinct @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_ldistinct__LNil__code) ).
thf(685,plain,
! [TA: $tType] : ( coindu6345450stinct @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',fact_217_llist__set__induct) ).
thf(1044,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)],[234]) ).
thf(133,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( coindu574146665prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_lstrict__prefix__code_I2_J) ).
thf(695,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( coindu574146665prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(67,axiom,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ? [C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B = C ) )
| ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
& ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
& ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_lprefix_Osimps) ).
thf(455,plain,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ? [C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B = C ) )
| ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
& ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
& ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(191,axiom,
! [A: a,B: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ B ) )
= ( ~ ( coindu335574135_lnull @ a @ B )
=> ( ( less_eq @ A @ ( coindu1046438764le_lhd @ a @ B ) )
& ( coindu543932918sorted @ a @ less_eq @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_lsorted__LCons_H) ).
thf(883,plain,
! [A: a,B: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ B ) )
= ( ~ ( coindu335574135_lnull @ a @ B )
=> ( ( less_eq @ A @ ( coindu1046438764le_lhd @ a @ B ) )
& ( coindu543932918sorted @ a @ less_eq @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(53,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( finite_finite @ TA @ ( coindu1112613586e_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_lfinite__imp__finite__lset) ).
thf(394,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( finite_finite @ TA @ ( coindu1112613586e_lset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(27,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_llist_Oleq__antisym) ).
thf(306,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(169,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_local_Oord__le__eq__trans) ).
thf(812,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(110,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_llist_Oleq__refl) ).
thf(617,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',fact_155_IntD2) ).
thf(355,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)],[40]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_31_lappend_Oexhaust) ).
thf(458,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)],[68]) ).
thf(201,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ B ) )
=> ( A @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1046438764le_lhd @ TA @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_ord_Olsorted__lhdD) ).
thf(927,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ B ) )
=> ( A @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1046438764le_lhd @ TA @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(48,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Collect__mem__eq) ).
thf(374,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',fact_216_lset__ltakeWhileD) ).
thf(525,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)],[87]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_202_llist_Oset__sel_I2_J) ).
thf(712,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)],[141]) ).
thf(182,axiom,
( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
= ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062) ).
thf(855,plain,
( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
= ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coindu1593790203_llist @ TA ) > TB,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu882539134_llist @ TB @ TA @ A @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_llist_Osimps_I5_J) ).
thf(690,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coindu1593790203_llist @ TA ) > TB,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu882539134_llist @ TB @ TA @ A @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(118,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_llist_Ocollapse_I1_J) ).
thf(640,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_26_lzip_Oexhaust) ).
thf(705,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)],[138]) ).
thf(213,axiom,
comple1193779247_chain @ ( coindu1593790203_llist @ a ) @ ( coindu1696667936prefix @ a ) @ ya,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_chain) ).
thf(971,plain,
comple1193779247_chain @ ( coindu1593790203_llist @ a ) @ ( coindu1696667936prefix @ a ) @ ya,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(210,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_compact__lfiniteD) ).
thf(954,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(149,axiom,
( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
= ( coindu1046438764le_lhd @ a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062) ).
thf(739,plain,
( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(235,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lhd__lSup__eq) ).
thf(1053,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_unfold__llist_Octr_I2_J) ).
thf(673,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(163,axiom,
! [A: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1598213697e_LNil @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_lsorted__code_I2_J) ).
thf(791,plain,
! [A: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1598213697e_LNil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(143,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_lprefix__ltlI) ).
thf(717,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(100,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ C @ A ) @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Le__LCons) ).
thf(576,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ C @ A ) @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(209,axiom,
! [A: a,B: a,C: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1121789889_LCons @ a @ B @ C ) ) )
= ( ( less_eq @ A @ B )
& ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_lsorted__LCons__LCons) ).
thf(951,plain,
! [A: a,B: a,C: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ A @ ( coindu1121789889_LCons @ a @ B @ C ) ) )
= ( ( less_eq @ A @ B )
& ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(42,axiom,
! [TA: $tType] : ( coindu6345450stinct @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_ldistinct_OLNil) ).
thf(359,plain,
! [TA: $tType] : ( coindu6345450stinct @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_lprefix__code_I2_J) ).
thf(643,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(151,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_lnull__lSup) ).
thf(744,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) )
= ( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(137,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1213758845finite @ TA @ B )
=> ( coindu1213758845finite @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_lprefix__lfiniteD) ).
thf(703,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1213758845finite @ TA @ B )
=> ( coindu1213758845finite @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(187,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ~ ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_lSup_Odisc_I2_J) ).
thf(876,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ~ ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu526335360e_lSup @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',fact_171_lnull__ltakeWhile) ).
thf(859,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)],[184]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_unfold__llist_Osimps_I3_J) ).
thf(845,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_159_Int__left__absorb) ).
thf(627,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)],[114]) ).
thf(65,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_LNil__lprefix) ).
thf(450,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',fact_169_ltakeWhile_Odisc__iff_I2_J) ).
thf(931,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)],[203]) ).
thf(196,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ( A
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_llist_Oexhaust__sel) ).
thf(903,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ( A
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(194,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ C @ A )
=> ( coindu1696667936prefix @ TA @ C @ B ) )
=> ( coindu1696667936prefix @ TA @ ( coindu526335360e_lSup @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_llist_Olub__least) ).
thf(891,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ C @ A )
=> ( coindu1696667936prefix @ TA @ C @ B ) )
=> ( coindu1696667936prefix @ TA @ ( coindu526335360e_lSup @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(178,axiom,
member @ ( coindu1593790203_llist @ a ) @ xs @ ya,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062xs_A_092_060in_062_AY_092_060close_062) ).
thf(844,plain,
member @ ( coindu1593790203_llist @ a ) @ xs @ ya,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(135,axiom,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_lfinite__code_I1_J) ).
thf(699,plain,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact_154_IntD1) ).
thf(517,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)],[84]) ).
thf(26,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_ord_OSingleton) ).
thf(304,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(122,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_lprefix__code_I1_J) ).
thf(652,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atLeast @ TA @ B @ C ) )
= ( B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_ord_OatLeast__iff) ).
thf(632,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atLeast @ TA @ B @ C ) )
= ( B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(229,axiom,
! [TA: $tType] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) )
= ( coindu1213758845finite @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_compact__eq__lfinite) ).
thf(1030,plain,
! [TA: $tType] :
( ( comple2143767107ompact @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) )
= ( coindu1213758845finite @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(5,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ! [C: coindu1593790203_llist @ TA] :
( ! [D: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_llist__less__induct) ).
thf(246,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ! [C: coindu1593790203_llist @ TA] :
( ! [D: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(81,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_lset__intros_I1_J) ).
thf(510,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(202,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( member @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_llist_Oset__sel_I1_J) ).
thf(929,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)],[202]) ).
thf(75,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: coindu1593790203_llist @ TA] :
( ? [C: TA] :
( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
=> ~ ( coindu1213758845finite @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_lfinite_Ocases) ).
thf(478,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: coindu1593790203_llist @ TA] :
( ? [C: TA] :
( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
=> ~ ( coindu1213758845finite @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(16,axiom,
! [TA: $tType] :
( ( coindu543932918sorted @ TA )
= ( ^ [A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1598213697e_LNil @ TA ) )
| ? [C: TA] :
( B
= ( coindu1121789889_LCons @ TA @ C @ ( coindu1598213697e_LNil @ TA ) ) )
| ? [C: TA,D: TA,E: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) )
& ( A @ C @ D )
& ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_ord_Olsorted_Osimps) ).
thf(272,plain,
! [TA: $tType] :
( ( coindu543932918sorted @ TA )
= ( ^ [A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1598213697e_LNil @ TA ) )
| ? [C: TA] :
( B
= ( coindu1121789889_LCons @ TA @ C @ ( coindu1598213697e_LNil @ TA ) ) )
| ? [C: TA,D: TA,E: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) )
& ( A @ C @ D )
& ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(91,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Int__commute) ).
thf(549,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)],[91]) ).
thf(64,axiom,
! [TA: $tType] :
( ( coindu6345450stinct @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
& ~ ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ C ) )
& ( coindu6345450stinct @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_ldistinct_Osimps) ).
thf(447,plain,
! [TA: $tType] :
( ( coindu6345450stinct @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
& ~ ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ C ) )
& ( coindu6345450stinct @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_llist_Oinject) ).
thf(315,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] : ( C @ D @ ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_llist_Oset__induct) ).
thf(432,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] : ( C @ D @ ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(56,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ B )
=> ( ( B
!= ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: TA] :
( B
!= ( coindu1121789889_LCons @ TA @ C @ ( coindu1598213697e_LNil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
=> ~ ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ord_Olsorted_Ocases) ).
thf(410,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ B )
=> ( ( B
!= ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: TA] :
( B
!= ( coindu1121789889_LCons @ TA @ C @ ( coindu1598213697e_LNil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
=> ~ ( coindu543932918sorted @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(12,axiom,
! [TA: $tType] :
( ( coindu574146665prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_lstrict__prefix__def) ).
thf(262,plain,
! [TA: $tType] :
( ( coindu574146665prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(105,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1696667936prefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_lprefix__LCons__conv) ).
thf(603,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1696667936prefix @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(147,axiom,
! [TA: $tType] : ( comple1412571634l_cont @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1047225960le_ltl @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_cont__ltl) ).
thf(735,plain,
! [TA: $tType] : ( comple1412571634l_cont @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ ( coindu1047225960le_ltl @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(96,axiom,
! [TA: $tType,A: TA > TA > $o] : ( coindu543932918sorted @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_ord_OLNil) ).
thf(564,plain,
! [TA: $tType,A: TA > TA > $o] : ( coindu543932918sorted @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(34,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( B @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_lfinite_Oinducts) ).
thf(326,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( B @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ A @ B )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_lstrict__prefix__lfinite1) ).
thf(242,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ A @ B )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(156,axiom,
! [TA: $tType] :
( ( coindu721411036eWhile @ TA )
= ( ^ [A: TA > $o,B: coindu1593790203_llist @ TA] :
( if @ ( coindu1593790203_llist @ TA )
@ ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) )
@ ( coindu1598213697e_LNil @ TA )
@ ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu721411036eWhile @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_ltakeWhile_Ocode) ).
thf(767,plain,
! [TA: $tType] :
( ( coindu721411036eWhile @ TA )
= ( ^ [A: TA > $o,B: coindu1593790203_llist @ TA] :
( if @ ( coindu1593790203_llist @ TA )
@ ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) )
@ ( coindu1598213697e_LNil @ TA )
@ ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu721411036eWhile @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(236,axiom,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ a ) )
=> ( ! [B: a] :
( A
!= ( coindu1121789889_LCons @ a @ B @ ( coindu1598213697e_LNil @ a ) ) )
=> ~ ! [B: a,C: a,D: coindu1593790203_llist @ a] :
( ( A
= ( coindu1121789889_LCons @ a @ B @ ( coindu1121789889_LCons @ a @ C @ D ) ) )
=> ( ( less_eq @ B @ C )
=> ~ ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_lsorted_Ocases) ).
thf(1056,plain,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ a ) )
=> ( ! [B: a] :
( A
!= ( coindu1121789889_LCons @ a @ B @ ( coindu1598213697e_LNil @ a ) ) )
=> ~ ! [B: a,C: a,D: coindu1593790203_llist @ a] :
( ( A
= ( coindu1121789889_LCons @ a @ B @ ( coindu1121789889_LCons @ a @ C @ D ) ) )
=> ( ( less_eq @ B @ C )
=> ~ ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(230,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_ltakeWhile_Octr_I2_J) ).
thf(1033,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(117,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_lset__cases) ).
thf(635,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(192,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1696667936prefix @ TA @ B @ ( coindu526335360e_lSup @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_chain__lprefix__lSup) ).
thf(886,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu1696667936prefix @ TA @ B @ ( coindu526335360e_lSup @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(22,axiom,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1213758845finite @ TA @ A )
=> ( coindu1571841457prefix @ TA @ A @ B ) )
& ( ~ ( coindu1213758845finite @ TA @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps) ).
thf(294,plain,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1213758845finite @ TA @ A )
=> ( coindu1571841457prefix @ TA @ A @ B ) )
& ( ~ ( coindu1213758845finite @ TA @ A )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(166,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ( coindu721411036eWhile @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( B
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ltakeWhile__eq__LNil__iff) ).
thf(801,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ( coindu721411036eWhile @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( B
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1598213697e_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_ltl__unfold__llist) ).
thf(796,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1598213697e_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(18,axiom,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_lnull__def) ).
thf(283,plain,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(176,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_lnull__ltlI) ).
thf(839,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)],[176]) ).
thf(219,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_local_OatLeast__iff) ).
thf(987,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1599971794_llist @ TB @ TA @ A @ C @ D @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_unfold__llist_Octr_I1_J) ).
thf(464,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1599971794_llist @ TB @ TA @ A @ C @ D @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(102,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_lnull__imp__lfinite) ).
thf(596,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(226,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_local_Oord__eq__le__trans) ).
thf(1019,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(88,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coindu1598213697e_LNil @ TA ) )
| ? [E: TA] :
( D
= ( coindu1121789889_LCons @ TA @ E @ ( coindu1598213697e_LNil @ TA ) ) )
| ? [E: TA,F: TA,G: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ E @ ( coindu1121789889_LCons @ TA @ F @ G ) ) )
& ( C @ E @ F )
& ( ( A @ ( coindu1121789889_LCons @ TA @ F @ G ) )
| ( coindu543932918sorted @ TA @ C @ ( coindu1121789889_LCons @ TA @ F @ G ) ) ) ) ) )
=> ( coindu543932918sorted @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ord_Olsorted_Ocoinduct) ).
thf(528,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coindu1598213697e_LNil @ TA ) )
| ? [E: TA] :
( D
= ( coindu1121789889_LCons @ TA @ E @ ( coindu1598213697e_LNil @ TA ) ) )
| ? [E: TA,F: TA,G: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ E @ ( coindu1121789889_LCons @ TA @ F @ G ) ) )
& ( C @ E @ F )
& ( ( A @ ( coindu1121789889_LCons @ TA @ F @ G ) )
| ( coindu543932918sorted @ TA @ C @ ( coindu1121789889_LCons @ TA @ F @ G ) ) ) ) ) )
=> ( coindu543932918sorted @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(221,axiom,
! [A: ( coindu1593790203_llist @ a ) > $o,B: coindu1593790203_llist @ a] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ a] :
( ( A @ C )
=> ( ( C
= ( coindu1598213697e_LNil @ a ) )
| ? [D: a] :
( C
= ( coindu1121789889_LCons @ a @ D @ ( coindu1598213697e_LNil @ a ) ) )
| ? [D: a,E: a,F: coindu1593790203_llist @ a] :
( ( C
= ( coindu1121789889_LCons @ a @ D @ ( coindu1121789889_LCons @ a @ E @ F ) ) )
& ( less_eq @ D @ E )
& ( ( A @ ( coindu1121789889_LCons @ a @ E @ F ) )
| ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ E @ F ) ) ) ) ) )
=> ( coindu543932918sorted @ a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_lsorted_Ocoinduct) ).
thf(992,plain,
! [A: ( coindu1593790203_llist @ a ) > $o,B: coindu1593790203_llist @ a] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ a] :
( ( A @ C )
=> ( ( C
= ( coindu1598213697e_LNil @ a ) )
| ? [D: a] :
( C
= ( coindu1121789889_LCons @ a @ D @ ( coindu1598213697e_LNil @ a ) ) )
| ? [D: a,E: a,F: coindu1593790203_llist @ a] :
( ( C
= ( coindu1121789889_LCons @ a @ D @ ( coindu1121789889_LCons @ a @ E @ F ) ) )
& ( less_eq @ D @ E )
& ( ( A @ ( coindu1121789889_LCons @ a @ E @ F ) )
| ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ E @ F ) ) ) ) ) )
=> ( coindu543932918sorted @ a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(145,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 @ E )
=> ( coindu335574135_lnull @ TA @ D ) )
& ( ~ ( 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 ) )
| ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_lprefix__coinduct) ).
thf(723,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 @ E )
=> ( coindu335574135_lnull @ TA @ D ) )
& ( ~ ( 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 ) )
| ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(172,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ B )
=> ( coindu543932918sorted @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_ord_Olsorted__ltlI) ).
thf(822,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu543932918sorted @ TA @ A @ B )
=> ( coindu543932918sorted @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(181,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( comple1986059218ssible @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ? [C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ C @ B )
& ( coindu1213758845finite @ TA @ C )
& ! [D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ C @ D )
=> ( ( coindu1696667936prefix @ TA @ D @ B )
=> ( ( coindu1213758845finite @ TA @ D )
=> ( A @ D ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_llist__gen__induct) ).
thf(850,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( comple1986059218ssible @ ( coindu1593790203_llist @ TA ) @ ( coindu526335360e_lSup @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ? [C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ C @ B )
& ( coindu1213758845finite @ TA @ C )
& ! [D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ C @ D )
=> ( ( coindu1696667936prefix @ TA @ D @ B )
=> ( ( coindu1213758845finite @ TA @ D )
=> ( A @ D ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(222,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( A @ C )
=> ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ~ ( member @ TA @ ( coindu1046438764le_lhd @ TA @ C ) @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ C ) ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ C ) )
| ( coindu6345450stinct @ TA @ ( coindu1047225960le_ltl @ TA @ C ) ) ) ) ) )
=> ( coindu6345450stinct @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_ldistinct__coinduct) ).
thf(1004,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA] :
( ( A @ B )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( A @ C )
=> ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ~ ( member @ TA @ ( coindu1046438764le_lhd @ TA @ C ) @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ C ) ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ C ) )
| ( coindu6345450stinct @ TA @ ( coindu1047225960le_ltl @ TA @ C ) ) ) ) ) )
=> ( coindu6345450stinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(46,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_neq__LNil__conv) ).
thf(369,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu574146665prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_lstrict__prefix__code_I4_J) ).
thf(254,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu574146665prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu574146665prefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(77,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ! [C: coindu1593790203_llist @ TA] : ( B != C ) )
=> ~ ! [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
=> ~ ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_lprefix_Ocases) ).
thf(486,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ! [C: coindu1593790203_llist @ TA] : ( B != C ) )
=> ~ ! [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
=> ~ ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(72,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
= ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_lprefix__lnull) ).
thf(469,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
= ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(223,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) )
=> ( ( coindu526335360e_lSup @ TA @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_lSup_Octr_I1_J) ).
thf(1009,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA )] :
( ! [B: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ B @ A )
=> ( coindu335574135_lnull @ TA @ B ) )
=> ( ( coindu526335360e_lSup @ TA @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_unfold__llist_Odisc__iff_I1_J) ).
thf(309,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(159,axiom,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ C @ A )
=> ( coindu1696667936prefix @ TA @ C @ B ) )
=> ( coindu1696667936prefix @ TA @ ( coindu526335360e_lSup @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_chain__lSup__lprefix) ).
thf(775,plain,
! [TA: $tType,A: set @ ( coindu1593790203_llist @ TA ),B: coindu1593790203_llist @ TA] :
( ( comple1193779247_chain @ ( coindu1593790203_llist @ TA ) @ ( coindu1696667936prefix @ TA ) @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( member @ ( coindu1593790203_llist @ TA ) @ C @ A )
=> ( coindu1696667936prefix @ TA @ C @ B ) )
=> ( coindu1696667936prefix @ TA @ ( coindu526335360e_lSup @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_134_IntI) ).
thf(676,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)],[127]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_LCons__lprefix__LCons) ).
thf(364,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(139,axiom,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
=> ( ~ ( coindu335574135_lnull @ a @ A )
=> ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ A ) )
=> ( less_eq @ ( coindu1046438764le_lhd @ a @ A ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_lsorted__lhdD) ).
thf(708,plain,
! [A: coindu1593790203_llist @ a] :
( ( coindu543932918sorted @ a @ less_eq @ A )
=> ( ~ ( coindu335574135_lnull @ a @ A )
=> ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ A ) )
=> ( less_eq @ ( coindu1046438764le_lhd @ a @ A ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(224,axiom,
~ ( coindu335574135_lnull @ a @ ( coindu526335360e_lSup @ a @ ya ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_lsorted_I3_J) ).
thf(1014,plain,
~ ( coindu335574135_lnull @ a @ ( coindu526335360e_lSup @ a @ ya ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(214,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ltl__simps_I2_J) ).
thf(972,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1077,plain,
$false,
inference(e,[status(thm)],[645,1036,809,1024,347,249,555,666,352,977,878,614,741,1073,384,472,747,945,670,320,436,257,841,417,389,570,719,372,619,344,934,357,817,770,289,261,969,606,475,789,443,834,514,687,956,396,265,312,1074,452,678,270,925,761,1067,714,512,942,439,546,793,894,778,1042,302,862,598,561,392,297,429,275,693,630,467,566,252,361,625,879,522,461,1027,710,697,948,1064,980,869,499,857,519,578,339,1016,1039,622,647,985,701,654,503,244,508,558,888,906,824,573,733,601,819,975,772,286,291,259,611,804,350,540,445,936,764,880,377,990,737,318,758,323,483,848,915,367,552,399,827,780,608,299,267,241,912,685,1044,695,455,883,394,306,812,617,355,458,927,374,525,712,855,690,640,705,971,954,739,1053,673,791,717,576,951,359,643,744,703,876,859,845,627,450,931,903,891,844,699,517,304,652,632,1030,246,510,929,478,272,549,447,315,432,410,262,603,735,564,326,242,767,1056,1033,635,886,294,801,796,283,839,987,464,596,1019,528,992,723,822,850,1004,369,254,486,469,1009,309,775,676,364,708,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : DAT130^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 11:31:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.90/1.18 % [INFO] Parsing done (290ms).
% 1.90/1.19 % [INFO] Running in sequential loop mode.
% 2.67/1.42 % [INFO] eprover registered as external prover.
% 2.67/1.43 % [INFO] cvc4 registered as external prover.
% 2.67/1.43 % [INFO] Scanning for conjecture ...
% 3.02/1.54 % [INFO] Found a conjecture and 263 axioms. Running axiom selection ...
% 3.37/1.63 % [INFO] Axiom selection finished. Selected 238 axioms (removed 25 axioms).
% 3.87/1.84 % [INFO] Problem is higher-order (TPTP THF).
% 3.87/1.86 % [INFO] Type checking passed.
% 3.87/1.87 % [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 ...
% 28.85/13.18 % External prover 'e' found a proof!
% 28.85/13.18 % [INFO] Killing All external provers ...
% 28.85/13.19 % Time passed: 12671ms (effective reasoning time: 11994ms)
% 28.85/13.19 % 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)>
% 28.85/13.19 % Axioms used in derivation (238): fact_9_lsorted_I3_J, fact_222_llexord_Ocoinduct, fact_206_llist_Oset__intros_I2_J, fact_25_lnull__lSup, fact_115_lhd__LCons, fact_117_llist_Ocollapse_I1_J, fact_167_lstrict__prefix__code_I1_J, fact_120_ltl__simps_I1_J, fact_245_compact__lfiniteD, fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062, fact_187_compact__LConsI, fact_179_ltakeWhile__eq__LNil__iff, fact_34_llist_Oleq__antisym, fact_173_lprefix__ltakeWhile, fact_82_lhd__LCons__ltl, fact_31_lappend_Oexhaust, fact_235_lprefix__lfiniteD, fact_119_llist_Odisc_I1_J, fact_130_ord_OatLeastAtMost__def, fact_0__092_060open_062xs_A_092_060in_062_AY_092_060close_062, fact_56_lprefix__ltlI, fact_15_local_OatLeastAtMost__iff, fact_203_llist_Oset__sel_I1_J, fact_188_compact__LConsD, fact_250_lfinite__imp__finite__lset, fact_62_LNil, fact_108_LCons__lprefix__conv, fact_215_ltakeWhile__cong, fact_131_ord_Olsorted__LCons_H, fact_159_Int__left__absorb, fact_174_llist__less__induct, fact_231_lfinite__LNil, fact_78_unfold__llist_Odisc__iff_I1_J, fact_99_ord_Olsorted_Ocoinduct, fact_21_chain, fact_224_lfinite__code_I2_J, fact_102_ord_Olsorted__code_I2_J, fact_7_local_Omin__def, fact_95_llist_Odistinct_I1_J, fact_44_Collect__mem__eq, fact_39_llist_Olub__upper, fact_193_llast__LCons2, fact_210_lset__induct_H, fact_116_lnull__def, fact_156_Int__assoc, fact_204_lset__intros_I2_J, fact_77_unfold__llist__eq__LCons, fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062xs_A_092_060in_062_AY_059_A_092_060not_062_Alnull_Axs_059_A_092_060not_062_Alnull_A_Iltl_Axs_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_132_ord_OatLeastAtMost__iff, fact_209_lset__induct, fact_30_lprefix__lnullD, fact_16__092_060open_062_092_060not_062_Alnull_Axs_092_060close_062, fact_87_lprefix_Osimps, fact_243_llimit__induct, fact_68_ord_OatMost__iff, fact_246_llexord_Ocases, fact_223_lfinite__LCons, fact_186_ltakeWhile_Octr_I2_J, fact_166_lstrict__prefix__code_I4_J, fact_178_lhd__ltakeWhile, fact_66_unfold__llist__id, fact_161_compact__LCons__iff, fact_35_lprefix__not__lnullD, fact_97_llist_Osimps_I5_J, fact_59_llist_Ocoinduct, fact_63_LCons__LCons, fact_199_ldistinct__coinduct, fact_207_llist_Oset__intros_I1_J, fact_76_lprefix__code_I1_J, fact_170_ltakeWhile_Odisc__iff_I1_J, fact_22_llist_Oexpand, fact_114_LNil__lprefix, fact_24_llist_Oleq__refl, fact_100_ord_Olsorted_Osimps, fact_38_chain__lSup__lprefix, fact_134_IntI, fact_18_local_OatMost__iff, fact_252_finite__Int, fact_171_lnull__ltakeWhile, fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J, fact_6_local_Omax__def, fact_229_lstrict__prefix__lfinite1, fact_50_lSup_Odisc_I1_J, fact_251_llist__gen__induct, fact_72_lsorted_Ocases, fact_192_ldistinct__LNil__code, fact_106_eq__LConsD, fact_103_ltl__unfold__llist, fact_26_lzip_Oexhaust, fact_216_lset__ltakeWhileD, fact_121_ord_Olsorted__LCons__LCons, fact_43_mem__Collect__eq, fact_253_llast__lappend__LCons, fact_155_IntD2, fact_60_local_OatLeastAtMost__def, fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062, fact_162_ltakeWhile_Ocode, fact_190_llast__singleton, fact_93_unfold__llist_Octr_I1_J, fact_55_ltakeWhile_Oexhaust, fact_10_lsorted_I4_J, fact_126_unfold__llist_Odisc_I2_J, help_If_1_1_T, fact_109_Le__LCons, fact_54_ord_Olsorted__lhdD, fact_83_lsorted__code_I1_J, fact_185_ltl__ltakeWhile, fact_168_ltakeWhile__LCons, fact_67_llist_Ocase__eq__if, fact_61_lsorted__LCons_H, fact_228_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps, fact_180_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def, fact_40_llist_Olub__least, fact_123_ord_OLNil, fact_96_llist_Osimps_I4_J, fact_28_lprefix__lnull, fact_89_lprefix__LCons__conv, fact_232_lnull__imp__lfinite, fact_105_llist_Osplit__sel__asm, fact_221_compact__eq__lfinite, fact_244_compact__lfiniteI, fact_153_IntE, fact_163_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J, fact_73_lsorted_Ocoinduct, fact_13_lsorted__ltlI, fact_41_lprefix__lhdD, fact_90_unfold__llist_Ocode, fact_196_ldistinct__lprefix, fact_237_llexord__LCons__less, fact_23_lprefix__refl, fact_69_ord_OatLeast__iff, fact_65_ord_Omin__def, fact_42_lhd__lSup__eq, fact_51_lSup_Odisc_I2_J, fact_129_lSup_Octr_I1_J, fact_234_not__lfinite__lprefix__conv__eq, fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062, fact_81_lsorted__LCons__LCons, fact_3_local_Oord__le__eq__trans, fact_191_cont__ltl, fact_202_llist_Oset__sel_I2_J, fact_113_ltl__simps_I2_J, fact_88_lprefix_Ocoinduct, fact_118_llist_OdiscI_I1_J, fact_160_Int__left__commute, fact_12_sorted, fact_57_ord_Olsorted__ltlI, fact_183_ltakeWhile_Octr_I1_J, fact_197_llast__LCons, fact_249_lfinite__lSup__chain, fact_177_ltakeWhile_Odisc_I1_J, fact_230_lfinite__lSupD, fact_8_lsorted_I2_J, fact_48_lprefix__expand, fact_217_llist__set__induct, fact_128_unfold__llist_Osimps_I3_J, fact_208_lset__cases, fact_27_lnull__lprefix, fact_37_chain__lprefix__lSup, fact_33_lprefix__antisym, fact_214_ltakeWhile__all, fact_219_ldistinct_Osimps, fact_52_lnull__ltlI, fact_241_lfinite_Osimps, help_If_3_1_T, fact_20_lsorted__lhdD, help_If_2_1_T, fact_169_ltakeWhile_Odisc__iff_I2_J, fact_53_ord_Olsorted__coinduct_H, fact_107_llist_Oexhaust__sel, fact_29_lprefix__trans, fact_74_lsorted_Osimps, fact_189_ldistinct__lSup, fact_91_neq__LNil__conv, fact_248_llist__induct, fact_225_lfinite__code_I1_J, fact_194_ldistinct__ltlI, fact_184_ltakeWhile_Osimps_I4_J, fact_165_ltakeWhile__LNil, fact_220_ldistinct_Ocoinduct, fact_195_ldistinct_OLNil, fact_84_lsorted__code_I2_J, fact_2_local_Oord__eq__le__trans, fact_49_lSup_Odisc__iff_I2_J, fact_175_lstrict__prefix__def, fact_238_llexord__LCons__eq, fact_80_lprefix__LNil, fact_79_unfold__llist_Odisc__iff_I2_J, fact_172_lstrict__prefix__code_I2_J, fact_164_lstrict__prefix__code_I3_J, fact_94_unfold__llist_Octr_I2_J, fact_47_lprefix__coinduct, fact_240_lfinite_Oinducts, fact_70_llist_Oinject, fact_154_IntD1, fact_112_llist_Odisc_I2_J, fact_205_lset__intros_I1_J, fact_45_Collect__cong, fact_226_lfinite__ltl, fact_75_LCons__lprefix__LCons, fact_92_llist_Oexhaust, fact_127_unfold__llist_Osimps_I4_J, fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J, fact_157_Int__absorb, fact_233_lfinite__LConsI, fact_239_lfinite__induct, fact_125_unfold__llist_Odisc_I1_J, fact_218_ldistinct_Ocases, fact_101_ord_Olsorted_Ocases, fact_158_Int__commute, fact_200_ldistinct__LCons, fact_133_Int__iff, fact_124_ord_Olsorted__code_I1_J, fact_198_ldistinct__lhdD, fact_227_lfinite__ltakeWhile, fact_212_llist_Oset__induct, fact_58_llist_Ocoinduct__strong, fact_19_lsorted__coinduct_H, fact_64_ord_Omax__def, fact_32_llist_Oleq__trans, fact_213_in__lset__ltlD, fact_104_llist_Osplit__sel, fact_71_Singleton, fact_122_ord_OLCons__LCons, fact_86_lprefix_Ocases, fact_85_lprefix__code_I2_J, fact_176_ltakeWhile_Odisc_I2_J, fact_111_llist_OdiscI_I2_J, fact_236_llexord__LNil, fact_247_llexord_Osimps, fact_110_not__lnull__conv, fact_11__092_060open_062_092_060not_062_Alnull_A_Iltl_Axs_J_092_060close_062, fact_17_local_OatLeast__iff, fact_211_llist_Oset__cases, fact_201_ldistinct_OLCons, fact_36_lprefix__down__linear, fact_242_lfinite_Ocases, fact_98_ord_OSingleton
% 28.85/13.19 % No. of inferences in proof: 480
% 28.85/13.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12671 ms resp. 11994 ms w/o parsing
% 29.98/13.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.98/13.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------