%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT177^1 : 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 : n015.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 07:48:05 AM UTC 2026
% Result : Theorem 17.35s 5.38s
% Output : Refutation 18.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 246
% Syntax : Number of formulae : 494 ( 295 unt; 0 typ; 0 def)
% Number of atoms : 1975 ( 572 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 7088 ( 160 ~; 28 |; 106 &;6462 @)
% ( 0 <=>; 332 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 8 con; 0-5 aty)
% Number of variables : 1602 ( 38 ^;1524 !; 40 ?;1602 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(topolo890362671_space_decl,type,
topolo890362671_space:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(topolo47006728_space_decl,type,
topolo47006728_space:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu328551480prefix_decl,type,
coindu328551480prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_gen_lset_decl,type,
coinductive_gen_lset:
!>[TA: $tType] : ( ( set @ TA ) > ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coinductive_lSup_decl,type,
coinductive_lSup:
!>[TA: $tType] : ( ( set @ ( coinductive_llist @ TA ) ) > ( coinductive_llist @ TA ) ) ).
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(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(lList2435255213lllsts_decl,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
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(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(lList21148268032oslsts_decl,type,
lList21148268032oslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
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(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_decl,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_decl,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(pairwise_decl,type,
pairwise:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(remove_decl,type,
remove:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(topolo406746546ounded_decl,type,
topolo406746546ounded:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_decl,type,
a2: set @ a ).
thf(l_decl,type,
l: coinductive_llist @ a ).
thf(r_decl,type,
r: coinductive_llist @ a ).
thf(sa_decl,type,
sa: coinductive_llist @ a ).
thf(197,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_23_finite__lemma) ).
thf(892,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)],[197]) ).
thf(120,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Int__commute) ).
thf(629,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(41,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Diff__UNIV) ).
thf(365,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(3,axiom,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_lstrict__prefix__code_I1_J) ).
thf(249,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(90,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Un__empty__left) ).
thf(518,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(76,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_241_lfinite_Osimps) ).
thf(468,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)],[76]) ).
thf(131,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_empty__iff) ).
thf(666,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(36,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_is__singletonI) ).
thf(352,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(161,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_206_ball__Un) ).
thf(777,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)],[161]) ).
thf(98,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_insert__is__Un) ).
thf(555,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(228,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_insertI2) ).
thf(1005,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(11,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Diff__cancel) ).
thf(276,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(224,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_207_bex__Un) ).
thf(994,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)],[224]) ).
thf(21,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_238_Un__Diff) ).
thf(308,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)],[21]) ).
thf(128,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Diff__insert__absorb) ).
thf(655,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(109,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(597,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)],[109]) ).
thf(87,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_148_lstrict__prefix__code_I2_J) ).
thf(500,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)],[87]) ).
thf(146,axiom,
member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ l @ sa ) @ ( lList21612149805nflsts @ a @ a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_LNil__fin_Oprems) ).
thf(715,plain,
member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ l @ sa ) @ ( lList21612149805nflsts @ a @ a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(175,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_IntE) ).
thf(814,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(140,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_169_Un__iff) ).
thf(698,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)],[140]) ).
thf(205,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_14_alllsts__UNIV) ).
thf(913,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)],[205]) ).
thf(32,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_9_lappend__is__LNil__conv) ).
thf(340,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)],[32]) ).
thf(212,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_alllsts_OLNil__all) ).
thf(930,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(133,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Int__insert__right__if0) ).
thf(670,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(200,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_85_finlsts__rec__LCons__def) ).
thf(898,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)],[200]) ).
thf(163,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lSup @ TA @ ( insert @ ( coinductive_llist @ TA ) @ A @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_lSup__singleton) ).
thf(782,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lSup @ TA @ ( insert @ ( coinductive_llist @ TA ) @ A @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(15,axiom,
! [TA: $tType] :
( ( topolo47006728_space @ TA @ ( type2 @ TA ) )
=> ( topolo406746546ounded @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_totally__bounded__empty) ).
thf(288,plain,
! [TA: $tType] :
( ( topolo47006728_space @ TA @ ( type2 @ TA ) )
=> ( topolo406746546ounded @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(65,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Un__empty) ).
thf(436,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(5,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_151_lstrict__prefix__code_I4_J) ).
thf(257,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)],[5]) ).
thf(194,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_84_finlsts__rec__LCons) ).
thf(885,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)],[194]) ).
thf(243,axiom,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( coinductive_lSup @ TA @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ A ) )
= ( coinductive_lSup @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_lSup__insert__LNil) ).
thf(1046,plain,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( coinductive_lSup @ TA @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ A ) )
= ( coinductive_lSup @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_insert__Diff1) ).
thf(724,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_IntD2) ).
thf(719,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(164,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Int__insert__left__if1) ).
thf(785,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(89,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_242_lfinite_Oinducts) ).
thf(504,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)],[89]) ).
thf(183,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_170_UnCI) ).
thf(838,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)],[183]) ).
thf(207,axiom,
! [TA: $tType] :
( ( coinductive_lSup @ TA @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_lSup__empty) ).
thf(917,plain,
! [TA: $tType] :
( ( coinductive_lSup @ TA @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(247,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_41_alllstsE) ).
thf(1059,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)],[247]) ).
thf(217,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_insert__Diff__if) ).
thf(949,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(73,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_226_lappend__inf) ).
thf(460,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)],[73]) ).
thf(214,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_insertCI) ).
thf(934,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(38,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( pairwise @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_pairwise__singleton) ).
thf(357,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( pairwise @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(201,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_singletonI) ).
thf(902,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(123,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_insert__UNIV) ).
thf(638,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(60,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_Diff__Int) ).
thf(421,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(112,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Diff__Diff__Int) ).
thf(606,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(27,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_49_lappend__eq__LNil__iff) ).
thf(325,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)],[27]) ).
thf(69,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_205_Un__assoc) ).
thf(448,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)],[69]) ).
thf(24,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Set_Ois__empty__def) ).
thf(316,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(107,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_181_Un__Diff__cancel2) ).
thf(591,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)],[107]) ).
thf(242,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_6_inflsts__cases) ).
thf(1040,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)],[242]) ).
thf(126,axiom,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_poslsts__empty) ).
thf(646,plain,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(82,axiom,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_remove__def) ).
thf(485,plain,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(234,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: set @ TA] :
( ( pairwise @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ! [D: TA] :
( ( ( member @ TA @ D @ C )
& ( D != B ) )
=> ( ( A @ B @ D )
& ( A @ D @ B ) ) )
& ( pairwise @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_pairwise__insert) ).
thf(1020,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: set @ TA] :
( ( pairwise @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ! [D: TA] :
( ( ( member @ TA @ D @ C )
& ( D != B ) )
=> ( ( A @ B @ D )
& ( A @ D @ B ) ) )
& ( pairwise @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(80,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_doubleton__eq__iff) ).
thf(480,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(52,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(397,plain,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(191,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_64_UNIV__eq__I) ).
thf(877,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)],[191]) ).
thf(17,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_240_lfinite_Ocases) ).
thf(293,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)],[17]) ).
thf(93,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_50_lappend__code_I2_J) ).
thf(527,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)],[93]) ).
thf(46,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_bot__set__def) ).
thf(380,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_insert__Diff__single) ).
thf(439,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(136,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_insertE) ).
thf(678,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(9,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_is__singleton__the__elem) ).
thf(270,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_mk__disjoint__insert) ).
thf(661,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Un__Diff__Int) ).
thf(546,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(210,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_UNIV__witness) ).
thf(925,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(169,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_138_DiffD2) ).
thf(798,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)],[169]) ).
thf(208,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_top__empty__eq) ).
thf(920,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1,conjecture,
member @ ( coinductive_llist @ a ) @ sa @ ( lList21612149805nflsts @ a @ a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ ( coinductive_llist @ a ) @ sa @ ( lList21612149805nflsts @ a @ a2 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(248,plain,
~ ( member @ ( coinductive_llist @ a ) @ sa @ ( lList21612149805nflsts @ a @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Diff__triv) ).
thf(334,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(204,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Int__insert__left__if0) ).
thf(910,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(198,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_disjoint__iff__not__equal) ).
thf(894,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(156,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_ex__in__conv) ).
thf(746,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(179,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_insert__Diff) ).
thf(825,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(19,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_Un__singleton__iff) ).
thf(302,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_finlsts_OLNil__fin) ).
thf(820,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(100,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Int__Diff) ).
thf(561,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(61,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_gen_lset @ TA @ ( insert @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_gen__lset__code_I2_J) ).
thf(424,plain,
! [TA: $tType,A: set @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_gen_lset @ TA @ ( insert @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(165,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_21_finT__simp) ).
thf(788,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(152,axiom,
! [TA: $tType] :
( ( lList2236698231inlsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finlsts__empty) ).
thf(729,plain,
! [TA: $tType] :
( ( lList2236698231inlsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(6,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_68_llist_Odistinct_I1_J) ).
thf(260,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)],[6]) ).
thf(35,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Diff__Un) ).
thf(349,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(239,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_5_inflstsI2) ).
thf(1032,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)],[239]) ).
thf(186,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_26_alllsts_Ocases) ).
thf(852,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)],[186]) ).
thf(181,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_126_Diff__iff) ).
thf(830,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)],[181]) ).
thf(144,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_27_alllsts_Osimps) ).
thf(710,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)],[144]) ).
thf(184,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_28_finlsts_Ocases) ).
thf(842,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)],[184]) ).
thf(231,axiom,
! [TA: $tType] :
( ( lList22096119349pslsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_fpslsts__def) ).
thf(1012,plain,
! [TA: $tType] :
( ( lList22096119349pslsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__absorb2) ).
thf(285,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(190,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_16_lapp__fin__fin__iff) ).
thf(874,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)],[190]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_Int__empty__left) ).
thf(615,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(54,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_164_llast__lappend__LCons) ).
thf(403,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)],[54]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Int__Un__distrib2) ).
thf(388,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(237,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_125_DiffI) ).
thf(1028,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)],[237]) ).
thf(83,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_Un__Int__distrib) ).
thf(488,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(28,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_the__elem__eq) ).
thf(328,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(77,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_65_lappend__assoc) ).
thf(471,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)],[77]) ).
thf(225,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(997,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(141,axiom,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_inflsts__empty) ).
thf(701,plain,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(154,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_Int__insert__left) ).
thf(738,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(72,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Int__absorb) ).
thf(457,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(149,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_15_same__lappend__eq) ).
thf(721,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)],[149]) ).
thf(227,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_disjoint__insert_I2_J) ).
thf(1002,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(103,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Int__assoc) ).
thf(569,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(43,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) @ ( inf_inf @ ( set @ TA ) @ C @ A ) )
= ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) @ ( sup_sup @ ( set @ TA ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_Un__Int__crazy) ).
thf(371,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) @ ( inf_inf @ ( set @ TA ) @ C @ A ) )
= ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) @ ( sup_sup @ ( set @ TA ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(33,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_223_Un__UNIV__left) ).
thf(343,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)],[33]) ).
thf(167,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_17_LConsE) ).
thf(792,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)],[167]) ).
thf(172,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_2_lapp__inf) ).
thf(805,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)],[172]) ).
thf(22,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Diff__Int__distrib2) ).
thf(311,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,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_67_neq__LNil__conv) ).
thf(558,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)],[99]) ).
thf(94,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_248_llimit__induct) ).
thf(530,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)],[94]) ).
thf(105,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Diff__Int__distrib) ).
thf(586,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(195,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_137_DiffD1) ).
thf(888,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)],[195]) ).
thf(57,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_singleton__inject) ).
thf(412,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(116,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_top__conj_I2_J) ).
thf(618,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(63,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_top__set__def) ).
thf(430,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(12,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Un__empty__right) ).
thf(279,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Int__insert__right__if1) ).
thf(904,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(229,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_210_UnI2) ).
thf(1007,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)],[229]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Int__emptyI) ).
thf(732,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(219,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_36_alllsts_OLCons__all) ).
thf(958,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)],[219]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_insert__iff) ).
thf(641,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(50,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_is__singleton__def) ).
thf(391,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(68,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_192_Un__left__commute) ).
thf(445,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)],[68]) ).
thf(104,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_247_lfinite__rev__induct) ).
thf(572,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)],[104]) ).
thf(145,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_emptyE) ).
thf(713,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Diff__insert0) ).
thf(704,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(55,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Diff__insert) ).
thf(406,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(137,axiom,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( coinductive_lSup @ TA @ ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ A @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) )
= ( coinductive_lSup @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_lSup__minus__LNil) ).
thf(681,plain,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( coinductive_lSup @ TA @ ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ A @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) )
= ( coinductive_lSup @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Un__insert__left) ).
thf(377,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(188,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_is__singletonI_H) ).
thf(863,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_singleton__Un__iff) ).
thf(362,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(70,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_183_lfinite__code_I2_J) ).
thf(451,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)],[70]) ).
thf(102,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_230_lstrict__prefix__lfinite1) ).
thf(567,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)],[102]) ).
thf(192,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_213_UnE) ).
thf(880,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)],[192]) ).
thf(127,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_Int__insert__right) ).
thf(649,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(196,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_18_inflstsI) ).
thf(890,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)],[196]) ).
thf(79,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_Diff__disjoint) ).
thf(477,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_equals0I) ).
thf(811,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(85,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Collect__empty__eq) ).
thf(494,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(97,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_196_Un__left__absorb) ).
thf(552,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)],[97]) ).
thf(113,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Collect__empty__eq__bot) ).
thf(609,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(108,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_44_LNil__eq__lappend__iff) ).
thf(594,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)],[108]) ).
thf(117,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_lappend__LNil2) ).
thf(621,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(81,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_lfinite__LNil) ).
thf(483,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(4,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ! [C: coinductive_llist @ TA] :
( ! [D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_llist__less__induct) ).
thf(251,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ! [C: coinductive_llist @ TA] :
( ! [D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(132,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_211_UnI1) ).
thf(668,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)],[132]) ).
thf(213,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_iso__tuple__UNIV__I) ).
thf(932,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(119,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Un__insert__right) ).
thf(626,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(206,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_19_lappT) ).
thf(915,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)],[206]) ).
thf(91,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Int__Un__distrib) ).
thf(521,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(162,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_24_finsubsetall) ).
thf(780,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)],[162]) ).
thf(232,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_insert__disjoint_I2_J) ).
thf(1015,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(51,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_201_Un__commute) ).
thf(394,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)],[51]) ).
thf(226,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_insertI1) ).
thf(1000,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Un__absorb) ).
thf(299,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,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_51_lappend__snocL1__conv__LCons2) ).
thf(267,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)],[8]) ).
thf(129,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_144_inflsts__def) ).
thf(658,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)],[129]) ).
thf(240,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_12_notinf__fin) ).
thf(1034,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)],[240]) ).
thf(135,axiom,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_poslsts__def) ).
thf(675,plain,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(106,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_228_lfinite__LConsI) ).
thf(589,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)],[106]) ).
thf(168,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_11_notfin__inf) ).
thf(795,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)],[168]) ).
thf(157,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_member__remove) ).
thf(749,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_IntD1) ).
thf(1018,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(244,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_39_inflstsE) ).
thf(1049,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)],[244]) ).
thf(211,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(927,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(44,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_8_LNil__is__lappend__conv) ).
thf(374,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)],[44]) ).
thf(236,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_74_poslsts__iff) ).
thf(1025,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)],[236]) ).
thf(13,axiom,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_llast__singleton) ).
thf(282,plain,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(143,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_all__not__in__conv) ).
thf(707,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Int__UNIV__left) ).
thf(409,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,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_107_finlsts__rec__LNil__def) ).
thf(263,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)],[7]) ).
thf(245,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_insert__absorb) ).
thf(1053,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(134,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_25_lappfin__finT) ).
thf(673,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)],[134]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_insert__inter__insert) ).
thf(331,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(88,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(502,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(74,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_149_lstrict__prefix__code_I3_J) ).
thf(463,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)],[74]) ).
thf(173,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_75_fpslsts__iff) ).
thf(808,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)],[173]) ).
thf(39,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Int__left__absorb) ).
thf(359,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(203,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_166_fin__Un__inf) ).
thf(907,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)],[203]) ).
thf(155,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_IntI) ).
thf(744,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(235,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_UNIV__I) ).
thf(1023,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(110,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Diff__insert2) ).
thf(600,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(151,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_37_finlsts_OLCons__fin) ).
thf(727,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)],[151]) ).
thf(48,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_top1I) ).
thf(386,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(23,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_lfinite__code_I1_J) ).
thf(314,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(114,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Un__Int__distrib2) ).
thf(612,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(86,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_empty__not__UNIV) ).
thf(497,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(223,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_singleton__iff) ).
thf(991,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(75,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( top_top @ ( set @ TA ) ) )
= ( ( A
= ( top_top @ ( set @ TA ) ) )
& ( B
= ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Int__UNIV) ).
thf(465,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( top_top @ ( set @ TA ) ) )
= ( ( A
= ( top_top @ ( set @ TA ) ) )
& ( B
= ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(92,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_180_Un__Diff__cancel) ).
thf(524,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)],[92]) ).
thf(160,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_32_finlsts_Oinducts) ).
thf(759,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)],[160]) ).
thf(42,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_127_Diff__idemp) ).
thf(368,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)],[42]) ).
thf(221,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_136_DiffE) ).
thf(963,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)],[221]) ).
thf(25,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_222_Un__UNIV__right) ).
thf(319,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)],[25]) ).
thf(216,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( inf_inf @ ( set @ TA ) @ A @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_disjoint__insert_I1_J) ).
thf(946,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( inf_inf @ ( set @ TA ) @ A @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(121,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_160_llast__LCons2) ).
thf(632,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)],[121]) ).
thf(59,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_Diff__Int2) ).
thf(418,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(238,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_22_fin__finite) ).
thf(1030,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)],[238]) ).
thf(16,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Int__UNIV__right) ).
thf(290,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64,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_182_lfinite__LCons) ).
thf(433,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)],[64]) ).
thf(47,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_20_llistE) ).
thf(383,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)],[47]) ).
thf(138,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_34_alllsts_Ocoinduct) ).
thf(684,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)],[138]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_insert__not__empty) ).
thf(346,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(96,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_109_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(549,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)],[96]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_fin__Int__inf) ).
thf(716,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(170,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_76_poslsts__UNIV) ).
thf(800,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)],[170]) ).
thf(158,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_insert__eq__iff) ).
thf(752,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(176,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_38_lapp__fin__fin__lemma) ).
thf(818,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)],[176]) ).
thf(166,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_3_infsubsetall) ).
thf(790,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)],[166]) ).
thf(10,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Diff__empty) ).
thf(273,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(111,axiom,
! [TA: $tType] :
( ( topolo890362671_space @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( top_top @ ( set @ TA ) )
!= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Topological__Spaces_OUNIV__not__singleton) ).
thf(603,plain,
! [TA: $tType] :
( ( topolo890362671_space @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( top_top @ ( set @ TA ) )
!= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(182,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Set_Oset__insert) ).
thf(833,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(222,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_31_finlsts__induct) ).
thf(967,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)],[222]) ).
thf(101,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_108_finlsts__rec__LNil) ).
thf(564,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)],[101]) ).
thf(20,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_empty__Collect__eq) ).
thf(305,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(246,axiom,
! [TA: $tType] :
( ( lList2435255213lllsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_alllsts__empty) ).
thf(1056,plain,
! [TA: $tType] :
( ( lList2435255213lllsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_top__conj_I1_J) ).
thf(400,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(180,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_30_lapp__all__invT) ).
thf(828,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)],[180]) ).
thf(139,axiom,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( coinductive_lfinite @ TA @ ( coinductive_lSup @ TA @ A ) )
=> ! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ( coinductive_lfinite @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_lfinite__lSupD) ).
thf(696,plain,
! [TA: $tType,A: set @ ( coinductive_llist @ TA )] :
( ( coinductive_lfinite @ TA @ ( coinductive_lSup @ TA @ A ) )
=> ! [B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ B @ A )
=> ( coinductive_lfinite @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(218,axiom,
! [TA: $tType] :
( ( pairwise @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_pairwise__def) ).
thf(955,plain,
! [TA: $tType] :
( ( pairwise @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(58,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_insert__commute) ).
thf(415,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(199,axiom,
member @ ( coinductive_llist @ a ) @ r @ ( lList2236698231inlsts @ a @ a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms) ).
thf(897,plain,
member @ ( coinductive_llist @ a ) @ r @ ( lList2236698231inlsts @ a @ a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(78,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_Int__empty__right) ).
thf(474,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(220,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_singletonD) ).
thf(960,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(122,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_52_llist_Oinject) ).
thf(635,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)],[122]) ).
thf(118,axiom,
! [TA: $tType,A: TA > TA > $o] : ( pairwise @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_pairwise__empty) ).
thf(624,plain,
! [TA: $tType,A: TA > TA > $o] : ( pairwise @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(62,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_185_lfinite__lappend) ).
thf(427,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)],[62]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( inf_inf @ ( set @ TA ) @ B @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_insert__disjoint_I1_J) ).
thf(860,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( inf_inf @ ( set @ TA ) @ B @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(125,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_4_infT__simp) ).
thf(644,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)],[125]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_insert__ident) ).
thf(822,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(185,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_7_lapp__fin__infT) ).
thf(850,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)],[185]) ).
thf(67,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lappend__code_I1_J) ).
thf(442,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(189,axiom,
! [TA: $tType] :
( ( lList22096119349pslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_fpslsts__empty) ).
thf(871,plain,
! [TA: $tType] :
( ( lList22096119349pslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(26,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_empty__Diff) ).
thf(322,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(171,axiom,
( l
= ( coinductive_LNil @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_LNil__fin_Ohyps) ).
thf(803,plain,
( l
= ( coinductive_LNil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(31,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_Int__left__commute) ).
thf(337,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(215,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_80_fpslsts__cases) ).
thf(940,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)],[215]) ).
thf(37,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_83_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(354,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)],[37]) ).
thf(230,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Int__iff) ).
thf(1009,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(209,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_40_fin__inf__cases) ).
thf(923,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)],[209]) ).
thf(241,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_bot__empty__eq) ).
thf(1037,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_equals0D) ).
thf(755,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(84,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_is__singletonE) ).
thf(491,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(71,axiom,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_gen__lset__code_I1_J) ).
thf(454,plain,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(193,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_29_finlsts_Osimps) ).
thf(882,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)],[193]) ).
thf(1112,plain,
$false,
inference(e,[status(thm)],[892,629,365,249,518,468,666,352,777,555,1005,276,994,308,655,597,500,715,814,698,913,340,930,670,898,782,288,436,257,885,1046,724,719,785,504,838,917,1059,949,460,934,357,902,638,421,606,325,448,316,591,1040,646,485,1020,480,397,877,293,527,380,439,678,270,661,546,925,798,920,248,334,910,894,746,825,302,820,561,424,788,729,260,349,1032,852,830,710,842,1012,285,874,615,403,388,1028,488,328,471,997,701,738,457,721,1002,569,371,343,792,805,311,558,530,586,888,412,618,430,279,904,1007,732,958,641,391,445,572,713,704,406,681,377,863,362,451,567,880,649,890,477,811,494,552,609,594,621,483,251,668,932,626,915,521,780,1015,394,1000,299,267,658,1034,675,589,795,749,1018,1049,927,374,1025,282,707,409,263,1053,673,331,502,463,808,359,907,744,1023,600,727,386,314,612,497,991,465,524,759,368,963,319,946,632,418,1030,290,433,383,684,346,549,716,800,752,818,790,273,603,833,967,564,305,1056,400,828,696,955,415,897,474,960,635,624,427,860,644,822,850,442,871,322,803,337,940,354,1009,923,1037,755,491,454,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT177^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.11/0.22 % Computer : n015.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 18:09:33 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.01/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.29/1.22 % [INFO] Parsing done (405ms).
% 2.29/1.23 % [INFO] Running in sequential loop mode.
% 3.12/1.57 % [INFO] eprover registered as external prover.
% 3.12/1.58 % [INFO] Scanning for conjecture ...
% 3.37/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 277 axioms. Running axiom selection ...
% 3.63/1.75 % [INFO] Axiom selection finished. Selected 245 axioms (removed 32 axioms).
% 4.35/2.00 % [INFO] Problem is higher-order (TPTP THF).
% 4.75/2.03 % [INFO] Type checking passed.
% 4.75/2.04 % [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 ...
% 17.35/5.37 % External prover 'e' found a proof!
% 17.35/5.37 % [INFO] Killing All external provers ...
% 17.35/5.37 % Time passed: 5006ms (effective reasoning time: 4132ms)
% 17.35/5.37 % 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)>
% 17.35/5.38 % Axioms used in derivation (245): fact_185_lfinite__lappend, fact_206_ball__Un, fact_154_lSup__singleton, fact_76_poslsts__UNIV, fact_114_bot__empty__eq, fact_111_Topological__Spaces_OUNIV__not__singleton, fact_145_top__conj_I1_J, fact_91_singletonI, fact_61_equals0D, fact_127_Diff__idemp, fact_202_Int__absorb, fact_25_lappfin__finT, fact_193_Un__Int__distrib2, fact_104_singleton__iff, fact_227_lfinite__LNil, fact_55_empty__iff, fact_161_pairwise__def, fact_101_singleton__inject, fact_28_finlsts_Ocases, fact_173_Int__insert__left__if0, fact_149_lstrict__prefix__code_I3_J, fact_122_fpslsts__def, fact_191_Int__left__commute, fact_99_insert__commute, fact_1_assms, fact_236_Int__Diff, fact_140_insert__Diff, fact_165_fin__Int__inf, fact_30_lapp__all__invT, fact_49_lappend__eq__LNil__iff, fact_247_lfinite__rev__induct, fact_38_lapp__fin__fin__lemma, fact_174_Int__insert__left__if1, fact_116_is__singletonI, fact_155_llist__less__induct, fact_230_lstrict__prefix__lfinite1, fact_153_lSup__empty, fact_229_lfinite__lSupD, fact_60_equals0I, fact_157_llast__singleton, fact_217_Int__UNIV__left, fact_10_inflsts__empty, fact_0_LNil__fin_Oprems, fact_126_Diff__iff, fact_83_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, fact_150_member__remove, fact_52_llist_Oinject, fact_106_insert__UNIV, fact_22_fin__finite, fact_223_Un__UNIV__left, fact_213_UnE, fact_224_Un__empty__right, fact_63_UNIV__witness, fact_8_LNil__is__lappend__conv, fact_169_Un__iff, fact_123_gen__lset__code_I2_J, fact_32_finlsts_Oinducts, fact_19_lappT, fact_175_insert__inter__insert, fact_26_alllsts_Ocases, fact_142_Diff__insert__absorb, fact_218_disjoint__iff__not__equal, fact_121_poslsts__def, fact_84_finlsts__rec__LCons, fact_176_Int__insert__right__if0, fact_225_Un__empty__left, fact_238_Un__Diff, fact_219_Int__empty__right, fact_226_lappend__inf, fact_20_llistE, fact_192_Un__left__commute, fact_65_lappend__assoc, fact_244_Un__singleton__iff, fact_186_insert__disjoint_I1_J, fact_40_fin__inf__cases, fact_237_Diff__Int, fact_31_finlsts__induct, fact_36_alllsts_OLCons__all, fact_243_singleton__Un__iff, fact_170_UnCI, fact_82_finlsts__empty, fact_158_totally__bounded__empty, fact_148_lstrict__prefix__code_I2_J, fact_46_Collect__mem__eq, fact_195_Int__Un__distrib2, fact_9_lappend__is__LNil__conv, fact_128_Diff__cancel, fact_216_Int__UNIV__right, fact_17_LConsE, fact_187_insert__disjoint_I2_J, fact_74_poslsts__iff, fact_132_insert__Diff1, fact_50_lappend__code_I2_J, fact_234_Un__Diff__Int, fact_115_Collect__empty__eq__bot, fact_205_Un__assoc, fact_78_top__set__def, fact_3_infsubsetall, fact_93_insertI1, fact_180_Un__Diff__cancel, fact_69_lappend__LNil__LNil, fact_125_DiffI, fact_66_empty__not__UNIV, fact_221_Int__emptyI, fact_37_finlsts_OLCons__fin, fact_120_is__singletonE, fact_62_emptyE, fact_75_fpslsts__iff, fact_67_neq__LNil__conv, fact_198_Int__Un__distrib, fact_13_LNil__fin_Ohyps, fact_27_alllsts_Osimps, fact_118_is__singletonI_H, fact_94_insertI2, fact_146_remove__def, fact_167_Int__iff, fact_183_lfinite__code_I2_J, fact_80_fpslsts__cases, fact_240_lfinite_Ocases, fact_42_lappend__code_I1_J, fact_58_Collect__empty__eq, fact_89_insert__absorb2, fact_210_UnI2, fact_242_lfinite_Oinducts, fact_7_lapp__fin__infT, fact_45_mem__Collect__eq, fact_139_Diff__insert, fact_6_inflsts__cases, fact_96_insert__ident, fact_137_DiffD1, fact_87_insertCI, fact_16_lapp__fin__fin__iff, fact_215_Int__insert__right, fact_21_finT__simp, fact_162_pairwise__empty, fact_138_DiffD2, fact_112_the__elem__eq, fact_152_lstrict__prefix__code_I1_J, fact_14_alllsts__UNIV, fact_39_inflstsE, fact_196_Un__left__absorb, fact_239_Diff__Un, fact_92_insertE, fact_156_lSup__insert__LNil, fact_33_alllsts_OLNil__all, fact_47_Collect__cong, fact_241_lfinite_Osimps, fact_129_empty__Diff, fact_108_finlsts__rec__LNil, fact_88_insert__iff, fact_194_Int__left__absorb, fact_95_Set_Oset__insert, fact_208_IntD2, fact_81_alllsts__empty, fact_248_llimit__induct, fact_160_llast__LCons2, fact_15_same__lappend__eq, fact_59_ex__in__conv, fact_133_Diff__UNIV, fact_56_all__not__in__conv, fact_214_Int__insert__left, fact_164_llast__lappend__LCons, fact_159_pairwise__singleton, fact_184_lfinite__code_I1_J, fact_103_doubleton__eq__iff, fact_245_insert__is__Un, fact_182_lfinite__LCons, fact_163_pairwise__insert, fact_135_insert__Diff__if, fact_54_iso__tuple__UNIV__I, fact_178_Un__insert__left, fact_231_Diff__Int__distrib2, fact_51_lappend__snocL1__conv__LCons2, fact_90_top1I, fact_207_bex__Un, fact_177_Int__insert__right__if1, fact_86_Set_Ois__empty__def, fact_73_fpslsts__empty, fact_11_notfin__inf, fact_98_insert__eq__iff, fact_53_UNIV__I, fact_72_poslsts__empty, fact_143_gen__lset__code_I1_J, fact_190_Diff__disjoint, fact_209_IntD1, fact_220_Int__empty__left, fact_147_lSup__minus__LNil, fact_110_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, fact_179_Un__insert__right, fact_211_UnI1, fact_85_finlsts__rec__LCons__def, fact_168_IntI, fact_200_Int__commute, fact_134_insert__Diff__single, fact_102_insert__not__empty, fact_68_llist_Odistinct_I1_J, fact_212_IntE, fact_232_Diff__Int__distrib, fact_199_Un__Int__crazy, fact_130_Diff__empty, fact_113_top__empty__eq, fact_18_inflstsI, fact_119_is__singleton__def, fact_29_finlsts_Osimps, fact_41_alllstsE, fact_57_empty__Collect__eq, fact_35_finlsts_OLNil__fin, fact_44_LNil__eq__lappend__iff, fact_203_Un__absorb, fact_64_UNIV__eq__I, fact_141_Diff__insert2, fact_222_Un__UNIV__right, fact_197_Un__Int__distrib, fact_124_top__conj_I2_J, fact_43_lappend__LNil2, fact_246_Diff__triv, fact_117_is__singleton__the__elem, fact_5_inflstsI2, fact_2_lapp__inf, fact_201_Un__commute, fact_107_finlsts__rec__LNil__def, fact_12_notinf__fin, fact_109_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, fact_228_lfinite__LConsI, fact_136_DiffE, fact_34_alllsts_Ocoinduct, fact_23_finite__lemma, fact_181_Un__Diff__cancel2, fact_188_disjoint__insert_I1_J, fact_189_disjoint__insert_I2_J, fact_235_Diff__Int2, fact_77_bot__set__def, fact_171_Int__UNIV, fact_97_insert__absorb, fact_4_infT__simp, fact_105_singletonD, fact_151_lstrict__prefix__code_I4_J, fact_233_Diff__Diff__Int, fact_100_mk__disjoint__insert, fact_24_finsubsetall, fact_166_fin__Un__inf, fact_204_Int__assoc, fact_131_Diff__insert0, fact_172_Un__empty, fact_144_inflsts__def
% 17.35/5.38 % No. of inferences in proof: 494
% 17.35/5.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5006 ms resp. 4132 ms w/o parsing
% 18.43/5.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.43/5.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------