TSTP Solution File: DAT187^1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT187^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 07:39:42 EDT 2024
% Result : Theorem 19.59s 7.14s
% Output : Refutation 20.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 333
% Syntax : Number of formulae : 614 ( 181 unt; 54 typ; 0 def)
% Number of atoms : 2414 ( 408 equ; 4 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 9086 ( 138 ~; 20 |; 103 &;8089 @)
% ( 0 <=>; 736 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 199 ( 199 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 11 con; 0-5 aty)
% Number of variables : 1947 ( 70 ^1780 !; 51 ?;1947 :)
% ( 46 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(top_type,type,
top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_top_type,type,
order_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu328551480prefix_type,type,
coindu328551480prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lappend_type,type,
coinductive_lappend:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_llast_type,type,
coinductive_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(coinductive_LCons_type,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_LNil_type,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(coindu1478340336prefix_type,type,
coindu1478340336prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(lList2435255213lllsts_type,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2236698231inlsts_type,type,
lList2236698231inlsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21916056377ts_rec_type,type,
lList21916056377ts_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coinductive_llist @ TA ) > TB > TB ) > ( coinductive_llist @ TA ) > TB ) ).
thf(lList21202317876inpref_type,type,
lList21202317876inpref:
!>[TA: $tType] : ( ( set @ TA ) > ( coinductive_llist @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList22096119349pslsts_type,type,
lList22096119349pslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21015763786veness_type,type,
lList21015763786veness:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList21612149805nflsts_type,type,
lList21612149805nflsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21015939545safety_type,type,
lList21015939545safety:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList2649413865nfsuff_type,type,
lList2649413865nfsuff:
!>[TA: $tType] : ( ( set @ TA ) > ( coinductive_llist @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2370560421utlast_type,type,
lList2370560421utlast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList2508575361_ldrop_type,type,
lList2508575361_ldrop:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat > ( coinductive_llist @ TA ) ) ).
thf(lList21805353693veness_type,type,
lList21805353693veness:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList2170638824_llast_type,type,
lList2170638824_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(lList21232602520length_type,type,
lList21232602520length:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat ) ).
thf(lList2281150353e_lrev_type,type,
lList2281150353e_lrev:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList22119844313_ltake_type,type,
lList22119844313_ltake:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat > ( coinductive_llist @ TA ) ) ).
thf(lList2467029176inpref_type,type,
lList2467029176inpref:
!>[TA: $tType] : ( ( set @ TA ) > ( coinductive_llist @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21952340509veness_type,type,
lList21952340509veness:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList21148268032oslsts_type,type,
lList21148268032oslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList292406316safety_type,type,
lList292406316safety:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList21974196564closed_type,type,
lList21974196564closed:
!>[TA: $tType] : ( ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList21638733016closed_type,type,
lList21638733016closed:
!>[TA: $tType] : ( ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList21350011628safety_type,type,
lList21350011628safety:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(lList21475143548e_suff_type,type,
lList21475143548e_suff:
!>[TA: $tType] : ( ( set @ TA ) > ( coinductive_llist @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2736192599closed_type,type,
lList2736192599closed:
!>[TA: $tType] : ( ( set @ ( coinductive_llist @ TA ) ) > $o ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: set @ ( coinductive_llist @ a ) ).
thf(r_type,type,
r: coinductive_llist @ a ).
thf(s_type,type,
s: coinductive_llist @ a ).
thf(t_type,type,
t: coinductive_llist @ a ).
thf(u_type,type,
u: coinductive_llist @ a ).
thf(v_type,type,
v: coinductive_llist @ a ).
thf(134,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_finlsts_Ocases) ).
thf(645,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(259,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_subsetD) ).
thf(1036,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(128,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_UNIV__I) ).
thf(629,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(172,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_top__greatest) ).
thf(760,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(257,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Diff__iff) ).
thf(1031,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(209,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lappend__LNil2) ).
thf(893,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(224,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
=> ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_lapp__inv2T) ).
thf(941,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
=> ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_order__subst1) ).
thf(352,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(271,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Diff__subset) ).
thf(1083,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ord__eq__le__trans) ).
thf(468,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(173,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_alllsts_OLNil__all) ).
thf(762,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(308,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(165,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finlsts_OLNil__fin) ).
thf(741,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(203,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( member @ TA @ A @ C )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_LConsE) ).
thf(873,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( member @ TA @ A @ C )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_ord__le__eq__trans) ).
thf(379,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(145,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_subset__UNIV) ).
thf(677,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(261,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_lapp__fin__infT) ).
thf(1041,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(58,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_llist_Oinject) ).
thf(440,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(86,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2508575361_ldrop @ TA @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21232602520length @ TA @ A ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_lapp__suff__llength) ).
thf(511,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2508575361_ldrop @ TA @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21232602520length @ TA @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(82,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_lappend__is__LNil__conv) ).
thf(500,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(180,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
=> ( C @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_finlsts__induct) ).
thf(797,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
=> ( C @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(157,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_DiffE) ).
thf(715,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(72,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_diff__mono) ).
thf(472,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(215,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_alllsts_OLCons__all) ).
thf(913,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(97,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_lbutlast__snoc) ).
thf(538,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(142,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21202317876inpref @ TA @ B @ A ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2649413865nfsuff @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_infsuff__finpref__iff) ).
thf(670,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21202317876inpref @ TA @ B @ A ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2649413865nfsuff @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(263,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21475143548e_suff @ TA @ B @ A ) )
=> ~ ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ B ) )
=> ( C
!= ( coinductive_lappend @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_suff__appE) ).
thf(1046,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21475143548e_suff @ TA @ B @ A ) )
=> ~ ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ B ) )
=> ( C
!= ( coinductive_lappend @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ( order_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top) ).
thf(436,plain,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ( order_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(187,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_app__invT) ).
thf(829,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(276,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_ldrop__inf__iffT) ).
thf(1095,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TB ) > TA,B: TA,C: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( A
= ( lList21916056377ts_rec @ TA @ TB @ B @ C ) )
=> ( ( A @ ( coinductive_LNil @ TB ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_finlsts__rec__LNil__def) ).
thf(320,plain,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TB ) > TA,B: TA,C: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( A
= ( lList21916056377ts_rec @ TA @ TB @ B @ C ) )
=> ( ( A @ ( coinductive_LNil @ TB ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(105,axiom,
member @ ( coinductive_llist @ a ) @ r @ ( lList2467029176inpref @ a @ ( top_top @ ( set @ a ) ) @ s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062r_A_092_060in_062_Apfinpref_AUNIV_As_092_060close_062) ).
thf(565,plain,
member @ ( coinductive_llist @ a ) @ r @ ( lList2467029176inpref @ a @ ( top_top @ ( set @ a ) ) @ s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(266,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ D )
=> ( ( member @ TA @ E @ B )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_finlsts_Oinducts) ).
thf(1055,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ D )
=> ( ( member @ TA @ E @ B )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(124,axiom,
! [TA: $tType] : ( order @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Oorder_16) ).
thf(619,plain,
! [TA: $tType] : ( order @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(217,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_alllsts_Osimps) ).
thf(917,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(66,axiom,
top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_13) ).
thf(460,plain,
top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(212,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ D ) )
=> ( ( member @ TA @ C @ B )
=> ~ ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_fpslsts__cases) ).
thf(902,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ D ) )
=> ( ( member @ TA @ C @ B )
=> ~ ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(196,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21475143548e_suff @ TA @ B @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_suff__all) ).
thf(853,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21475143548e_suff @ TA @ B @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(416,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(6,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_le__cases3) ).
thf(289,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(448,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(278,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_finT__simp) ).
thf(1100,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(250,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA ),C: coinductive_llist @ TA] :
( ( lList292406316safety @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_possafetyD) ).
thf(1013,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA ),C: coinductive_llist @ TA] :
( ( lList292406316safety @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(4,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ! [C: coinductive_llist @ TA] :
( ! [D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_llist__less__induct) ).
thf(284,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ! [C: coinductive_llist @ TA] :
( ! [D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( A
!= ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_llistE) ).
thf(443,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( A
!= ( coinductive_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(34,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_order__class_Oorder_Oantisym) ).
thf(376,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(87,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21202317876inpref @ TA @ C @ A ) @ ( lList21202317876inpref @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_finpref__mono2) ).
thf(514,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21202317876inpref @ TA @ C @ A ) @ ( lList21202317876inpref @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(253,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_notinf__fin) ).
thf(1020,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(184,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_llist__le__anti__sym) ).
thf(821,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(175,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA ),C: coinductive_llist @ TA] :
( ( lList21805353693veness @ TA @ A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
=> ~ ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) )
=> ~ ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_livenessE) ).
thf(766,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA ),C: coinductive_llist @ TA] :
( ( lList21805353693veness @ TA @ A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
=> ~ ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) )
=> ~ ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(130,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_inflstsE) ).
thf(634,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_top__apply) ).
thf(866,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(39,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_order_Otrans) ).
thf(396,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(92,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Diff__mono) ).
thf(527,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(267,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_lappend__snocL1__conv__LCons2) ).
thf(1072,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(63,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_le__cases) ).
thf(453,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(218,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) )
=> ( lList292406316safety @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_possafetyI) ).
thf(920,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) )
=> ( lList292406316safety @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(93,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ B ) @ ( lList2281150353e_lrev @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_lrev__lappend) ).
thf(529,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ B ) @ ( lList2281150353e_lrev @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(219,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_rev__subsetD) ).
thf(925,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(181,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= C ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( lList2170638824_llast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_LList2__Mirabelle__hamjzmohle_Ollast__LCons) ).
thf(810,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= C ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( lList2170638824_llast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_contra__subsetD) ).
thf(534,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(214,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_UNIV__eq__I) ).
thf(910,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(230,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_in__mono) ).
thf(957,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(228,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_top_Oextremum__uniqueI) ).
thf(952,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(24,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_47_Collect__cong) ).
thf(349,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)],[24]) ).
thf(119,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_finlsts__rev__cases) ).
thf(598,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(44,axiom,
! [TA: $tType,A: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_LList2__Mirabelle__hamjzmohle_Oltake__LNil) ).
thf(407,plain,
! [TA: $tType,A: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(178,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_fin__finite) ).
thf(788,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(161,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_llist__le__refl) ).
thf(729,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(167,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_lappend__eq__LNil__iff) ).
thf(746,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(274,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_ldrop__finT) ).
thf(1091,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(70,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_10) ).
thf(467,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_diff__eq__diff__less__eq) ).
thf(361,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(205,axiom,
member @ ( coinductive_llist @ a ) @ t @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tP) ).
thf(879,plain,
member @ ( coinductive_llist @ a ) @ t @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(17,axiom,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_lbutlast__LNil) ).
thf(329,plain,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(140,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(665,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(90,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_8) ).
thf(522,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(67,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).
thf(461,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(79,axiom,
! [TA: $tType] :
( ( lList21974196564closed @ TA )
= ( ^ [A: set @ ( coinductive_llist @ TA )] :
! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ! [C: coinductive_llist @ TA] :
( ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ B )
& ( C
!= ( coinductive_LNil @ TA ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_pprefix__closed__def) ).
thf(493,plain,
! [TA: $tType] :
( ( lList21974196564closed @ TA )
= ( ^ [A: set @ ( coinductive_llist @ TA )] :
! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ! [C: coinductive_llist @ TA] :
( ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ B )
& ( C
!= ( coinductive_LNil @ TA ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(171,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( lList2281150353e_lrev @ TA @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_lrev__is__lrev__conv) ).
thf(757,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( lList2281150353e_lrev @ TA @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(101,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LNil @ TA ) ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LCons @ TA @ C @ ( lList2370560421utlast @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_lbutlast__LCons) ).
thf(551,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LNil @ TA ) ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LCons @ TA @ C @ ( lList2370560421utlast @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(192,axiom,
! [TA: $tType] :
( ( lList21015939545safety @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList21612149805nflsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_infsafety__def) ).
thf(842,plain,
! [TA: $tType] :
( ( lList21015939545safety @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList21612149805nflsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_lstrict__prefix__code_I3_J) ).
thf(324,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(194,axiom,
! [TA: $tType] :
( ( lList21952340509veness @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList22096119349pslsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_posliveness__def) ).
thf(847,plain,
! [TA: $tType] :
( ( lList21952340509veness @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList22096119349pslsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(106,axiom,
lList292406316safety @ a @ ( top_top @ ( set @ a ) ) @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_psafety) ).
thf(566,plain,
lList292406316safety @ a @ ( top_top @ ( set @ a ) ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(151,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_top__empty__eq) ).
thf(697,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(239,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_iso__tuple__UNIV__I) ).
thf(980,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(247,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_lapp__infT) ).
thf(1006,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(201,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_alllstsE) ).
thf(869,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(50,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_diff__left__mono) ).
thf(420,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(242,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_poslsts__iff) ).
thf(989,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(198,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ A )
=> ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ C ) ) )
=> ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_prefix__lemma) ).
thf(857,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ A )
=> ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ C ) ) )
=> ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(89,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_lrev__is__LNil__conv) ).
thf(519,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TB,D: TA > ( coinductive_llist @ TA ) > TB > TB,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21916056377ts_rec @ TB @ TA @ C @ D @ ( coinductive_LCons @ TA @ E @ A ) )
= ( D @ E @ A @ ( lList21916056377ts_rec @ TB @ TA @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_finlsts__rec__LCons) ).
thf(578,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TB,D: TA > ( coinductive_llist @ TA ) > TB > TB,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21916056377ts_rec @ TB @ TA @ C @ D @ ( coinductive_LCons @ TA @ E @ A ) )
= ( D @ E @ A @ ( lList21916056377ts_rec @ TB @ TA @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(256,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Collect__mono__iff) ).
thf(1028,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_le__fun__def) ).
thf(339,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(133,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_top_Oextremum__unique) ).
thf(642,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( coinductive_LCons @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_lappend__code_I2_J) ).
thf(637,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( coinductive_LCons @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(77,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21475143548e_suff @ TA @ C @ B ) @ ( lList21475143548e_suff @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_suff__mono2) ).
thf(489,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21475143548e_suff @ TA @ C @ B ) @ ( lList21475143548e_suff @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(251,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_UNIV__witness) ).
thf(1016,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(154,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) )
=> ( lList21350011628safety @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_safetyI) ).
thf(706,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) )
=> ( lList21350011628safety @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(149,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ C ) ) )
& ( member @ TA @ F @ C ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_alllsts_Ocoinduct) ).
thf(686,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ C ) ) )
& ( member @ TA @ F @ C ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(268,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2281150353e_lrev @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_lrevT) ).
thf(1075,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2281150353e_lrev @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_ord__eq__le__subst) ).
thf(476,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(146,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_DiffD1) ).
thf(679,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(235,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList22096119349pslsts @ TA @ A ) @ ( lList22096119349pslsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_fpslsts__mono) ).
thf(970,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList22096119349pslsts @ TA @ A ) @ ( lList22096119349pslsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(38,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_neq__LNil__conv) ).
thf(393,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(241,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_equalityD2) ).
thf(985,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(136,axiom,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_lappend__LNil__LNil) ).
thf(654,plain,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21612149805nflsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_inflsts__mono) ).
thf(569,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21612149805nflsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(264,axiom,
! [TA: $tType,A: set @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList21475143548e_suff @ TA @ A @ B ) )
= ( B
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_LNil__suff) ).
thf(1050,plain,
! [TA: $tType,A: set @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList21475143548e_suff @ TA @ A @ B ) )
= ( B
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(65,axiom,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_llast__singleton) ).
thf(457,plain,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(83,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( coinductive_lappend @ TA @ A @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_lapp__inf) ).
thf(503,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( coinductive_lappend @ TA @ A @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(120,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_set__mp) ).
thf(605,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(28,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).
thf(360,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(98,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Collect__mono) ).
thf(541,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(137,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_7) ).
thf(657,plain,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(40,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_order__trans) ).
thf(398,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(115,axiom,
( s
!= ( coinductive_LNil @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_spos) ).
thf(586,plain,
( s
!= ( coinductive_LNil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(139,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList22119844313_ltake @ TA @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21232602520length @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_ltake__lappend__llength) ).
thf(662,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList22119844313_ltake @ TA @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21232602520length @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(158,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inflstsI) ).
thf(718,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(52,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_dual__order_Otrans) ).
thf(425,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(54,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_antisym__conv) ).
thf(430,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(280,axiom,
! [TA: $tType] :
( ( lList21638733016closed @ TA )
= ( ^ [A: set @ ( coinductive_llist @ TA )] :
! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ! [C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_prefix__closed__def) ).
thf(1103,plain,
! [TA: $tType] :
( ( lList21638733016closed @ TA )
= ( ^ [A: set @ ( coinductive_llist @ TA )] :
! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ! [C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(185,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2649413865nfsuff @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21202317876inpref @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_infsuff__finpref) ).
thf(824,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2649413865nfsuff @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21202317876inpref @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(110,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_lappfin__finT) ).
thf(573,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(114,axiom,
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062) ).
thf(584,plain,
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(150,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_top__set__def) ).
thf(694,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(166,axiom,
! [TA: $tType] :
( ( ord_less @ ( coinductive_llist @ TA ) )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
& ~ ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_llist__less__le__not__le) ).
thf(743,plain,
! [TA: $tType] :
( ( ord_less @ ( coinductive_llist @ TA ) )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
& ~ ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1,conjecture,
? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(281,plain,
~ ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA] :
( ( lList2649413865nfsuff @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( lList21612149805nflsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_infsuff__LNil) ).
thf(413,plain,
! [TA: $tType,A: set @ TA] :
( ( lList2649413865nfsuff @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( lList21612149805nflsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(104,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( coinductive_lappend @ TA @ A @ C )
= ( coinductive_lappend @ TA @ A @ D ) )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_same__lappend__eq) ).
thf(562,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( coinductive_lappend @ TA @ A @ C )
= ( coinductive_lappend @ TA @ A @ D ) )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(237,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ( A
= ( coinductive_lappend @ TA @ ( lList2370560421utlast @ TA @ A ) @ ( coinductive_LCons @ TA @ ( lList2170638824_llast @ TA @ A ) @ ( coinductive_LNil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_lbutlast__lapp__llast) ).
thf(975,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ( A
= ( coinductive_lappend @ TA @ ( lList2370560421utlast @ TA @ A ) @ ( coinductive_LCons @ TA @ ( lList2170638824_llast @ TA @ A ) @ ( coinductive_LNil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ( lList21350011628safety @ TA @ A @ B )
=> ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_safetyE) ).
thf(826,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ( lList21350011628safety @ TA @ A @ B )
=> ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(155,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_subset__trans) ).
thf(711,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(153,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_llist__less__finT) ).
thf(704,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(226,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_lappend__code_I1_J) ).
thf(947,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(156,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_top1I) ).
thf(713,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(81,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_fin__inf__cases) ).
thf(498,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(174,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_infsubsetall) ).
thf(764,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(188,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_lappT) ).
thf(831,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(147,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_set__eq__subset) ).
thf(681,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(163,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ A ) @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_lrev__LCons) ).
thf(736,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ A ) @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(107,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_take__fin) ).
thf(567,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(12,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_dual__order_Orefl) ).
thf(318,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(249,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_infT__simp) ).
thf(1011,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(49,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_12) ).
thf(419,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(85,axiom,
! [TA: $tType] : ( preorder @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Opreorder_15) ).
thf(509,plain,
! [TA: $tType] : ( preorder @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(206,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ ( coinductive_lappend @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_le__lappend) ).
thf(880,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ ( coinductive_lappend @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(262,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( coinductive_LNil @ TA )
= ( lList2281150353e_lrev @ TA @ A ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_LNil__is__lrev__conv) ).
thf(1043,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( coinductive_LNil @ TA )
= ( lList2281150353e_lrev @ TA @ A ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(123,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_notfin__inf) ).
thf(616,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(7,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(303,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(270,axiom,
! [TA: $tType] :
( ( lList21350011628safety @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_safety__def) ).
thf(1080,plain,
! [TA: $tType] :
( ( lList21350011628safety @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(129,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
= ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21475143548e_suff @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_suff__finpref__iff) ).
thf(631,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
= ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21475143548e_suff @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(22,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_14) ).
thf(345,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(182,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( ord_less_eq @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_not__LCons__le__LNil) ).
thf(816,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( ord_less_eq @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(125,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_subset__iff) ).
thf(621,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(75,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( suc @ C ) )
= ( coinductive_LCons @ TA @ A @ ( lList22119844313_ltake @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_ltake__LCons__Suc) ).
thf(483,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( suc @ C ) )
= ( coinductive_LCons @ TA @ A @ ( lList22119844313_ltake @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(152,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_equalityD1) ).
thf(700,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(233,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_top__conj_I2_J) ).
thf(964,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(216,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] : ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ltake__fin) ).
thf(915,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] : ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(176,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_lrev__induct) ).
thf(769,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(141,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_4) ).
thf(668,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(68,axiom,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_lstrict__prefix__code_I1_J) ).
thf(462,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(222,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( A != C )
=> ~ ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ A )
=> ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_inf__neqE) ).
thf(932,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( A != C )
=> ~ ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ A )
=> ( ord_less_eq @ ( coinductive_llist @ TA ) @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(231,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite__lemma) ).
thf(959,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__funE) ).
thf(455,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(245,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA ),C: coinductive_llist @ TA] :
( ( lList21350011628safety @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_safetyD) ).
thf(1000,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA ),C: coinductive_llist @ TA] :
( ( lList21350011628safety @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21202317876inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(279,axiom,
ord_less_eq @ ( coinductive_llist @ a ) @ s @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_st) ).
thf(1102,plain,
ord_less_eq @ ( coinductive_llist @ a ) @ s @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(57,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_order__refl) ).
thf(438,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(258,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_6) ).
thf(1034,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(144,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_finpref__fin) ).
thf(675,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(116,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ C )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_llist__inf__le) ).
thf(589,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ C )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(225,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_finlsts_Osimps) ).
thf(944,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(100,axiom,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_inflsts__def) ).
thf(548,plain,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(220,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_alllsts__mono) ).
thf(927,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(168,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
? [C: coinductive_llist @ TA] :
( B
= ( coinductive_lappend @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_llist__le__def) ).
thf(749,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
? [C: coinductive_llist @ TA] :
( B
= ( coinductive_lappend @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_subsetI) ).
thf(516,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(223,axiom,
! [TA: $tType] : ( ord @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Oord_17) ).
thf(939,plain,
! [TA: $tType] : ( ord @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(21,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ D ) )
& ( coindu328551480prefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(342,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ D ) )
& ( coindu328551480prefix @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(252,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21475143548e_suff @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finpref__suff) ).
thf(1018,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21475143548e_suff @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(26,axiom,
! [TA: $tType,A: nat,B: nat,C: coinductive_llist @ TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( lList2508575361_ldrop @ TA @ C @ A )
= ( coinductive_LNil @ TA ) )
=> ( ( lList2508575361_ldrop @ TA @ C @ B )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_ldrop__LNil__less) ).
thf(355,plain,
! [TA: $tType,A: nat,B: nat,C: coinductive_llist @ TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( lList2508575361_ldrop @ TA @ C @ A )
= ( coinductive_LNil @ TA ) )
=> ( ( lList2508575361_ldrop @ TA @ C @ B )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(170,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_lapp__allT__iff) ).
thf(754,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(190,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_le__LNil) ).
thf(836,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(197,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_ldrop__infT) ).
thf(855,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(132,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_finsubsetall) ).
thf(640,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(255,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_subset__antisym) ).
thf(1025,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_le__funD) ).
thf(327,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(164,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_DiffD2) ).
thf(739,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(102,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_double__diff) ).
thf(557,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(246,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_lappend__assoc) ).
thf(1003,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(277,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2649413865nfsuff @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_finpref__infsuff) ).
thf(1098,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2649413865nfsuff @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(10,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_wlog__linorder__le) ).
thf(310,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(265,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_lapp__all__invT) ).
thf(1053,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(143,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21475143548e_suff @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21202317876inpref @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_suff__finpref) ).
thf(673,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21475143548e_suff @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21202317876inpref @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(272,axiom,
! [TA: $tType] :
( ( lList21015763786veness @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_infliveness__def) ).
thf(1085,plain,
! [TA: $tType] :
( ( lList21015763786veness @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(260,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_subset__eq) ).
thf(1038,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(32,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_antisym) ).
thf(370,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TA ) > TB,B: TB,C: TA > ( coinductive_llist @ TA ) > TB > TB,D: coinductive_llist @ TA,E: set @ TA,F: TA] :
( ( A
= ( lList21916056377ts_rec @ TB @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ E ) )
=> ( ( A @ ( coinductive_LCons @ TA @ F @ D ) )
= ( C @ F @ D @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_finlsts__rec__LCons__def) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TA ) > TB,B: TB,C: TA > ( coinductive_llist @ TA ) > TB > TB,D: coinductive_llist @ TA,E: set @ TA,F: TA] :
( ( A
= ( lList21916056377ts_rec @ TB @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ E ) )
=> ( ( A @ ( coinductive_LCons @ TA @ F @ D ) )
= ( C @ F @ D @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(213,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_LNil__eq__lappend__iff) ).
thf(907,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(254,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ C )
=> ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_llist__le__trans) ).
thf(1023,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ C )
=> ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(199,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_set__rev__mp) ).
thf(864,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(160,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_alllsts__UNIV) ).
thf(727,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(238,axiom,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( lList21350011628safety @ TA @ ( top_top @ ( set @ TA ) ) @ A )
=> ( lList21638733016closed @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_safety__prefix__closed) ).
thf(978,plain,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( lList21350011628safety @ TA @ ( top_top @ ( set @ TA ) ) @ A )
=> ( lList21638733016closed @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(118,axiom,
! [TA: $tType] :
( ( lList21805353693veness @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_liveness__def) ).
thf(595,plain,
! [TA: $tType] :
( ( lList21805353693veness @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(122,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2649413865nfsuff @ TA @ B @ A ) )
=> ~ ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( C
!= ( coinductive_lappend @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_infsuff__appE) ).
thf(612,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2649413865nfsuff @ TA @ B @ A ) )
=> ~ ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( C
!= ( coinductive_lappend @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(204,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) )
=> ( lList21805353693veness @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_livenessI) ).
thf(876,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ A ) )
=> ? [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ C @ D ) @ B ) ) )
=> ( lList21805353693veness @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(60,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_lift__Suc__mono__le) ).
thf(446,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( ord_less @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_LNil__less__LCons) ).
thf(571,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( ord_less @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(193,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_finlsts_OLCons__fin) ).
thf(845,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(127,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2649413865nfsuff @ TA @ B @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_infsuff__inf) ).
thf(627,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2649413865nfsuff @ TA @ B @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(62,axiom,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_lrev__LNil) ).
thf(450,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(208,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_ldropT) ).
thf(891,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(31,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_linear) ).
thf(368,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(91,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_lapp__fin__fin__iff) ).
thf(524,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(113,axiom,
! [TA: $tType] :
( ( lList292406316safety @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_possafety__def) ).
thf(581,plain,
! [TA: $tType] :
( ( lList292406316safety @ TA )
= ( ^ [A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(232,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_fpslsts__iff) ).
thf(961,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(210,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2467029176inpref @ TA @ B @ C ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_pfinpref__iff) ).
thf(896,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2467029176inpref @ TA @ B @ C ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21202317876inpref @ TA @ B @ C ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(135,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_lapp__fin__fin__lemma) ).
thf(652,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(37,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( ( lList2508575361_ldrop @ TA @ A @ B )
!= ( coinductive_LNil @ TA ) )
=> ( ( lList21232602520length @ TA @ ( lList22119844313_ltake @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_llength__drop__take) ).
thf(390,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( ( lList2508575361_ldrop @ TA @ A @ B )
!= ( coinductive_LNil @ TA ) )
=> ( ( lList21232602520length @ TA @ ( lList22119844313_ltake @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( ( lList2508575361_ldrop @ TA @ A @ B )
!= ( coinductive_LNil @ TA ) )
=> ( A
!= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_drop__nonLNil) ).
thf(401,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( ( lList2508575361_ldrop @ TA @ A @ B )
!= ( coinductive_LNil @ TA ) )
=> ( A
!= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(244,axiom,
~ ! [A: coinductive_llist @ a] :
( t
!= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_At_A_061_Ar_A_064_064_Au_A_064_064_Av_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(995,plain,
~ ! [A: coinductive_llist @ a] :
( t
!= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(162,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_inflsts__cases) ).
thf(731,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(48,axiom,
order_top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_9) ).
thf(418,plain,
order_top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_subset__refl) ).
thf(786,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(55,axiom,
! [TA: $tType,A: nat] :
( ( lList2508575361_ldrop @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_LList2__Mirabelle__hamjzmohle_Oldrop__LNil) ).
thf(433,plain,
! [TA: $tType,A: nat] :
( ( lList2508575361_ldrop @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(221,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_llast__snoc) ).
thf(929,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(269,axiom,
! [TA: $tType,A: set @ TA] :
( ( lList21475143548e_suff @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_suff__LNil) ).
thf(1077,plain,
! [TA: $tType,A: set @ TA] :
( ( lList21475143548e_suff @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ord__le__eq__subst) ).
thf(383,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(211,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_le__LCons) ).
thf(899,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(148,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_5) ).
thf(684,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1478340336prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_lstrict__prefix__code_I4_J) ).
thf(346,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1478340336prefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(96,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_finlsts__mono) ).
thf(536,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(5,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_lift__Suc__antimono__le) ).
thf(287,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(169,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21148268032oslsts @ TA @ A ) @ ( lList21148268032oslsts @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_poslsts__mono) ).
thf(752,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList21148268032oslsts @ TA @ A ) @ ( lList21148268032oslsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_llast__LCons2) ).
thf(315,plain,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(227,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( ord_less_eq @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_LNil__le) ).
thf(950,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( ord_less_eq @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(183,axiom,
! [TA: $tType] :
( ( ord_less @ ( coinductive_llist @ TA ) )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_llist__less__def) ).
thf(818,plain,
! [TA: $tType] :
( ( ord_less @ ( coinductive_llist @ TA ) )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_lstrict__prefix__code_I2_J) ).
thf(405,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(33,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_eq__iff) ).
thf(373,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(189,axiom,
! [TA: $tType] :
( ( lList2736192599closed @ TA )
= ( ^ [A: set @ ( coinductive_llist @ TA )] :
! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ! [C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ C )
=> ( member @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_suffix__closed__def) ).
thf(833,plain,
! [TA: $tType] :
( ( lList2736192599closed @ TA )
= ( ^ [A: set @ ( coinductive_llist @ TA )] :
! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ! [C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ B @ C )
=> ( member @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(45,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_dual__order_Oantisym) ).
thf(410,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(234,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_top__conj_I1_J) ).
thf(967,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( lList21916056377ts_rec @ TA @ TB @ A @ B @ ( coinductive_LNil @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_finlsts__rec__LNil) ).
thf(422,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( lList21916056377ts_rec @ TA @ TB @ A @ B @ ( coinductive_LNil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(179,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_alllsts_Ocases) ).
thf(790,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_llist_Odistinct_I1_J) ).
thf(305,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
preorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).
thf(326,plain,
preorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(84,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( lList2281150353e_lrev @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_lrev__lrev__ident) ).
thf(506,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( lList2281150353e_lrev @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(358,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_diff__right__mono) ).
thf(474,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_11) ).
thf(400,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(94,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ord_less @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_take__inf__less) ).
thf(532,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ord_less @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_equalityE) ).
thf(720,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(229,axiom,
( s
= ( coinductive_lappend @ a @ r @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_scons) ).
thf(955,plain,
( s
= ( coinductive_lappend @ a @ r @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(3,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(283,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(464,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(18,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_linorder__wlog) ).
thf(332,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(111,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ord_less @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( ord_less @ ( coinductive_llist @ TA ) @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_less__LCons) ).
thf(575,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ord_less @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( ord_less @ ( coinductive_llist @ TA ) @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_order__subst2) ).
thf(427,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(243,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_LNil__is__lappend__conv) ).
thf(992,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(195,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( A
!= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_poslsts__UNIV) ).
thf(850,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( A
!= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(240,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( coinductive_lappend @ TA @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2508575361_ldrop @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_ltake__ldrop__id) ).
thf(982,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( coinductive_lappend @ TA @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2508575361_ldrop @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_DiffI) ).
thf(871,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(121,axiom,
~ ! [A: coinductive_llist @ a] :
( s
!= ( coinductive_lappend @ a @ r @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062u_O_As_A_061_Ar_A_064_064_Au_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(607,plain,
~ ! [A: coinductive_llist @ a] :
( s
!= ( coinductive_lappend @ a @ r @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(275,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2649413865nfsuff @ TA @ C @ B ) @ ( lList2649413865nfsuff @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_infsuff__mono2) ).
thf(1093,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2649413865nfsuff @ TA @ C @ B ) @ ( lList2649413865nfsuff @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(126,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( suc @ ( lList21232602520length @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_LList2__Mirabelle__hamjzmohle_Ollength__LCons) ).
thf(624,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( suc @ ( lList21232602520length @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(191,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) )
= ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_LList2__Mirabelle__hamjzmohle_Ollast__lappend) ).
thf(839,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) )
= ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(76,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ( lList292406316safety @ TA @ A @ B )
=> ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_possafetyE) ).
thf(486,plain,
! [TA: $tType,A: set @ TA,B: set @ ( coinductive_llist @ TA )] :
( ( lList292406316safety @ TA @ A @ B )
=> ! [C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21148268032oslsts @ TA @ A ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2467029176inpref @ TA @ A @ C ) )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ A ) )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ D @ E ) @ B ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_le__funI) ).
thf(337,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(248,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_llist__le__finT) ).
thf(1009,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Diff__idemp) ).
thf(659,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_inflstsI2) ).
thf(560,plain,
! [TA: $tType,A: TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(117,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ldrop__fin__iffT) ).
thf(592,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(80,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ C )
| ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_pref__locally__linear) ).
thf(496,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( coinductive_llist @ TA ) @ A @ C )
| ( ord_less_eq @ ( coinductive_llist @ TA ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(30,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_eq__refl) ).
thf(364,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(207,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList22096119349pslsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_fps__induct) ).
thf(882,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList22096119349pslsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(236,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(972,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(78,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_subsetCE) ).
thf(491,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(273,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( lList22119844313_ltake @ TA @ A @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_llength__take) ).
thf(1088,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( lList22119844313_ltake @ TA @ A @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1106,plain,
$false,
inference(e,[status(thm)],[645,1036,629,760,1031,893,941,352,1083,468,762,308,741,873,379,677,1041,440,511,500,797,715,472,913,538,670,1046,436,829,1095,320,565,1055,619,917,460,902,853,416,289,448,1100,1013,284,443,376,514,1020,821,766,634,866,396,527,1072,453,920,529,925,810,534,910,957,952,349,598,407,788,729,746,1091,467,361,879,329,665,522,461,493,757,551,842,324,847,566,697,980,1006,869,420,989,857,519,578,1028,339,642,637,489,1016,706,686,1075,476,679,970,393,985,654,569,1050,457,503,605,360,541,657,398,586,662,718,425,430,1103,824,573,584,694,743,281,413,562,975,826,711,704,947,713,498,764,831,681,736,567,318,1011,419,509,880,1043,616,303,1080,631,345,816,621,483,700,964,915,769,668,462,932,959,455,1000,1102,438,1034,675,589,944,548,927,749,516,939,342,1018,355,754,836,855,640,1025,327,739,557,1003,1098,310,1053,673,1085,1038,370,544,907,1023,864,727,978,595,612,876,446,571,845,627,450,891,368,524,581,961,896,652,390,401,995,731,418,786,433,929,1077,383,899,684,346,536,287,752,315,950,818,405,373,833,410,967,422,790,305,326,506,358,474,400,532,720,955,283,464,332,575,427,992,850,982,871,607,1093,624,839,486,337,1009,659,560,592,496,364,882,972,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT187^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 11:33:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 1.00/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.17 % [INFO] Parsing done (282ms).
% 1.59/1.18 % [INFO] Running in sequential loop mode.
% 2.67/1.42 % [INFO] eprover registered as external prover.
% 2.67/1.42 % [INFO] cvc4 registered as external prover.
% 2.67/1.43 % [INFO] Scanning for conjecture ...
% 3.05/1.53 % [INFO] Found a conjecture and 279 axioms. Running axiom selection ...
% 3.36/1.62 % [INFO] Axiom selection finished. Selected 278 axioms (removed 1 axioms).
% 4.03/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 4.03/1.81 % [INFO] Type checking passed.
% 4.14/1.81 % [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 ...
% 19.59/7.14 % External prover 'e' found a proof!
% 19.59/7.14 % [INFO] Killing All external provers ...
% 19.59/7.14 % Time passed: 6623ms (effective reasoning time: 5960ms)
% 19.59/7.14 % 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)>
% 19.59/7.14 % Axioms used in derivation (278): fact_15_UNIV__witness, fact_233_Diff__iff, fact_163_finlsts_Osimps, fact_150_Collect__mono, fact_49_same__lappend__eq, fact_135_LList2__Mirabelle__hamjzmohle_Oltake__LNil, fact_100_finpref__fin, fact_223_lstrict__prefix__code_I4_J, fact_109_LNil__is__lrev__conv, fact_194_lapp__fin__infT, fact_154_Collect__mono__iff, fact_137_lbutlast__snoc, tcon_HOL_Obool___Orderings_Olinorder_11, tcon_Nat_Onat___Orderings_Oorder_2, fact_228_finlsts__rec__LNil__def, fact_87_llist__le__trans, fact_171_infsuff__mono2, fact_218_ldrop__LNil__less, fact_245_diff__left__mono, fact_2_psafety, fact_229_finlsts__rec__LNil, fact_141_subsetCE, fact_114_lrev__is__lrev__conv, fact_192_inflsts__cases, tcon_HOL_Obool___Orderings_Oorder__top_9, fact_221_lstrict__prefix__code_I3_J, fact_201_inflsts__mono, fact_140_subsetD, fact_143_subset__eq, fact_187_infsuff__inf, fact_250_llast__LCons2, fact_243_lift__Suc__mono__le, fact_120_subset__UNIV, fact_17_suff__all, tcon_Nat_Onat___Orderings_Olinorder, fact_176_lbutlast__lapp__llast, fact_0_tP, fact_156_neq__LNil__conv, fact_118_fpslsts__mono, fact_197_app__invT, fact_188_infT__simp, fact_77_order__class_Oorder_Oantisym, fact_208_infsafety__def, fact_14_UNIV__eq__I, fact_200_inf__neqE, fact_36_order__refl, fact_235_ltake__LCons__Suc, fact_7_lappT, fact_207_infsuff__appE, fact_183_notinf__fin, fact_16_posliveness__def, fact_96_top_Oextremum__unique, fact_167_alllsts_Ocoinduct, fact_173_finlsts__rev__cases, fact_219_ltake__ldrop__id, fact_75_ord__eq__le__trans, fact_29_possafetyE, fact_191_inflstsI2, tcon_fun___Orderings_Oord, fact_90_fin__finite, fact_110_lrev__is__LNil__conv, fact_71_le__cases, fact_160_lappend__snocL1__conv__LCons2, fact_175_LList2__Mirabelle__hamjzmohle_Ollast__lappend, fact_88_llist__le__finT, fact_94_finsubsetall, fact_99_llist__le__def, fact_41_lappend__code_I1_J, fact_30_possafetyD, fact_155_llistE, fact_74_antisym__conv, fact_232_DiffI, fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062u_O_As_A_061_Ar_A_064_064_Au_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_227_finlsts__rec__LCons__def, fact_79_dual__order_Orefl, fact_122_suff__mono2, fact_199_prefix__lemma, fact_67_antisym, tcon_Coinductive__List_Ollist___Orderings_Oord_17, fact_80_linorder__wlog, fact_55_poslsts__UNIV, fact_58_le__funD, fact_185_llength__take, fact_119_poslsts__mono, fact_21_spos, fact_190_infsubsetall, fact_222_lstrict__prefix__code_I2_J, fact_54_LNil__suff, fact_64_ord__eq__le__subst, fact_107_suffix__closed__def, fact_133_LConsE, fact_112_lrev__LNil, fact_68_linear, fact_181_lapp__inf, fact_105_livenessI, fact_152_set__eq__subset, fact_46_Collect__mem__eq, fact_148_rev__subsetD, fact_27_possafety__def, fact_206_lapp__allT__iff, fact_95_top__greatest, fact_72_order_Otrans, fact_126_infsuff__finpref, fact_255_llist__less__le__not__le, fact_91_lappfin__finT, fact_3_scons, fact_214_ldrop__infT, fact_158_finlsts_OLCons__fin, fact_217_drop__nonLNil, fact_132_lappend__code_I2_J, fact_172_lrev__induct, fact_40_lappend__is__LNil__conv, fact_115_lrev__lrev__ident, fact_249_take__inf__less, fact_116_finlsts__mono, fact_144_equalityD1, fact_166_alllsts_Osimps, fact_231_LList2__Mirabelle__hamjzmohle_Ollength__LCons, fact_43_LNil__eq__lappend__iff, fact_23_top__set__def, fact_149_subset__refl, fact_186_inflstsI, fact_22_st, fact_6__092_060open_062r_A_092_060in_062_Apfinpref_AUNIV_As_092_060close_062, tcon_Set_Oset___Orderings_Oorder_6, fact_180_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062, fact_204_finpref__infsuff, fact_121_finpref__mono2, fact_42_lappend__LNil2, tcon_HOL_Obool___Orderings_Oorder_12, tcon_HOL_Obool___Orderings_Oord_14, fact_251_less__LCons, fact_169_fps__induct, fact_52_LNil__le, fact_45_mem__Collect__eq, fact_179_infsuff__finpref__iff, tcon_HOL_Obool___Orderings_Opreorder_10, fact_203_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, fact_44_lappend__eq__LNil__iff, fact_242_lift__Suc__antimono__le, fact_89_finT__simp, fact_101_alllsts_OLNil__all, fact_111_top__conj_I2_J, fact_209_infliveness__def, fact_161_finlsts_Oinducts, fact_20_safetyI, fact_226_finlsts__rec__LCons, fact_26_safety__prefix__closed, fact_215_ldropT, fact_202_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, fact_205_inflstsE, fact_146_set__rev__mp, fact_157_llist_Odistinct_I1_J, fact_37_llist__le__refl, tcon_Nat_Onat___Orderings_Oord_3, tcon_Coinductive__List_Ollist___Orderings_Opreorder_15, fact_128_lbutlast__LNil, fact_244_diff__mono, fact_70_wlog__linorder__le, fact_247_diff__right__mono, fact_97_top_Oextremum__uniqueI, fact_113_lrevT, fact_124_lrev__LCons, fact_5_alllsts__UNIV, fact_47_Collect__cong, fact_83_pref__locally__linear, fact_210_llength__drop__take, fact_25_safety__def, fact_234_Diff__idemp, fact_131_llist_Oinject, fact_92_lapp__fin__fin__lemma, fact_134_le__LCons, fact_195_lapp__inv2T, fact_253_LNil__less__LCons, tcon_Set_Oset___Orderings_Oord_8, fact_198_alllstsE, tcon_Set_Oset___Orderings_Oorder__top_4, fact_53_le__lappend, fact_168_not__LCons__le__LNil, tcon_fun___Orderings_Otop, fact_159_alllsts_OLCons__all, fact_56_fpslsts__iff, fact_225_llist__less__induct, fact_78_order__trans, fact_61_le__fun__def, fact_39_LNil__is__lappend__conv, fact_252_llist__less__finT, fact_103_pprefix__closed__def, fact_170_fpslsts__cases, fact_18_safetyD, fact_93_finite__lemma, fact_130_subset__antisym, fact_50_lapp__fin__fin__iff, fact_73_le__cases3, fact_104_livenessE, fact_189_llist__inf__le, tcon_Coinductive__List_Ollist___Orderings_Oorder_16, fact_62_order__subst1, fact_237_DiffD1, fact_31_pfinpref__iff, fact_123_top__conj_I1_J, tcon_fun___Orderings_Opreorder, fact_254_llist__less__def, fact_34_suff__LNil, fact_57_poslsts__iff, fact_38_top1I, tcon_fun___Orderings_Oorder__top, fact_241_double__diff, tcon_Nat_Onat___Orderings_Opreorder_1, fact_13_lappend__assoc, fact_60_le__funI, fact_174_llast__snoc, tcon_HOL_Obool___Orderings_Otop_13, fact_246_diff__eq__diff__less__eq, fact_248_llast__singleton, fact_117_alllsts__mono, fact_102_suff__finpref, fact_66_eq__iff, fact_125_take__fin, fact_81_dual__order_Otrans, tcon_fun___Orderings_Oorder, fact_127_ltake__fin, fact_178_ltake__lappend__llength, fact_63_order__subst2, fact_69_eq__refl, fact_230_inflsts__def, fact_164_finlsts_Ocases, fact_138_set__mp, fact_151_subset__trans, fact_51_le__LNil, fact_11_iso__tuple__UNIV__I, fact_147_subset__iff, fact_177_LList2__Mirabelle__hamjzmohle_Ollast__LCons, fact_196_lapp__infT, fact_216_ldrop__finT, fact_106_liveness__def, fact_59_le__funE, fact_142_equalityE, fact_213_ldrop__inf__iffT, fact_76_ord__le__eq__trans, fact_129_subsetI, fact_239_Diff__mono, fact_12_top__apply, tcon_Set_Oset___Orderings_Opreorder_5, fact_182_notfin__inf, fact_28_possafetyI, fact_193_fin__inf__cases, fact_65_ord__le__eq__subst, fact_33_suff__appE, fact_86_finlsts_OLNil__fin, fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_At_A_061_Ar_A_064_064_Au_A_064_064_Av_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_211_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, fact_98_lappend__LNil__LNil, fact_212_ldrop__fin__iffT, fact_84_prefix__closed__def, fact_35_top__empty__eq, fact_136_lbutlast__LCons, fact_184_infsuff__LNil, fact_139_in__mono, fact_24_finpref__suff, fact_85_llist__le__anti__sym, tcon_Set_Oset___Orderings_Otop_7, fact_224_lstrict__prefix__code_I1_J, fact_82_dual__order_Oantisym, fact_19_safetyE, fact_236_DiffE, fact_8_lapp__all__invT, fact_32_suff__finpref__iff, fact_238_DiffD2, fact_162_finlsts__induct, fact_145_equalityD2, fact_240_Diff__subset, fact_10_UNIV__I, fact_108_lrev__lappend, fact_220_lapp__suff__llength, fact_165_alllsts_Ocases, fact_153_contra__subsetD
% 19.59/7.14 % No. of inferences in proof: 560
% 19.59/7.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6623 ms resp. 5960 ms w/o parsing
% 20.24/7.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.63/7.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------