%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT183^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:06 AM UTC 2026
% Result : Theorem 65.76s 21.05s
% Output : Refutation 66.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 287
% Syntax : Number of formulae : 630 ( 229 unt; 0 typ; 2 def)
% Number of atoms : 2134 ( 501 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 8196 ( 252 ~; 82 |; 102 &;7058 @)
% ( 0 <=>; 702 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 191 ( 191 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 53 usr; 6 con; 0-5 aty)
% Number of variables : 1989 ( 37 ^;1846 !; 104 ?;1989 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(top_decl,type,
top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_decl,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_bot_decl,type,
no_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_top_decl,type,
no_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_top_decl,type,
order_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_order_decl,type,
dense_order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_field_decl,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bounded_lattice_top_decl,type,
bounded_lattice_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(condit1656338222tinuum_decl,type,
condit1656338222tinuum:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu328551480prefix_decl,type,
coindu328551480prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lappend_decl,type,
coinductive_lappend:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lfinite_decl,type,
coinductive_lfinite:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_llast_decl,type,
coinductive_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(coinductive_LCons_decl,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_LNil_decl,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(coinductive_lnull_decl,type,
coinductive_lnull:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lmember_decl,type,
coinductive_lmember:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > $o ) ).
thf(coindu1478340336prefix_decl,type,
coindu1478340336prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(undefined_decl,type,
undefined:
!>[TA: $tType] : TA ).
thf(lList2435255213lllsts_decl,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21511617539llstsp_decl,type,
lList21511617539llstsp:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(lList2236698231inlsts_decl,type,
lList2236698231inlsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21916056377ts_rec_decl,type,
lList21916056377ts_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coinductive_llist @ TA ) > TB > TB ) > ( coinductive_llist @ TA ) > TB ) ).
thf(lList2860480441nlstsp_decl,type,
lList2860480441nlstsp:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(lList22096119349pslsts_decl,type,
lList22096119349pslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21612149805nflsts_decl,type,
lList21612149805nflsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2370560421utlast_decl,type,
lList2370560421utlast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList2508575361_ldrop_decl,type,
lList2508575361_ldrop:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat > ( coinductive_llist @ TA ) ) ).
thf(lList2170638824_llast_decl,type,
lList2170638824_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(lList21232602520length_decl,type,
lList21232602520length:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat ) ).
thf(lList2281150353e_lrev_decl,type,
lList2281150353e_lrev:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList22119844313_ltake_decl,type,
lList22119844313_ltake:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat > ( coinductive_llist @ TA ) ) ).
thf(lList21148268032oslsts_decl,type,
lList21148268032oslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(type2_decl,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(r_decl,type,
r: coinductive_llist @ a ).
thf(sk1_decl,type,
sk1:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA ) ).
thf(sk4_decl,type,
sk4:
!>[TA: $tType] : TA ).
thf(sk1_def,definition,
( sk1
= ( ^ [TA: $tType,A: TA > $o,B: TA > $o] :
@+[C: TA] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [TA: $tType] :
@+[A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ) ).
thf(124,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_minf_I7_J) ).
thf(629,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(27,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_9) ).
thf(347,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(241,axiom,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_ex__gt__or__lt) ).
thf(1110,plain,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(21,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_5) ).
thf(333,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(227,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_lappend_Octr_I1_J) ).
thf(1031,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(79,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_ball__Un) ).
thf(481,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(29,axiom,
preorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_3) ).
thf(352,plain,
preorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(51,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_UnE) ).
thf(408,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(137,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_194_inflstsI2) ).
thf(683,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)],[137]) ).
thf(146,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_225_inflstsE) ).
thf(730,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)],[146]) ).
thf(12,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(308,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_UnCI) ).
thf(449,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(90,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_7) ).
thf(510,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(511,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[510]) ).
thf(134,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_less__not__sym) ).
thf(677,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(250,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_llist_OdiscI_I1_J) ).
thf(1139,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1140,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
| ( coinductive_lnull @ TA @ A ) ),
inference(cnf,[status(esa)],[1139]) ).
thf(1141,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
| ( coinductive_lnull @ TA @ A ) ),
inference(lifteq,[status(thm)],[1140]) ).
thf(1142,plain,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
inference(simp,[status(thm)],[1141]) ).
thf(39,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(379,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(249,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order_Ostrict__trans) ).
thf(1137,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(76,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_199_ltake__LCons__Suc) ).
thf(472,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)],[76]) ).
thf(275,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_alllsts_OLNil__all) ).
thf(1233,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(172,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_20_fps__induct) ).
thf(814,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)],[172]) ).
thf(141,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_195_inflsts__cases) ).
thf(698,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)],[141]) ).
thf(196,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_213_alllsts_Ocoinduct) ).
thf(913,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)],[196]) ).
thf(99,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lnull @ TA @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_llist_Odisc_I2_J) ).
thf(538,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lnull @ TA @ ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(199,axiom,
! [TA: $tType] : ( order @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Oorder_20) ).
thf(930,plain,
! [TA: $tType] : ( order @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(245,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_1_LNil__less__LCons) ).
thf(1127,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)],[245]) ).
thf(54,axiom,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_6) ).
thf(417,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(186,axiom,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_lrev__LNil) ).
thf(885,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1,conjecture,
~ ( ord_less @ ( coinductive_llist @ a ) @ r @ ( coinductive_LNil @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ~ ( ord_less @ ( coinductive_llist @ a ) @ r @ ( coinductive_LNil @ a ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(287,plain,
~ ~ ( ord_less @ ( coinductive_llist @ a ) @ r @ ( coinductive_LNil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(288,plain,
ord_less @ ( coinductive_llist @ a ) @ r @ ( coinductive_LNil @ a ),
inference(polarity_switch,[status(thm)],[287]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_top__conj_I1_J) ).
thf(301,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(62,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_Un__left__commute) ).
thf(436,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(286,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_191_ldrop__inf__iffT) ).
thf(1265,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)],[286]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_bex__Un) ).
thf(504,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(235,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ( A @ ( coinductive_LNil @ TA ) )
=> ( ! [C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
=> ( ( A @ D )
=> ( A @ ( coinductive_LCons @ TA @ C @ D ) ) ) )
=> ( ( ! [C: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ C @ B )
=> ( A @ C ) )
=> ( A @ B ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_llimit__induct) ).
thf(1059,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ( A @ ( coinductive_LNil @ TA ) )
=> ( ! [C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
=> ( ( A @ D )
=> ( A @ ( coinductive_LCons @ TA @ C @ D ) ) ) )
=> ( ( ! [C: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ C @ B )
=> ( A @ C ) )
=> ( A @ B ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(206,axiom,
! [TA: $tType] : ( preorder @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Opreorder_19) ).
thf(949,plain,
! [TA: $tType] : ( preorder @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(114,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( top_top @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_top_Oextremum__strict) ).
thf(587,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( top_top @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(120,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_less__trans) ).
thf(619,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(175,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_less__imp__triv) ).
thf(838,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(108,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_41_LList2__Mirabelle__hamjzmohle_Ollast__LCons) ).
thf(559,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)],[108]) ).
thf(128,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_llist_Ocollapse_I1_J) ).
thf(638,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(281,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_57_lappend__eq__LNil__iff) ).
thf(1247,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)],[281]) ).
thf(160,axiom,
! [TA: $tType,A: nat] :
( ( lList2508575361_ldrop @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_LList2__Mirabelle__hamjzmohle_Oldrop__LNil) ).
thf(770,plain,
! [TA: $tType,A: nat] :
( ( lList2508575361_ldrop @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_order__less__subst1) ).
thf(1115,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(3,axiom,
bounded_lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(289,plain,
bounded_lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(77,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_lappend_Odisc__iff_I2_J) ).
thf(475,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(166,axiom,
! [TA: $tType] :
( ( lList21511617539llstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList21511617539llstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_alllstsp_Osimps) ).
thf(789,plain,
! [TA: $tType] :
( ( lList21511617539llstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList21511617539llstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(65,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_not__lnull__conv) ).
thf(443,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(230,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_less__imp__not__less) ).
thf(1040,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(38,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Un__Diff) ).
thf(376,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(122,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_219_lappT) ).
thf(623,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)],[122]) ).
thf(173,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_200_fin__inf__cases) ).
thf(834,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)],[173]) ).
thf(92,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Un__absorb) ).
thf(514,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(30,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_lappend__lnull2) ).
thf(353,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(224,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_19_llist_Odistinct_I1_J) ).
thf(1020,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)],[224]) ).
thf(348,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[347]) ).
thf(44,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_11) ).
thf(396,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(397,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[396]) ).
thf(126,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_180_lapp__suff__llength) ).
thf(634,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)],[126]) ).
thf(147,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_lappend__code_I1_J) ).
thf(734,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(5,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_top1I) ).
thf(292,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(293,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(cnf,[status(esa)],[292]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_lfinite__code_I2_J) ).
thf(453,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(244,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_37_finlsts_Ocases) ).
thf(1119,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)],[244]) ).
thf(89,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_lappend__lnull1) ).
thf(507,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(58,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_lnull__imp__lfinite) ).
thf(428,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(266,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_29_fpslsts__iff) ).
thf(1201,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)],[266]) ).
thf(279,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_99_lrev__is__LNil__conv) ).
thf(1242,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)],[279]) ).
thf(180,axiom,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lbutlast__LNil) ).
thf(849,plain,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(268,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_pinf_I3_J) ).
thf(1206,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(102,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_UNIV__witness) ).
thf(545,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(546,plain,
! [TA: $tType] : ( member @ TA @ ( sk4 @ TA ) @ ( top_top @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[545]) ).
thf(197,axiom,
! [TA: $tType] :
( ( coinductive_lfinite @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
| ? [B: coinductive_llist @ TA,C: TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ B ) )
& ( coinductive_lfinite @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_lfinite_Osimps) ).
thf(925,plain,
! [TA: $tType] :
( ( coinductive_lfinite @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
| ? [B: coinductive_llist @ TA,C: TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ B ) )
& ( coinductive_lfinite @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(40,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_67_llist__less__induct) ).
thf(381,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)],[40]) ).
thf(169,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_linorder__cases) ).
thf(798,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(91,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_UNIV__I) ).
thf(512,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(63,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_230_Diff__idemp) ).
thf(439,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)],[63]) ).
thf(253,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_82_LList2__Mirabelle__hamjzmohle_Ollast__lappend) ).
thf(1153,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)],[253]) ).
thf(156,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_72_lappend__snocL1__conv__LCons2) ).
thf(761,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)],[156]) ).
thf(22,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_18) ).
thf(334,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(195,axiom,
! [TA: $tType] :
( ( coinductive_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_Coinductive__List_Ollast__LNil) ).
thf(910,plain,
! [TA: $tType] :
( ( coinductive_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(209,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_pinf_I7_J) ).
thf(957,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(163,axiom,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_gt__ex) ).
thf(778,plain,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(231,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_61_same__lappend__eq) ).
thf(1042,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)],[231]) ).
thf(284,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(1255,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(28,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_Un__left__absorb) ).
thf(349,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,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(295,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)],[7]) ).
thf(296,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( ( A @ ( sk1 @ TA @ B @ A ) )
!= ( B @ ( sk1 @ TA @ B @ A ) ) )
| ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(297,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( ( A @ ( sk1 @ TA @ B @ A ) )
!= ( B @ ( sk1 @ TA @ B @ A ) ) )
| ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(57,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ~ ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_llist_OdiscI_I2_J) ).
thf(424,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ~ ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(277,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_minf_I5_J) ).
thf(1238,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(123,axiom,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_dense) ).
thf(625,plain,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(181,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_12_llistE) ).
thf(852,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)],[181]) ).
thf(95,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Un__iff) ).
thf(522,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_ord__less__eq__trans) ).
thf(757,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(144,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_30_fpslsts__cases) ).
thf(710,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)],[144]) ).
thf(69,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_10) ).
thf(456,plain,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(220,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_28_llist__less__finT) ).
thf(1012,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)],[220]) ).
thf(240,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_50_finlsts__rec__LCons__def) ).
thf(1106,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)],[240]) ).
thf(179,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_lfinite__code_I1_J) ).
thf(847,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(109,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_201_app__invT) ).
thf(566,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)],[109]) ).
thf(80,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(484,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(255,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_202_lapp__infT) ).
thf(1159,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)],[255]) ).
thf(71,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_176_UNIV__eq__I) ).
thf(461,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)],[71]) ).
thf(83,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_UnI1) ).
thf(493,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(269,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_224_alllstsE) ).
thf(1210,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)],[269]) ).
thf(237,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( B @ ( coinductive_LNil @ TA ) )
=> ( ! [C: coinductive_llist @ TA,D: TA] :
( ( coinductive_lfinite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coinductive_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_lfinite_Oinducts) ).
thf(1079,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( B @ ( coinductive_LNil @ TA ) )
=> ( ! [C: coinductive_llist @ TA,D: TA] :
( ( coinductive_lfinite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coinductive_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(226,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_ord__eq__less__trans) ).
thf(1027,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(251,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_linordered__field__no__lb) ).
thf(1143,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Un__Diff__cancel) ).
thf(403,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(31,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_63_llast__LCons2) ).
thf(356,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)],[31]) ).
thf(165,axiom,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_less__induct) ).
thf(783,plain,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(86,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_lfinite__LConsI) ).
thf(499,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmember @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coinductive_lmember @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_lmember__code_I2_J) ).
thf(519,plain,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmember @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coinductive_lmember @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(150,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_98_LNil__is__lrev__conv) ).
thf(742,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)],[150]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top) ).
thf(290,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(291,plain,
! [TA: $tType,TB: $tType] :
( ~ ( bounded_lattice @ TB @ ( type2 @ TB ) )
| ( bounded_lattice_top @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) ) ),
inference(cnf,[status(esa)],[290]) ).
thf(1268,plain,
! [TA: $tType,TB: $tType] :
( ~ $true
| ( bounded_lattice_top @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
| ( ( bounded_lattice @ $o @ ( type2 @ $o ) )
!= ( bounded_lattice @ TB @ ( type2 @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,291]) ).
thf(1269,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice_top @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
| ( ( bounded_lattice @ $o @ ( type2 @ $o ) )
!= ( bounded_lattice @ TB @ ( type2 @ TB ) ) ) ),
inference(simp,[status(thm)],[1268]) ).
thf(1270,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[1269:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( $o ))]]) ).
thf(15,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList21511617539llstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_alllstsp_OLCons__all) ).
thf(317,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList21511617539llstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(66,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_top__empty__eq) ).
thf(446,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(447,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(cnf,[status(esa)],[446]) ).
thf(448,plain,
! [TA: $tType] :
( ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( top_top @ ( TA > $o ) ) ),
inference(lifteq,[status(thm)],[447]) ).
thf(1329,plain,
! [TA: $tType] :
( ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ^ [A: TA] : $true ) ),
inference(rewrite,[status(thm)],[448,293]) ).
thf(261,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_95_lrevT) ).
thf(1182,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)],[261]) ).
thf(236,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_less__imp__not__eq) ).
thf(1075,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ C @ B )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_minf_I11_J) ).
thf(637,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(271,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_order_Ostrict__implies__not__eq) ).
thf(1214,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(222,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_106_fin__finite) ).
thf(1016,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)],[222]) ).
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_71_lapp__fin__fin__lemma) ).
thf(679,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(103,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_217_alllsts_OLCons__all) ).
thf(547,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)],[103]) ).
thf(19,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ B )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_lstrict__prefix__lfinite1) ).
thf(328,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ B )
=> ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(75,axiom,
no_top @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top) ).
thf(471,plain,
no_top @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(106,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_100_lrev__lappend) ).
thf(554,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)],[106]) ).
thf(154,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_73_finlsts__rec__LNil__def) ).
thf(753,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)],[154]) ).
thf(43,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_54_lappend__code_I2_J) ).
thf(393,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)],[43]) ).
thf(216,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_187_llength__take) ).
thf(997,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)],[216]) ).
thf(148,axiom,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_lstrict__prefix__code_I1_J) ).
thf(737,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(738,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(cnf,[status(esa)],[737]) ).
thf(247,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_fin__Un__inf) ).
thf(1131,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(457,plain,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[456]) ).
thf(218,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_49_lstrict__prefix__code_I2_J) ).
thf(1002,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)],[218]) ).
thf(280,axiom,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_lmember__code_I1_J) ).
thf(1245,plain,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1246,plain,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(cnf,[status(esa)],[1245]) ).
thf(36,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_64_lstrict__prefix__code_I4_J) ).
thf(371,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)],[36]) ).
thf(167,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_dual__order_Oasym) ).
thf(792,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(202,axiom,
! [TA: $tType,A: TA > $o] : ( lList21511617539llstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_alllstsp_OLNil__all) ).
thf(938,plain,
! [TA: $tType,A: TA > $o] : ( lList21511617539llstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(13,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_lstrict__prefix__lappend__conv) ).
thf(311,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(259,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_pinf_I1_J) ).
thf(1170,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(45,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(398,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(107,axiom,
! [TA: $tType] : ( ord @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Oord_21) ).
thf(557,plain,
! [TA: $tType] : ( ord @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(558,plain,
! [TA: $tType] : ( ord @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(cnf,[status(esa)],[557]) ).
thf(133,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_79_lbutlast__lapp__llast) ).
thf(674,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)],[133]) ).
thf(258,axiom,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_lnull__def) ).
thf(1167,plain,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(187,axiom,
! [TA: $tType] :
( ( lList2170638824_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_LList2__Mirabelle__hamjzmohle_Ollast__LNil) ).
thf(888,plain,
! [TA: $tType] :
( ( lList2170638824_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(161,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_70_lappfin__finT) ).
thf(773,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)],[161]) ).
thf(168,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_pinf_I4_J) ).
thf(794,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(193,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_149_ltake__fin) ).
thf(906,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)],[193]) ).
thf(8,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_top__conj_I2_J) ).
thf(298,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(59,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_4) ).
thf(430,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(239,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_210_LConsE) ).
thf(1103,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)],[239]) ).
thf(399,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[398]) ).
thf(1271,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( bounded_lattice_top @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( bounded_lattice @ TC @ ( type2 @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[399,291]) ).
thf(1272,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bounded_lattice_top @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( bounded_lattice @ TC @ ( type2 @ TC ) ) ) ),
inference(simp,[status(thm)],[1271]) ).
thf(1273,plain,
! [TA: $tType,TB: $tType] : ( bounded_lattice_top @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[1272:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( set @ TA ))]]) ).
thf(151,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( top_top @ TA ) )
= ( ord_less @ TA @ A @ ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_top_Onot__eq__extremum) ).
thf(745,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( top_top @ TA ) )
= ( ord_less @ TA @ A @ ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(112,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_222_finsubsetall) ).
thf(573,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)],[112]) ).
thf(139,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: coinductive_llist @ TA] :
( ? [C: TA] :
( A
= ( coinductive_LCons @ TA @ C @ B ) )
=> ~ ( coinductive_lfinite @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_lfinite_Ocases) ).
thf(689,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: coinductive_llist @ TA] :
( ? [C: TA] :
( A
= ( coinductive_LCons @ TA @ C @ B ) )
=> ~ ( coinductive_lfinite @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(212,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_56_LNil__is__lappend__conv) ).
thf(965,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)],[212]) ).
thf(153,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_150_ldrop__fin__iffT) ).
thf(750,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)],[153]) ).
thf(192,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_44_lstrict__prefix__code_I3_J) ).
thf(904,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)],[192]) ).
thf(56,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_8) ).
thf(422,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(423,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[422]) ).
thf(48,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_14) ).
thf(402,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(177,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_207_inflstsI) ).
thf(843,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)],[177]) ).
thf(273,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_203_lapp__inv2T) ).
thf(1226,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)],[273]) ).
thf(129,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 @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ord__eq__less__subst) ).
thf(641,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 @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(117,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_dual__order_Oirrefl) ).
thf(611,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(85,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Un__commute) ).
thf(496,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(497,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(cnf,[status(esa)],[496]) ).
thf(498,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(lifteq,[status(thm)],[497]) ).
thf(73,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_68_lappend__assoc) ).
thf(466,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)],[73]) ).
thf(23,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_231_Diff__iff) ).
thf(335,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)],[23]) ).
thf(171,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_minf_I1_J) ).
thf(804,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(142,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_58_LNil__eq__lappend__iff) ).
thf(704,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)],[142]) ).
thf(100,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ( coinductive_lfinite @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_lfinite__lappend) ).
thf(540,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ( coinductive_lfinite @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(157,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_lappend__LNil2) ).
thf(764,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(136,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_216_ldropT) ).
thf(681,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)],[136]) ).
thf(55,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_sup__top__left) ).
thf(419,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(233,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_78_finlsts__rev__cases) ).
thf(1048,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)],[233]) ).
thf(33,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Coinductive__List_Ollast__LCons) ).
thf(362,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(119,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_62_lapp__fin__fin__iff) ).
thf(616,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)],[119]) ).
thf(191,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_minf_I4_J) ).
thf(900,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(50,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finlstsp_OLCons__fin) ).
thf(406,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(130,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_208_lapp__allT__iff) ).
thf(649,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)],[130]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(434,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(41,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Un__UNIV__left) ).
thf(387,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(125,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_212_poslsts__iff) ).
thf(631,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)],[125]) ).
thf(256,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_55_lappend__is__LNil__conv) ).
thf(1162,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)],[256]) ).
thf(121,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finlsts_OLNil__fin) ).
thf(621,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(848,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(cnf,[status(esa)],[847]) ).
thf(189,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_pinf_I5_J) ).
thf(895,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(20,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_Un__UNIV__right) ).
thf(330,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(200,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_179_llength__drop__take) ).
thf(932,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)],[200]) ).
thf(242,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_lift__Suc__mono__less__iff) ).
thf(1112,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(26,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_246_DiffD1) ).
thf(345,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)],[26]) ).
thf(183,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_77_lrev__induct) ).
thf(858,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)],[183]) ).
thf(105,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_less__irrefl) ).
thf(552,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(204,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_less__linear) ).
thf(943,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1021,plain,
! [TA: $tType,B: coinductive_llist @ TA,A: TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[1020]) ).
thf(1022,plain,
! [TA: $tType,B: coinductive_llist @ TA,A: TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[1021]) ).
thf(138,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dual__order_Ostrict__implies__not__eq) ).
thf(685,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(265,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_43_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(1198,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)],[265]) ).
thf(210,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_minf_I3_J) ).
thf(959,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(159,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_less__asym) ).
thf(768,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(164,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_not__less__iff__gr__or__eq) ).
thf(780,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(185,axiom,
! [TA: $tType,A: TA > $o] : ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_finlstsp_OLNil__fin) ).
thf(883,plain,
! [TA: $tType,A: TA > $o] : ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(217,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_order_Oasym) ).
thf(1000,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(282,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_linordered__field__no__ub) ).
thf(1250,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(850,plain,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(cnf,[status(esa)],[849]) ).
thf(851,plain,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(lifteq,[status(thm)],[850]) ).
thf(60,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_157_ltake__ldrop__id) ).
thf(431,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)],[60]) ).
thf(140,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_antisym__conv3) ).
thf(695,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(228,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_42_lbutlast__snoc) ).
thf(1034,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)],[228]) ).
thf(82,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
& ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_lnull__lappend) ).
thf(490,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
& ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(553,plain,
! [TA: $tType,A: TA] :
( ~ ( preorder @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ A @ A ) ),
inference(cnf,[status(esa)],[552]) ).
thf(1302,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ~ ( ord_less @ TA @ A @ A )
| ( ( preorder @ nat @ ( type2 @ nat ) )
!= ( preorder @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[352,553]) ).
thf(1303,plain,
! [TA: $tType,A: TA] :
( ~ ( ord_less @ TA @ A @ A )
| ( ( preorder @ nat @ ( type2 @ nat ) )
!= ( preorder @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[1302]) ).
thf(1304,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(pattern_uni,[status(thm)],[1303:[bind_type(TA,$thf( nat ))]]) ).
thf(115,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( lList2860480441nlstsp @ TA @ A @ D )
=> ( ( C @ D )
=> ( ( A @ E )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_finlstsp_Oinducts) ).
thf(589,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( lList2860480441nlstsp @ TA @ A @ D )
=> ( ( C @ D )
=> ( ( A @ E )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(37,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_245_DiffD2) ).
thf(374,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)],[37]) ).
thf(248,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_214_alllsts_Osimps) ).
thf(1134,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)],[248]) ).
thf(174,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_173_ldrop__finT) ).
thf(836,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)],[174]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_ord__less__eq__subst) ).
thf(1145,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(223,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_209_alllsts__UNIV) ).
thf(1018,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)],[223]) ).
thf(213,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_39_finlsts__induct) ).
thf(968,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)],[213]) ).
thf(70,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_17_llist_Oinject) ).
thf(458,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)],[70]) ).
thf(96,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_89_top__apply) ).
thf(525,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)],[96]) ).
thf(182,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_linorder__neqE__linordered__idom) ).
thf(855,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(254,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(1156,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)],[254]) ).
thf(143,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_74_finlsts__rec__LNil) ).
thf(707,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)],[143]) ).
thf(886,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(cnf,[status(esa)],[885]) ).
thf(887,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(lifteq,[status(thm)],[886]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_lfinite__LCons) ).
thf(414,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(149,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_190_notinf__fin) ).
thf(739,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)],[149]) ).
thf(274,axiom,
! [TA: $tType] :
( ( lList2860480441nlstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList2860480441nlstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finlstsp_Osimps) ).
thf(1230,plain,
! [TA: $tType] :
( ( lList2860480441nlstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList2860480441nlstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(208,axiom,
! [TA: $tType,A: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_LList2__Mirabelle__hamjzmohle_Oltake__LNil) ).
thf(954,plain,
! [TA: $tType,A: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(283,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_neqE) ).
thf(1252,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(176,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_51_finlsts__rec__LCons) ).
thf(840,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)],[176]) ).
thf(276,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_18_neq__LNil__conv) ).
thf(1235,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)],[276]) ).
thf(24,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_llast__lappend__LCons) ).
thf(338,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(207,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_188_lapp__inf) ).
thf(951,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)],[207]) ).
thf(32,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Un__assoc) ).
thf(359,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(272,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList2860480441nlstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finlstsp_Ocases) ).
thf(1218,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList2860480441nlstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pinf_I2_J) ).
thf(1188,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(263,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_107_finT__simp) ).
thf(1186,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)],[263]) ).
thf(285,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_215_alllsts_Ocases) ).
thf(1257,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)],[285]) ).
thf(118,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_97_lrev__lrev__ident) ).
thf(613,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)],[118]) ).
thf(14,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(314,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(184,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_21_lbutlast__LCons) ).
thf(876,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)],[184]) ).
thf(278,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_223_infsubsetall) ).
thf(1240,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)],[278]) ).
thf(132,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_40_finlsts_Oinducts) ).
thf(656,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)],[132]) ).
thf(225,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_172_drop__nonLNil) ).
thf(1023,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)],[225]) ).
thf(111,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_less__asym_H) ).
thf(571,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(178,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_204_lapp__fin__infT) ).
thf(845,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)],[178]) ).
thf(11,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_top__set__def) ).
thf(305,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(306,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [TA: $tType] :
( ( collect @ TA @ ( top_top @ ( TA > $o ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(1316,plain,
! [TA: $tType] :
( ( collect @ TA
@ ^ [A: TA] : $true )
= ( top_top @ ( set @ TA ) ) ),
inference(rewrite,[status(thm)],[307,293]) ).
thf(260,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_dual__order_Ostrict__trans) ).
thf(1180,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(931,plain,
! [TA: $tType] : ( order @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(cnf,[status(esa)],[930]) ).
thf(84,axiom,
order_top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_13) ).
thf(495,plain,
order_top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(188,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_less__imp__not__eq2) ).
thf(891,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(34,axiom,
wellorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(368,plain,
wellorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(588,plain,
! [TA: $tType,A: TA] :
( ~ ( order_top @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ ( top_top @ TA ) @ A ) ),
inference(cnf,[status(esa)],[587]) ).
thf(16,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_sup__top__right) ).
thf(319,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(152,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_31_finlsts_OLCons__fin) ).
thf(748,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)],[152]) ).
thf(10,axiom,
top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_17) ).
thf(304,plain,
top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(205,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_neq__iff) ).
thf(946,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(131,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_less__imp__neq) ).
thf(652,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(42,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_lappend__inf) ).
thf(390,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(47,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(401,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(418,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[417]) ).
thf(215,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_lfinite__LNil) ).
thf(995,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(211,axiom,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_lt__ex) ).
thf(963,plain,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(93,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_iso__tuple__UNIV__I) ).
thf(517,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(110,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_96_lrev__is__lrev__conv) ).
thf(568,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)],[110]) ).
thf(78,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Un__Diff__cancel2) ).
thf(478,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(270,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_220_lapp__all__invT) ).
thf(1212,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)],[270]) ).
thf(104,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_189_notfin__inf) ).
thf(549,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)],[104]) ).
thf(98,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(536,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)],[98]) ).
thf(232,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_75_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(1045,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)],[232]) ).
thf(145,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( B @ ( coinductive_LNil @ TA ) )
=> ( ! [C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
=> ( ( B @ D )
=> ( B @ ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_lfinite__rev__induct) ).
thf(716,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( B @ ( coinductive_LNil @ TA ) )
=> ( ! [C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
=> ( ( B @ D )
=> ( B @ ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1278,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ~ ( ord_less @ TA @ ( top_top @ TA ) @ A )
| ( ( order_top @ $o @ ( type2 @ $o ) )
!= ( order_top @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[495,588]) ).
thf(1279,plain,
! [TA: $tType,A: TA] :
( ~ ( ord_less @ TA @ ( top_top @ TA ) @ A )
| ( ( order_top @ $o @ ( type2 @ $o ) )
!= ( order_top @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[1278]) ).
thf(1280,plain,
! [A: $o] :
~ ( ord_less @ $o @ ( top_top @ $o ) @ A ),
inference(pattern_uni,[status(thm)],[1279:[bind_type(TA,$thf( $o ))]]) ).
thf(52,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_lappend_Oexhaust) ).
thf(410,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(950,plain,
! [TA: $tType] : ( preorder @ ( coinductive_llist @ TA ) @ ( type2 @ ( coinductive_llist @ TA ) ) ),
inference(cnf,[status(esa)],[949]) ).
thf(18,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(326,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,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_247_DiffE) ).
thf(341,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)],[25]) ).
thf(234,axiom,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_llast__singleton) ).
thf(1056,plain,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(257,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_193_ldrop__infT) ).
thf(1165,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)],[257]) ).
thf(198,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_lift__Suc__mono__less) ).
thf(928,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(6,axiom,
bounded_lattice_top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__top_12) ).
thf(294,plain,
bounded_lattice_top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(170,axiom,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_lappend__LNil__LNil) ).
thf(801,plain,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(190,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_186_LList2__Mirabelle__hamjzmohle_Ollength__LCons) ).
thf(897,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)],[190]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ B @ C )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pinf_I11_J) ).
thf(767,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(1286,plain,
! [TA: $tType,TB: $tType,A: TB] :
( ~ $true
| ~ ( ord_less @ TB @ ( top_top @ TB ) @ A )
| ( ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( order_top @ TB @ ( type2 @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[511,588]) ).
thf(1287,plain,
! [TA: $tType,TB: $tType,A: TB] :
( ~ ( ord_less @ TB @ ( top_top @ TB ) @ A )
| ( ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( order_top @ TB @ ( type2 @ TB ) ) ) ),
inference(simp,[status(thm)],[1286]) ).
thf(1288,plain,
! [TA: $tType,A: set @ TA] :
~ ( ord_less @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A ),
inference(pattern_uni,[status(thm)],[1287:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( set @ TA ))]]) ).
thf(46,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_15) ).
thf(400,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_minf_I2_J) ).
thf(1093,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(72,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(464,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)],[72]) ).
thf(246,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ? [C: TA] : ( member @ TA @ C @ ( minus_minus @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_psubset__imp__ex__mem) ).
thf(1129,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ? [C: TA] : ( member @ TA @ C @ ( minus_minus @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(113,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > $o] :
( ( 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 )
| ( lList21511617539llstsp @ TA @ C @ E ) )
& ( C @ F ) ) ) )
=> ( lList21511617539llstsp @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_alllstsp_Ocoinduct) ).
thf(575,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > $o] :
( ( 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 )
| ( lList21511617539llstsp @ TA @ C @ E ) )
& ( C @ F ) ) ) )
=> ( lList21511617539llstsp @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(425,plain,
! [TA: $tType,C: coinductive_llist @ TA,B: TA,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LCons @ TA @ B @ C ) )
| ~ ( coinductive_lnull @ TA @ A ) ),
inference(cnf,[status(esa)],[424]) ).
thf(426,plain,
! [TA: $tType,C: coinductive_llist @ TA,B: TA,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LCons @ TA @ B @ C ) )
| ~ ( coinductive_lnull @ TA @ A ) ),
inference(lifteq,[status(thm)],[425]) ).
thf(427,plain,
! [TA: $tType,B: coinductive_llist @ TA,A: TA] :
~ ( coinductive_lnull @ TA @ ( coinductive_LCons @ TA @ A @ B ) ),
inference(simp,[status(thm)],[426]) ).
thf(97,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) )
& ( ~ ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( undefined @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_Coinductive__List_Ollast__lappend) ).
thf(528,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) )
& ( ~ ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( undefined @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(219,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList21511617539llstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_alllstsp_Ocases) ).
thf(1004,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList21511617539llstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(64,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_16) ).
thf(442,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(87,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ A )
= ( undefined @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_llast__linfinite) ).
thf(501,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ A )
= ( undefined @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(194,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_211_take__fin) ).
thf(908,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)],[194]) ).
thf(214,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_66_llast__snoc) ).
thf(992,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)],[214]) ).
thf(35,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_UnI2) ).
thf(369,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_order__less__subst2) ).
thf(607,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(17,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_lappend_Odisc_I2_J) ).
thf(322,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_lzip_Oexhaust) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(201,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_81_lrev__LCons) ).
thf(935,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)],[201]) ).
thf(262,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_221_finite__lemma) ).
thf(1184,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)],[262]) ).
thf(101,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(543,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(267,axiom,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_llist_Odisc_I1_J) ).
thf(1204,plain,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(221,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_196_infT__simp) ).
thf(1014,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)],[221]) ).
thf(74,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_lappend_Odisc_I1_J) ).
thf(469,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(203,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_226_inflsts__def) ).
thf(940,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)],[203]) ).
thf(229,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_38_finlsts_Osimps) ).
thf(1037,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)],[229]) ).
thf(162,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_148_poslsts__UNIV) ).
thf(775,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)],[162]) ).
thf(2160,plain,
$false,
inference(e,[status(thm)],[629,347,1110,333,1031,481,352,408,683,730,308,449,511,677,1142,379,1137,472,1233,814,698,913,538,930,1127,417,885,288,301,436,1265,504,1059,949,587,619,838,559,638,1247,770,1115,289,475,789,443,1040,376,623,834,514,353,1020,348,397,634,734,293,453,1119,396,507,428,1201,1242,849,292,1206,546,925,381,798,512,439,1153,761,334,910,957,778,1042,1255,349,297,424,1238,625,852,522,757,710,456,1012,1106,847,566,484,1159,461,493,1210,1079,1027,1143,403,356,783,499,519,742,1270,317,1329,1182,1075,637,1214,1016,679,547,328,471,554,753,393,997,738,1131,457,1002,1246,371,792,938,311,1170,398,558,674,1167,888,773,794,906,298,430,1103,1273,745,573,689,965,750,904,423,402,843,291,1226,545,641,1139,611,498,466,335,804,704,540,764,681,419,1048,362,737,616,900,406,649,434,387,631,1162,621,848,895,330,932,1112,345,858,552,943,1022,685,1198,399,959,768,780,883,1000,1250,851,431,695,1245,1034,490,1304,589,374,1134,553,836,1145,1018,968,458,525,557,855,295,1156,707,887,414,739,1230,954,1252,840,1235,338,951,359,1218,1188,1186,1257,613,314,876,1240,656,1023,446,571,845,1316,1180,931,495,891,368,588,319,748,304,946,652,390,401,418,995,963,517,568,290,510,478,1212,549,536,1045,716,287,1280,410,950,422,305,326,341,1056,1165,928,294,801,897,767,1288,400,1093,464,1129,575,427,528,1004,442,501,908,992,369,607,322,486,935,1184,543,1204,496,1014,469,940,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT183^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 18:06:45 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.84/1.43 % [INFO] Parsing done (617ms).
% 2.84/1.45 % [INFO] Running in sequential loop mode.
% 4.07/2.03 % [INFO] eprover registered as external prover.
% 4.34/2.04 % [INFO] Scanning for conjecture ...
% 4.69/2.26 % [INFO] Found a conjecture (or negated_conjecture) and 285 axioms. Running axiom selection ...
% 5.11/2.48 % [INFO] Axiom selection finished. Selected 284 axioms (removed 1 axioms).
% 6.41/2.89 % [INFO] Problem is higher-order (TPTP THF).
% 6.80/2.93 % [INFO] Type checking passed.
% 6.80/2.93 % [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 ...
% 65.76/21.04 % External prover 'e' found a proof!
% 65.76/21.04 % [INFO] Killing All external provers ...
% 65.76/21.04 % Time passed: 20686ms (effective reasoning time: 19581ms)
% 65.76/21.04 % 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)>
% 65.76/21.04 % Axioms used in derivation (284): fact_212_poslsts__iff, fact_27_alllstsp_Ocases, fact_112_lfinite__rev__induct, fact_241_Un__assoc, fact_100_lrev__lappend, fact_25_finlstsp_Ocases, fact_149_ltake__fin, fact_226_inflsts__def, fact_180_lapp__suff__llength, fact_121_order_Oasym, fact_233_Un__Diff__cancel2, fact_92_lfinite__code_I1_J, fact_34_alllstsp_OLCons__all, fact_6_minf_I3_J, fact_20_fps__induct, fact_23_finlstsp_Oinducts, fact_95_lrevT, fact_29_fpslsts__iff, fact_216_ldropT, fact_4_minf_I5_J, fact_169_lappend_Odisc_I1_J, fact_0_lbutlast__LNil, fact_219_lappT, fact_138_linorder__cases, tcon_Nat_Onat___Orderings_Olinorder, tcon_Set_Oset___Orderings_Opreorder_8, fact_33_finlstsp_OLCons__fin, tcon_Nat_Onat___Orderings_Ono__top, fact_39_finlsts__induct, fact_204_lapp__fin__infT, fact_158_lappend_Oexhaust, fact_225_inflstsE, fact_191_ldrop__inf__iffT, tcon_Nat_Onat___Orderings_Oord_5, fact_224_alllstsE, fact_220_lapp__all__invT, fact_13_pinf_I1_J, fact_44_lstrict__prefix__code_I3_J, fact_119_neqE, fact_88_linordered__field__no__ub, fact_105_lappend__inf, fact_217_alllsts_OLCons__all, fact_74_finlsts__rec__LNil, fact_67_llist__less__induct, fact_82_LList2__Mirabelle__hamjzmohle_Ollast__lappend, fact_185_Coinductive__List_Ollast__lappend, fact_3_minf_I7_J, fact_190_notinf__fin, tcon_fun___Orderings_Oord, fact_231_Diff__iff, fact_36_finlstsp_OLNil__fin, fact_19_llist_Odistinct_I1_J, fact_162_not__lnull__conv, fact_156_top__set__def, fact_76_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, fact_197_Coinductive__List_Ollast__LNil, fact_192_LList2__Mirabelle__hamjzmohle_Ollast__LNil, fact_127_less__linear, fact_206_lift__Suc__mono__less, fact_9_pinf_I11_J, fact_184_top__conj_I2_J, fact_155_LList2__Mirabelle__hamjzmohle_Oltake__LNil, fact_145_linordered__field__no__lb, fact_15_pinf_I3_J, fact_133_less__not__sym, tcon_HOL_Obool___Orderings_Olinorder_15, fact_50_finlsts__rec__LCons__def, fact_91_lfinite__code_I2_J, fact_122_dense, fact_86_linorder__neqE__linordered__idom, fact_165_llist_OdiscI_I1_J, fact_72_lappend__snocL1__conv__LCons2, fact_199_ltake__LCons__Suc, fact_232_DiffI, fact_161_llist_OdiscI_I2_J, fact_52_llast__singleton, fact_139_dual__order_Oirrefl, fact_154_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, fact_10_pinf_I7_J, fact_90_lfinite__LCons, fact_5_minf_I4_J, fact_249_UnI1, fact_64_lstrict__prefix__code_I4_J, fact_66_llast__snoc, fact_54_lappend__code_I2_J, fact_46_Collect__mem__eq, fact_8_minf_I1_J, fact_193_ldrop__infT, fact_242_ball__Un, fact_118_gt__ex, fact_120_neq__iff, fact_65_lstrict__prefix__code_I1_J, fact_240_Un__absorb, fact_134_less__induct, fact_135_antisym__conv3, fact_130_ord__less__eq__trans, fact_205_lift__Suc__mono__less__iff, tcon_Coinductive__List_Ollist___Orderings_Oord_21, tcon_fun___Lattices_Obounded__lattice_2, fact_93_lfinite__lappend, fact_239_Un__commute, fact_179_llength__drop__take, fact_166_llist_Odisc_I1_J, fact_94_lrev__LNil, fact_69_lappend__LNil__LNil, fact_22_alllstsp_Ocoinduct, fact_222_finsubsetall, fact_26_alllstsp_Osimps, fact_103_lfinite__LConsI, fact_174_lappend_Octr_I1_J, fact_49_lstrict__prefix__code_I2_J, fact_116_order__less__subst2, fact_63_llast__LCons2, fact_207_inflstsI, tcon_Nat_Onat___Orderings_Opreorder_3, fact_244_bex__Un, fact_167_lappend__lnull2, fact_186_LList2__Mirabelle__hamjzmohle_Ollength__LCons, fact_106_fin__finite, fact_230_Diff__idemp, fact_142_dual__order_Ostrict__trans, tcon_Nat_Onat___Orderings_Oorder_4, fact_201_app__invT, fact_247_DiffE, fact_114_ord__less__eq__subst, fact_62_lapp__fin__fin__iff, fact_194_inflstsI2, fact_144_order_Ostrict__implies__not__eq, tcon_Nat_Onat___Orderings_Owellorder, fact_253_sup__top__left, fact_208_lapp__allT__iff, fact_177_UNIV__witness, fact_68_lappend__assoc, fact_37_finlsts_Ocases, fact_18_neq__LNil__conv, fact_152_lnull__lappend, fact_98_LNil__is__lrev__conv, fact_187_llength__take, tcon_Coinductive__List_Ollist___Orderings_Opreorder_19, fact_159_lzip_Oexhaust, fact_146_iso__tuple__UNIV__I, fact_210_LConsE, fact_248_UnI2, fact_41_LList2__Mirabelle__hamjzmohle_Ollast__LCons, fact_160_llist_Odisc_I2_J, tcon_HOL_Obool___Orderings_Oorder_16, fact_227_fin__Un__inf, fact_110_lfinite_Osimps, fact_250_UnE, fact_123_less__imp__neq, fact_45_mem__Collect__eq, fact_196_infT__simp, fact_181_top1I, fact_243_Un__Diff, fact_148_poslsts__UNIV, fact_102_top_Oextremum__strict, fact_96_lrev__is__lrev__conv, fact_17_llist_Oinject, fact_7_minf_I2_J, fact_21_lbutlast__LCons, fact_97_lrev__lrev__ident, tcon_HOL_Obool___Orderings_Oorder__top_13, fact_81_lrev__LCons, fact_35_alllstsp_OLNil__all, fact_229_UnCI, fact_30_fpslsts__cases, fact_168_lappend__lnull1, fact_252_sup__top__right, fact_126_less__trans, fact_73_finlsts__rec__LNil__def, fact_235_Un__UNIV__right, fact_128_less__irrefl, fact_183_top__conj_I1_J, fact_251_psubset__imp__ex__mem, fact_99_lrev__is__LNil__conv, fact_79_lbutlast__lapp__llast, fact_195_inflsts__cases, fact_198_llast__linfinite, fact_58_LNil__eq__lappend__iff, fact_47_Collect__cong, fact_2_minf_I11_J, fact_237_Un__left__commute, fact_32_finlsts_OLNil__fin, fact_238_Un__left__absorb, tcon_fun___Lattices_Obounded__lattice__top, fact_203_lapp__inv2T, fact_223_infsubsetall, tcon_Set_Oset___Lattices_Obounded__lattice_1, fact_113_ord__eq__less__subst, tcon_Set_Oset___Lattices_Obounded__lattice__top_6, fact_55_lappend__is__LNil__conv, tcon_fun___Orderings_Otop, fact_84_llimit__induct, fact_140_order_Ostrict__trans, fact_153_lappend_Odisc__iff_I2_J, tcon_Set_Oset___Orderings_Oorder_9, fact_245_DiffD2, fact_176_UNIV__eq__I, fact_43_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, fact_173_ldrop__finT, fact_137_less__imp__triv, fact_132_less__imp__not__eq, fact_171_lnull__imp__lfinite, fact_211_take__fin, fact_246_DiffD1, fact_124_less__asym, fact_57_lappend__eq__LNil__iff, fact_117_lt__ex, tcon_fun___Orderings_Oorder__top, tcon_fun___Orderings_Opreorder, fact_147_UNIV__I, fact_78_finlsts__rev__cases, fact_80_lmember__code_I2_J, tcon_Set_Oset___Orderings_Oorder__top_7, fact_125_less__asym_H, fact_51_finlsts__rec__LCons, fact_40_finlsts_Oinducts, fact_61_same__lappend__eq, tcon_Set_Oset___Orderings_Otop_10, fact_115_order__less__subst1, fact_70_lappfin__finT, fact_16_pinf_I4_J, fact_141_less__imp__not__less, fact_150_ldrop__fin__iffT, fact_31_finlsts_OLCons__fin, fact_209_alllsts__UNIV, fact_200_fin__inf__cases, fact_42_lbutlast__snoc, fact_77_lrev__induct, fact_28_llist__less__finT, tcon_fun___Orderings_Oorder, fact_107_finT__simp, fact_143_not__less__iff__gr__or__eq, fact_178_ltake__lappend__llength, tcon_HOL_Obool___Orderings_Opreorder_14, tcon_HOL_Obool___Orderings_Otop_17, fact_71_lapp__fin__fin__lemma, fact_163_lnull__def, fact_202_lapp__infT, fact_83_llast__lappend__LCons, fact_85_ex__gt__or__lt, fact_60_lappend__code_I1_J, fact_234_Un__Diff__cancel, fact_38_finlsts_Osimps, fact_11_pinf_I5_J, fact_87_dual__order_Ostrict__implies__not__eq, fact_221_finite__lemma, fact_215_alllsts_Ocases, fact_108_lstrict__prefix__lfinite1, tcon_Set_Oset___Orderings_Oord_11, fact_236_Un__UNIV__left, fact_111_lfinite_Ocases, fact_89_top__apply, tcon_HOL_Obool___Lattices_Obounded__lattice, tcon_Coinductive__List_Ollist___Orderings_Oorder_20, fact_109_lfinite_Oinducts, fact_151_lstrict__prefix__lappend__conv, tcon_HOL_Obool___Lattices_Obounded__lattice__top_12, fact_75_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, fact_131_dual__order_Oasym, fact_228_Un__iff, tcon_HOL_Obool___Orderings_Oord_18, fact_104_lfinite__LNil, fact_170_lappend_Odisc_I2_J, fact_136_less__imp__not__eq2, fact_53_lmember__code_I1_J, fact_14_pinf_I2_J, fact_189_notfin__inf, fact_214_alllsts_Osimps, fact_56_LNil__is__lappend__conv, fact_1_LNil__less__LCons, fact_129_ord__eq__less__trans, fact_172_drop__nonLNil, fact_175_Coinductive__List_Ollast__LCons, fact_213_alllsts_Ocoinduct, fact_157_ltake__ldrop__id, fact_101_top_Onot__eq__extremum, fact_164_llist_Ocollapse_I1_J, fact_24_finlstsp_Osimps, fact_12_llistE, fact_182_top__empty__eq, fact_59_lappend__LNil2, fact_188_lapp__inf, fact_218_alllsts_OLNil__all
% 65.76/21.04 % No. of inferences in proof: 628
% 65.76/21.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20686 ms resp. 19581 ms w/o parsing
% 66.63/21.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.63/21.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------