TSTP Solution File: DAT178^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT178^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:41 EDT 2024
% Result : Theorem 17.05s 5.17s
% Output : Refutation 17.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 269
% Syntax : Number of formulae : 503 ( 224 unt; 37 typ; 0 def)
% Number of atoms : 1576 ( 458 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 7032 ( 186 ~; 60 |; 128 &;6154 @)
% ( 0 <=>; 504 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 254 ( 254 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 38 usr; 7 con; 0-5 aty)
% Number of variables : 1694 ( 28 ^1558 !; 76 ?;1694 :)
% ( 32 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(coindu328551480prefix_type,type,
coindu328551480prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_gen_lset_type,type,
coinductive_gen_lset:
!>[TA: $tType] : ( ( set @ TA ) > ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coinductive_lappend_type,type,
coinductive_lappend:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coindu351974385stinct_type,type,
coindu351974385stinct:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lfilter_type,type,
coinductive_lfilter:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lfinite_type,type,
coinductive_lfinite:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_llast_type,type,
coinductive_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(coinductive_llexord_type,type,
coinductive_llexord:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_LCons_type,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_LNil_type,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(coinductive_lnull_type,type,
coinductive_lnull:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lset_type,type,
coinductive_lset:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coinductive_lmember_type,type,
coinductive_lmember:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > $o ) ).
thf(coindu1478340336prefix_type,type,
coindu1478340336prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(undefined_type,type,
undefined:
!>[TA: $tType] : TA ).
thf(lList2435255213lllsts_type,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21511617539llstsp_type,type,
lList21511617539llstsp:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(lList2236698231inlsts_type,type,
lList2236698231inlsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21916056377ts_rec_type,type,
lList21916056377ts_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coinductive_llist @ TA ) > TB > TB ) > ( coinductive_llist @ TA ) > TB ) ).
thf(lList2860480441nlstsp_type,type,
lList2860480441nlstsp:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(lList22096119349pslsts_type,type,
lList22096119349pslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21612149805nflsts_type,type,
lList21612149805nflsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2370560421utlast_type,type,
lList2370560421utlast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList2170638824_llast_type,type,
lList2170638824_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(lList2281150353e_lrev_type,type,
lList2281150353e_lrev:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList21148268032oslsts_type,type,
lList21148268032oslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(sup_sup_type,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_type,type,
a2: set @ a ).
thf(p_type,type,
p: ( coinductive_llist @ a ) > $o ).
thf(l_type,type,
l: coinductive_llist @ a ).
thf(la_type,type,
la: coinductive_llist @ a ).
thf(xs_type,type,
xs: coinductive_llist @ a ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',fact_35_lappend__code_I2_J) ).
thf(629,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)],[120]) ).
thf(37,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ ( coinductive_LNil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_llexord__LNil) ).
thf(365,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ ( coinductive_LNil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',fact_96_alllsts_Ocases) ).
thf(760,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)],[155]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',fact_89_inflstsI2) ).
thf(893,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)],[191]) ).
thf(90,axiom,
! [TA: $tType,A: TA > $o] : ( lList21511617539llstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_alllstsp_OLNil__all) ).
thf(518,plain,
! [TA: $tType,A: TA > $o] : ( lList21511617539llstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(213,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_UNIV__eq__I) ).
thf(962,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)],[213]) ).
thf(1,conjecture,
p @ ( lList2281150353e_lrev @ a @ la ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( p @ ( lList2281150353e_lrev @ a @ la ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(234,plain,
~ ( p @ ( lList2281150353e_lrev @ a @ la ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(77,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Un__commute) ).
thf(481,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)],[77]) ).
thf(52,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coinductive_lset @ TA @ A ) @ ( coinductive_lset @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_lset__lappend__lfinite) ).
thf(408,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coinductive_lset @ TA @ A ) @ ( coinductive_lset @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_21_finT__simp) ).
thf(683,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)],[138]) ).
thf(223,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ B ) @ ( lList2281150353e_lrev @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_lrev__lappend) ).
thf(994,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ B ) @ ( lList2281150353e_lrev @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(23,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ C @ F ) ) )
& ( coinductive_lfinite @ TA @ E )
& ! [G: TA] :
( ( member @ TA @ G @ ( coinductive_lset @ TA @ E ) )
=> ~ ( A @ G ) )
& ( A @ C )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_lfilter__eq__LConsD) ).
thf(308,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ C @ F ) ) )
& ( coinductive_lfinite @ TA @ E )
& ! [G: TA] :
( ( member @ TA @ G @ ( coinductive_lset @ TA @ E ) )
=> ~ ( A @ G ) )
& ( A @ C )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_lfilter @ TA @ A @ B ) )
= ( coinductive_lfilter @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_lfilter__idem) ).
thf(269,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_lfilter @ TA @ A @ B ) )
= ( coinductive_lfilter @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(184,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_lset__induct) ).
thf(861,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(43,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ B )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_lstrict__prefix__lfinite1) ).
thf(384,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)],[43]) ).
thf(102,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu351974385stinct @ TA @ A )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ( ~ ( member @ TA @ B @ ( coinductive_lset @ TA @ C ) )
=> ~ ( coindu351974385stinct @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_ldistinct_Ocases) ).
thf(550,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu351974385stinct @ TA @ A )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ( ~ ( member @ TA @ B @ ( coinductive_lset @ TA @ C ) )
=> ~ ( coindu351974385stinct @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(84,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_llist_Ocollapse_I1_J) ).
thf(500,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',fact_146_lfinite__rev__induct) ).
thf(747,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)],[154]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',fact_130_UnI2) ).
thf(945,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)],[206]) ).
thf(97,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_lstrict__prefix__lappend__conv) ).
thf(538,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_129_DiffE) ).
thf(670,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)],[133]) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',fact_91_lappT) ).
thf(829,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)],[173]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',fact_37_lappend__snocL1__conv__LCons2) ).
thf(898,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)],[193]) ).
thf(226,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( lList2281150353e_lrev @ TA @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_lrev__is__lrev__conv) ).
thf(1001,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( lList2281150353e_lrev @ TA @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_65_finlsts__rec__LNil) ).
thf(782,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)],[161]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',fact_92_finsubsetall) ).
thf(885,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)],[188]) ).
thf(21,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Coinductive__List_Ollast__LCons) ).
thf(301,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',fact_127_DiffD2) ).
thf(841,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)],[178]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_103_llast__lappend__LCons) ).
thf(417,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)],[55]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',fact_25_finlsts_Osimps) ).
thf(570,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)],[106]) ).
thf(162,axiom,
! [TA: $tType] :
( ( lList21511617539llstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList21511617539llstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_alllstsp_Osimps) ).
thf(785,plain,
! [TA: $tType] :
( ( lList21511617539llstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList21511617539llstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(198,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(917,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
= ( coinductive_lmember @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_lset__lmember) ).
thf(357,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
= ( coinductive_lmember @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(117,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LNil @ TA ) ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LCons @ TA @ C @ ( lList2370560421utlast @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_lbutlast__LCons) ).
thf(619,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LNil @ TA ) ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LCons @ TA @ C @ ( lList2370560421utlast @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',fact_34_lappend__eq__LNil__iff) ).
thf(838,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)],[177]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_75_notinf__fin) ).
thf(559,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)],[104]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',fact_26_finlsts__induct) ).
thf(870,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)],[186]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',fact_145_lfinite_Oinducts) ).
thf(606,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)],[116]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_ldistinct_OLCons) ).
thf(325,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [TA: $tType,A: TA > $o] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_lfilter__LNil) ).
thf(261,plain,
! [TA: $tType,A: TA > $o] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(231,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( coinductive_LNil @ TA )
= ( lList2281150353e_lrev @ TA @ A ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_LNil__is__lrev__conv) ).
thf(1013,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( coinductive_LNil @ TA )
= ( lList2281150353e_lrev @ TA @ A ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(16,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ A )
= ( undefined @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_llast__linfinite) ).
thf(284,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ A )
= ( undefined @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(157,axiom,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_lappend__LNil__LNil) ).
thf(770,plain,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(75,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ B @ C ) ) )
= ( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
| ( ( coinductive_lfinite @ TA @ B )
& ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_in__lset__lappend__iff) ).
thf(475,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ B @ C ) ) )
= ( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
| ( ( coinductive_lfinite @ TA @ B )
& ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(41,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ A ) )
=> ~ ( B @ E @ E ) )
=> ( ( coinductive_llexord @ TA @ B @ ( coinductive_lappend @ TA @ A @ C ) @ ( coinductive_lappend @ TA @ A @ D ) )
= ( coinductive_llexord @ TA @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_llexord__lappend__left) ).
thf(376,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ A ) )
=> ~ ( B @ E @ E ) )
=> ( ( coinductive_llexord @ TA @ B @ ( coinductive_lappend @ TA @ A @ C ) @ ( coinductive_lappend @ TA @ A @ D ) )
= ( coinductive_llexord @ TA @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(7,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lfilter @ TA @ A @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_lnull__lfilter) ).
thf(253,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lfilter @ TA @ A @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',fact_23_lappfin__finT) ).
thf(834,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)],[175]) ).
thf(219,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= C ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( lList2170638824_llast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_LList2__Mirabelle__hamjzmohle_Ollast__LCons) ).
thf(981,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= C ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( lList2170638824_llast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(67,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_lfinite__LNil) ).
thf(453,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(53,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: TA,E: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ ( coinductive_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ( B = D )
& ( coinductive_llexord @ TA @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_llexord__code_I3_J) ).
thf(411,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: TA,E: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ ( coinductive_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ( B = D )
& ( coinductive_llexord @ TA @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(5,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coinductive_lfilter @ TA @ C @ A )
= ( coinductive_lfilter @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_lfilter__cong) ).
thf(243,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coinductive_lfilter @ TA @ C @ A )
= ( coinductive_lfilter @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(86,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: TA,E: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ ( coinductive_LCons @ TA @ D @ E ) )
= ( ( ( B = D )
& ( coinductive_llexord @ TA @ A @ C @ E ) )
| ( A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_llexord__LCons__LCons) ).
thf(507,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: TA,E: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ ( coinductive_LCons @ TA @ D @ E ) )
= ( ( ( B = D )
& ( coinductive_llexord @ TA @ A @ C @ E ) )
| ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_llexord @ TA @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_lnull__llexord) ).
thf(527,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_llexord @ TA @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',fact_79_llast__LCons2) ).
thf(397,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)],[48]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',fact_50_neq__LNil__conv) ).
thf(687,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)],[140]) ).
thf(18,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_lfilter__LCons__found) ).
thf(292,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',fact_98_lapp__fin__infT) ).
thf(920,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)],[199]) ).
thf(63,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ D @ B ) @ ( coinductive_LCons @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_llexord__LCons__eq) ).
thf(439,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ D @ B ) @ ( coinductive_LCons @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',fact_132_UnE) ).
thf(678,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)],[136]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
& ( coindu351974385stinct @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_ldistinct__LCons) ).
thf(529,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
& ( coindu351974385stinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',fact_111_Diff__iff) ).
thf(661,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)],[130]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',fact_27_finlsts_Oinducts) ).
thf(810,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)],[171]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_lfinite__code_I2_J) ).
thf(381,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)],[42]) ).
thf(148,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( lList2860480441nlstsp @ TA @ A @ D )
=> ( ( C @ D )
=> ( ( A @ E )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_finlstsp_Oinducts) ).
thf(714,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( lList2860480441nlstsp @ TA @ A @ D )
=> ( ( C @ D )
=> ( ( A @ E )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(167,axiom,
! [TA: $tType] :
( ( coindu351974385stinct @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
| ? [B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
& ~ ( member @ TA @ B @ ( coinductive_lset @ TA @ C ) )
& ( coindu351974385stinct @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_ldistinct_Osimps) ).
thf(798,plain,
! [TA: $tType] :
( ( coindu351974385stinct @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
| ? [B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
& ~ ( member @ TA @ B @ ( coinductive_lset @ TA @ C ) )
& ( coindu351974385stinct @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',fact_86_alllsts_OLCons__all) ).
thf(546,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)],[100]) ).
thf(165,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA] :
~ ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_llexord__code_I2_J) ).
thf(793,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA] :
~ ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(211,axiom,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_gen__lset__code_I1_J) ).
thf(957,plain,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(31,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_llexord__LCons__less) ).
thf(349,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(115,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( lList21511617539llstsp @ TA @ C @ E ) )
& ( C @ F ) ) ) )
=> ( lList21511617539llstsp @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_alllstsp_Ocoinduct) ).
thf(598,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( lList21511617539llstsp @ TA @ C @ E ) )
& ( C @ F ) ) ) )
=> ( lList21511617539llstsp @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',fact_94_alllsts_Ocoinduct) ).
thf(693,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)],[142]) ).
thf(59,axiom,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_lstrict__prefix__code_I1_J) ).
thf(429,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(163,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_UNIV__I) ).
thf(788,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',fact_110_Diff__idemp) ).
thf(467,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)],[72]) ).
thf(78,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_top1I) ).
thf(484,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(118,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_llist_Oset__intros_I1_J) ).
thf(625,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(62,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ~ ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_llist_OdiscI_I2_J) ).
thf(435,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ~ ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(92,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coinductive_lset @ TA @ A ) @ ( coinductive_lset @ TA @ B ) ) ) )
& ( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lset @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_lset__lappend__conv) ).
thf(522,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coinductive_lset @ TA @ A ) @ ( coinductive_lset @ TA @ B ) ) ) )
& ( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lset @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',fact_29_finlsts_OLCons__fin) ).
thf(710,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)],[146]) ).
thf(217,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_llist_Oset__induct) ).
thf(974,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(230,axiom,
p @ ( coinductive_LNil @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_init) ).
thf(1012,plain,
p @ ( coinductive_LNil @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',fact_30_lapp__fin__fin__lemma) ).
thf(742,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)],[152]) ).
thf(228,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( lList2281150353e_lrev @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_lrev__lrev__ident) ).
thf(1006,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( lList2281150353e_lrev @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(45,axiom,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_lnull__def) ).
thf(388,plain,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(113,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_top__empty__eq) ).
thf(593,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',fact_123_Un__assoc) ).
thf(420,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)],[56]) ).
thf(8,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( coindu351974385stinct @ TA @ A )
=> ( coindu351974385stinct @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_ldistinct__lfilterI) ).
thf(256,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( coindu351974385stinct @ TA @ A )
=> ( coindu351974385stinct @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(80,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(488,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)],[80]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(901,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(124,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList21511617539llstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_alllstsp_Ocases) ).
thf(642,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList21511617539llstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(232,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2281150353e_lrev @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_lrevT) ).
thf(1016,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2281150353e_lrev @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(224,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_lrev__is__LNil__conv) ).
thf(997,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',fact_95_alllsts_Osimps) ).
thf(701,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)],[143]) ).
thf(89,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_lappend_Odisc_I2_J) ).
thf(515,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(127,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_lapp__infT) ).
thf(654,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(196,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(911,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)],[196]) ).
thf(160,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_lapp__allT__iff) ).
thf(779,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(39,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_fin__Un__inf) ).
thf(371,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)],[39]) ).
thf(85,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( ( coinductive_llexord @ TA @ A @ C @ D )
=> ( ! [E: TA,F: TA,G: TA] :
( ( A @ E @ F )
=> ( ( A @ F @ G )
=> ( A @ E @ G ) ) )
=> ( coinductive_llexord @ TA @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_llexord__trans) ).
thf(503,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( ( coinductive_llexord @ TA @ A @ C @ D )
=> ( ! [E: TA,F: TA,G: TA] :
( ( A @ E @ F )
=> ( ( A @ F @ G )
=> ( A @ E @ G ) ) )
=> ( coinductive_llexord @ TA @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(204,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lstrict__prefix__code_I3_J) ).
thf(938,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)],[204]) ).
thf(35,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList21511617539llstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_alllstsp_OLCons__all) ).
thf(360,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList21511617539llstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList21511617539llstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(98,axiom,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_llist_Odisc_I1_J) ).
thf(541,plain,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',fact_128_DiffD1) ).
thf(657,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)],[128]) ).
thf(209,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(953,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',fact_15_lappend__is__LNil__conv) ).
thf(773,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)],[158]) ).
thf(111,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_alllsts__UNIV) ).
thf(586,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)],[111]) ).
thf(20,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_lappend_Odisc__iff_I2_J) ).
thf(298,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(214,axiom,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_llast__singleton) ).
thf(965,plain,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(88,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_finlstsp_OLCons__fin) ).
thf(513,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( A @ C )
=> ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(11,axiom,
! [TA: $tType] :
( ( coinductive_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Coinductive__List_Ollast__LNil) ).
thf(264,plain,
! [TA: $tType] :
( ( coinductive_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(107,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_lset__induct_H) ).
thf(573,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(65,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_lfinite__LConsI) ).
thf(444,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)],[65]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',fact_97_fin__inf__cases) ).
thf(584,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)],[110]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_114_Un__Diff__cancel) ).
thf(423,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)],[57]) ).
thf(50,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) @ ( coinductive_lappend @ TA @ B @ D ) )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ~ ( A @ E @ E ) )
=> ( coinductive_llexord @ TA @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_llexord__lappend__leftD) ).
thf(402,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) @ ( coinductive_lappend @ TA @ B @ D ) )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ~ ( A @ E @ E ) )
=> ( coinductive_llexord @ TA @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',fact_55_fpslsts__cases) ).
thf(843,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)],[179]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_59_finlsts__rec__LCons__def) ).
thf(577,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)],[108]) ).
thf(15,axiom,
! [TA: $tType] :
( ( lList2170638824_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_LList2__Mirabelle__hamjzmohle_Ollast__LNil) ).
thf(281,plain,
! [TA: $tType] :
( ( lList2170638824_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(105,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ( A @ B )
=> ( ! [C: coinductive_llist @ TA] :
( ( A @ C )
=> ( ( C
= ( coinductive_LNil @ TA ) )
| ? [D: TA,E: coinductive_llist @ TA] :
( ( C
= ( coinductive_LCons @ TA @ D @ E ) )
& ~ ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
& ( ( A @ E )
| ( coindu351974385stinct @ TA @ E ) ) ) ) )
=> ( coindu351974385stinct @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_ldistinct_Ocoinduct) ).
thf(562,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ( A @ B )
=> ( ! [C: coinductive_llist @ TA] :
( ( A @ C )
=> ( ( C
= ( coinductive_LNil @ TA ) )
| ? [D: TA,E: coinductive_llist @ TA] :
( ( C
= ( coinductive_LCons @ TA @ D @ E ) )
& ~ ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
& ( ( A @ E )
| ( coindu351974385stinct @ TA @ E ) ) ) ) )
=> ( coindu351974385stinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(195,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList2860480441nlstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_finlstsp_Ocases) ).
thf(904,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( lList2860480441nlstsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( lList2860480441nlstsp @ TA @ A @ C )
=> ~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',fact_64_llist__less__induct) ).
thf(391,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)],[46]) ).
thf(29,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ ( coinductive_LNil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_llexord__code_I1_J) ).
thf(335,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ ( coinductive_LNil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(169,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_lappend_Octr_I1_J) ).
thf(804,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(144,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Un__UNIV__left) ).
thf(704,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)],[144]) ).
thf(207,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_split__llist) ).
thf(947,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(174,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/sandbox2/benchmark/theBenchmark.p',fact_60_finlsts__rec__LCons) ).
thf(831,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)],[174]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_49_lappend__assoc) ).
thf(736,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)],[150]) ).
thf(221,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ A ) @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lrev__LCons) ).
thf(990,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ A ) @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',fact_125_Un__Diff) ).
thf(362,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)],[36]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_llist_Odistinct_I1_J) ).
thf(649,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)],[125]) ).
thf(190,axiom,
! [TA: $tType] :
( ( lList2860480441nlstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList2860480441nlstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_finlstsp_Osimps) ).
thf(890,plain,
! [TA: $tType] :
( ( lList2860480441nlstsp @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ C ) )
& ( lList2860480441nlstsp @ TA @ A @ C )
& ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(82,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_lappend__lnull1) ).
thf(494,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(38,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_llist_OdiscI_I1_J) ).
thf(367,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_lfinite__LCons) ).
thf(535,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)],[96]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_lfilter__empty__conv) ).
thf(240,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',fact_102_inflsts__def) ).
thf(895,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)],[192]) ).
thf(28,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( ( coinductive_llexord @ TA @ A @ C @ B )
=> ( ! [D: TA,E: TA] :
( ( A @ D @ E )
=> ~ ( A @ E @ D ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_llexord__antisym) ).
thf(330,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( ( coinductive_llexord @ TA @ A @ C @ B )
=> ( ! [D: TA,E: TA] :
( ( A @ D @ E )
=> ~ ( A @ E @ D ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',fact_14_LNil__is__lappend__conv) ).
thf(848,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)],[180]) ).
thf(91,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_lnull__imp__lfinite) ).
thf(520,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',fact_93_finite__lemma) ).
thf(685,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)],[139]) ).
thf(172,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_lset__intros_I2_J) ).
thf(827,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',fact_56_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(636,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)],[122]) ).
thf(225,axiom,
member @ ( coinductive_llist @ a ) @ l @ ( lList2236698231inlsts @ a @ a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062l_A_092_060in_062_AA_092_060_094sup_062_092_060star_062_092_060close_062) ).
thf(1000,plain,
member @ ( coinductive_llist @ a ) @ l @ ( lList2236698231inlsts @ a @ a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(60,axiom,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_ldistinct__LNil__code) ).
thf(431,plain,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_143_lfinite_Ocases) ).
thf(922,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)],[200]) ).
thf(68,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llexord @ TA @ B @ C @ A )
= ( coinductive_lnull @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_llexord__LNil__right) ).
thf(455,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llexord @ TA @ B @ C @ A )
= ( coinductive_lnull @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finlsts_OLNil__fin) ).
thf(883,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(47,axiom,
! [TA: $tType] :
( ( coinductive_gen_lset @ TA )
= ( ^ [A: set @ TA,B: coinductive_llist @ TA] : ( sup_sup @ ( set @ TA ) @ A @ ( coinductive_lset @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_gen__lset__def) ).
thf(394,plain,
! [TA: $tType] :
( ( coinductive_gen_lset @ TA )
= ( ^ [A: set @ TA,B: coinductive_llist @ TA] : ( sup_sup @ ( set @ TA ) @ A @ ( coinductive_lset @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(22,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( coinductive_llexord @ TA @ A @ ( coinductive_lappend @ TA @ D @ B ) @ ( coinductive_lappend @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_llexord__lappend__leftI) ).
thf(306,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( coinductive_llexord @ TA @ A @ ( coinductive_lappend @ TA @ D @ B ) @ ( coinductive_lappend @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_lfinite__lfilterI) ).
thf(267,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',fact_144_lfinite_Osimps) ).
thf(851,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)],[181]) ).
thf(74,axiom,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_ldistinct_OLNil) ).
thf(473,plain,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',fact_77_LConsE) ).
thf(675,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)],[135]) ).
thf(58,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_top__conj_I1_J) ).
thf(426,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',fact_90_lapp__all__invT) ).
thf(548,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)],[101]) ).
thf(233,axiom,
( la
= ( coinductive_LNil @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_LNil__fin_Ohyps) ).
thf(1018,plain,
( la
= ( coinductive_LNil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(176,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_UNIV__witness) ).
thf(836,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmember @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coinductive_lmember @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_lmember__code_I2_J) ).
thf(795,plain,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmember @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coinductive_lmember @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(137,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Un__UNIV__right) ).
thf(680,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)],[137]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_112_DiffI) ).
thf(927,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)],[201]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lnull @ TA @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_llist_Odisc_I2_J) ).
thf(374,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lnull @ TA @ ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',fact_17_lapp__fin__fin__iff) ).
thf(968,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)],[215]) ).
thf(69,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ! [D: TA,E: TA] :
( ( A @ D @ E )
| ( D = E )
| ( A @ E @ D ) )
=> ( ( coinductive_llexord @ TA @ A @ B @ C )
| ( coinductive_llexord @ TA @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_llexord__linear) ).
thf(458,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ! [D: TA,E: TA] :
( ( A @ D @ E )
| ( D = E )
| ( A @ E @ D ) )
=> ( ( coinductive_llexord @ TA @ A @ B @ C )
| ( coinductive_llexord @ TA @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_38_llist_Oinject) ).
thf(776,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)],[159]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',fact_108_Un__iff) ).
thf(690,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)],[141]) ).
thf(19,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfilter @ TA @ B @ ( coinductive_lappend @ TA @ A @ C ) )
= ( coinductive_lappend @ TA @ ( coinductive_lfilter @ TA @ B @ A ) @ ( coinductive_lfilter @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_lfilter__lappend__lfinite) ).
thf(295,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfilter @ TA @ B @ ( coinductive_lappend @ TA @ A @ C ) )
= ( coinductive_lappend @ TA @ ( coinductive_lfilter @ TA @ B @ A ) @ ( coinductive_lfilter @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',fact_109_UnCI) ).
thf(707,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)],[145]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',fact_33_LNil__eq__lappend__iff) ).
thf(887,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)],[189]) ).
thf(27,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_lappend__lnull2) ).
thf(327,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',fact_83_inflstsE) ).
thf(739,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)],[151]) ).
thf(222,axiom,
member @ ( coinductive_llist @ a ) @ xs @ ( lList2236698231inlsts @ a @ a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_fin) ).
thf(993,plain,
member @ ( coinductive_llist @ a ) @ xs @ ( lList2236698231inlsts @ a @ a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(147,axiom,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_lmember__code_I1_J) ).
thf(712,plain,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_lset__intros_I1_J) ).
thf(557,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(54,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
& ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_lnull__lappend) ).
thf(414,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
& ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(216,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_lappend__code_I1_J) ).
thf(971,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',fact_80_inflstsI) ).
thf(673,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)],[134]) ).
thf(64,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ D )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ F ) )
& ( ( ( B = E )
& ( coinductive_llexord @ TA @ A @ C @ F ) )
| ( A @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_llexord__LCons__left) ).
thf(441,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) @ D )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ F ) )
& ( ( ( B = E )
& ( coinductive_llexord @ TA @ A @ C @ F ) )
| ( A @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(70,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_lappend_Odisc_I1_J) ).
thf(463,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(73,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Un__absorb) ).
thf(470,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',fact_22_fin__finite) ).
thf(951,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)],[208]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',fact_53_fpslsts__iff) ).
thf(744,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)],[153]) ).
thf(66,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) )
& ( ~ ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( undefined @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_llast__lappend) ).
thf(446,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) )
& ( ~ ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( undefined @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(83,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_top__conj_I2_J) ).
thf(497,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',fact_131_UnI1) ).
thf(859,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)],[183]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',fact_72_poslsts__iff) ).
thf(978,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)],[218]) ).
thf(44,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_llexord__refl) ).
thf(386,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(119,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_alllsts_OLNil__all) ).
thf(627,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(203,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/sandbox2/benchmark/theBenchmark.p',fact_24_finlsts_Ocases) ).
thf(931,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)],[203]) ).
thf(109,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
=> ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_lapp__inv2T) ).
thf(581,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
=> ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_lfilter__LCons__seek) ).
thf(250,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(71,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_lfinite__code_I1_J) ).
thf(465,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_split__llist__first) ).
thf(588,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(24,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_not__lnull__conv) ).
thf(319,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_lfilter__id__conv) ).
thf(258,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_66_finlsts__rec__LNil__def) ).
thf(632,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)],[121]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_88_inflsts__cases) ).
thf(731,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(126,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).
thf(652,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(32,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_lappend_Oexhaust) ).
thf(351,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(197,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_lappend__LNil2) ).
thf(914,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(3,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ~ ( B @ C ) )
=> ( ( coinductive_lfilter @ TA @ B @ A )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_diverge__lfilter__LNil) ).
thf(235,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ~ ( B @ C ) )
=> ( ( coinductive_lfilter @ TA @ B @ A )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',fact_74_notfin__inf) ).
thf(667,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)],[132]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_lstrict__prefix__code_I2_J) ).
thf(929,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)],[202]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_62_lstrict__prefix__code_I4_J) ).
thf(478,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)],[76]) ).
thf(14,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_lappend @ TA @ C @ D ) )
=> ( ( coinductive_lfinite @ TA @ C )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ F ) )
& ( coinductive_lfinite @ TA @ E )
& ( C
= ( coinductive_lfilter @ TA @ A @ E ) )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_lfilter__eq__lappend__lfiniteD) ).
thf(272,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_lappend @ TA @ C @ D ) )
=> ( ( coinductive_lfinite @ TA @ C )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ F ) )
& ( coinductive_lfinite @ TA @ E )
& ( C
= ( coinductive_lfilter @ TA @ A @ E ) )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_lfilter__LCons) ).
thf(287,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(61,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ B @ ( coinductive_lappend @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_llexord__append__right) ).
thf(433,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ B @ ( coinductive_lappend @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_119_Un__left__commute) ).
thf(510,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)],[87]) ).
thf(51,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_lappend__inf) ).
thf(405,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)],[51]) ).
thf(182,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_lset__cases) ).
thf(854,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_78_lapp__inf) ).
thf(790,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)],[164]) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',fact_126_bex__Un) ).
thf(867,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)],[185]) ).
thf(168,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/sandbox2/benchmark/theBenchmark.p',fact_54_poslsts__UNIV) ).
thf(801,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)],[168]) ).
thf(170,axiom,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_lbutlast__LNil) ).
thf(807,plain,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',fact_16_same__lappend__eq) ).
thf(767,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)],[156]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fact_20_llistE) ).
thf(664,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)],[131]) ).
thf(49,axiom,
! [TA: $tType,A: TA > $o] : ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_finlstsp_OLNil__fin) ).
thf(400,plain,
! [TA: $tType,A: TA > $o] : ( lList2860480441nlstsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(212,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_app__invT) ).
thf(960,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_113_Un__Diff__cancel2) ).
thf(532,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)],[95]) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',fact_85_infT__simp) ).
thf(955,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)],[210]) ).
thf(220,axiom,
! [A: coinductive_llist @ a,B: a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2236698231inlsts @ a @ a2 ) )
=> ( ( p @ A )
=> ( ( member @ a @ B @ a2 )
=> ( p @ ( coinductive_lappend @ a @ A @ ( coinductive_LCons @ a @ B @ ( coinductive_LNil @ a ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_local_Ostep) ).
thf(987,plain,
! [A: coinductive_llist @ a,B: a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2236698231inlsts @ a @ a2 ) )
=> ( ( p @ A )
=> ( ( member @ a @ B @ a2 )
=> ( p @ ( coinductive_lappend @ a @ A @ ( coinductive_LCons @ a @ B @ ( coinductive_LNil @ a ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_81_alllstsE) ).
thf(596,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)],[114]) ).
thf(227,axiom,
( l
= ( lList2281150353e_lrev @ a @ xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_l__def) ).
thf(1004,plain,
( l
= ( lList2281150353e_lrev @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(25,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_top__set__def) ).
thf(322,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',fact_82_infsubsetall) ).
thf(486,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)],[79]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',fact_147_llimit__induct) ).
thf(337,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)],[30]) ).
thf(205,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_llist_Oset__cases) ).
thf(940,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_lzip_Oexhaust) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(229,axiom,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lrev__LNil) ).
thf(1009,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(129,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_llist_Oset__intros_I2_J) ).
thf(659,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_118_lfinite__lappend) ).
thf(543,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)],[99]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',fact_124_ball__Un) ).
thf(639,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)],[123]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_120_Un__left__absorb) ).
thf(491,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)],[81]) ).
thf(1020,plain,
$false,
inference(e,[status(thm)],[629,365,760,893,518,962,234,481,408,683,994,308,269,861,384,550,500,747,945,538,670,829,898,1001,782,885,301,841,417,570,785,917,357,619,838,559,870,606,325,261,1013,284,770,475,376,253,834,981,453,411,243,507,527,397,687,292,920,439,678,529,661,810,381,714,798,546,793,957,349,598,693,429,788,467,484,625,435,522,710,974,1012,742,1006,388,593,420,256,488,901,642,1016,997,701,515,654,911,779,371,503,938,360,541,657,953,773,586,298,965,513,264,573,444,584,423,402,843,577,281,562,904,391,335,804,704,947,831,736,990,362,649,890,494,367,535,240,895,330,848,520,685,827,636,1000,431,922,455,883,394,306,267,851,473,675,426,548,1018,836,795,680,927,374,968,458,776,690,295,707,887,327,739,993,712,557,414,971,673,441,463,470,951,744,446,497,859,978,386,627,931,581,250,465,588,319,258,632,731,652,351,914,235,667,929,478,272,287,433,510,405,854,790,867,801,807,767,664,400,960,532,955,987,596,1004,322,486,337,940,354,1009,659,543,639,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : DAT178^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n022.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 11:33:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.91/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/1.09 % [INFO] Parsing done (243ms).
% 1.67/1.10 % [INFO] Running in sequential loop mode.
% 2.58/1.31 % [INFO] eprover registered as external prover.
% 2.58/1.31 % [INFO] cvc4 registered as external prover.
% 2.67/1.31 % [INFO] Scanning for conjecture ...
% 2.72/1.41 % [INFO] Found a conjecture and 272 axioms. Running axiom selection ...
% 3.13/1.50 % [INFO] Axiom selection finished. Selected 231 axioms (removed 41 axioms).
% 3.65/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 3.65/1.69 % [INFO] Type checking passed.
% 3.65/1.70 % [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 ...
% 17.05/5.17 % External prover 'e' found a proof!
% 17.05/5.17 % [INFO] Killing All external provers ...
% 17.05/5.17 % Time passed: 4648ms (effective reasoning time: 4067ms)
% 17.05/5.17 % 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)>
% 17.05/5.17 % Axioms used in derivation (231): fact_217_LList2__Mirabelle__hamjzmohle_Ollast__LNil, fact_117_lfinite__code_I1_J, fact_238_llexord__refl, fact_101_app__invT, fact_112_DiffI, fact_94_alllsts_Ocoinduct, fact_210_lfilter__eq__LConsD, fact_54_poslsts__UNIV, fact_192_llist_Oset__cases, fact_88_inflsts__cases, fact_230_ldistinct__LNil__code, fact_224_lfilter__eq__lappend__lfiniteD, fact_222_lfilter__LCons__found, fact_111_Diff__iff, fact_142_finlstsp_OLNil__fin, fact_219_lfilter__cong, fact_231_ldistinct__LCons, fact_6_lrev__lrev__ident, fact_212_lfilter__LCons, fact_145_lfinite_Oinducts, fact_198_lset__intros_I1_J, fact_172_lset__lappend__lfinite, fact_106_finlstsp_Oinducts, fact_16_same__lappend__eq, fact_52_lappend__LNil__LNil, fact_2_l__def, fact_70_top__conj_I2_J, fact_121_Un__commute, fact_214_diverge__lfilter__LNil, fact_102_inflsts__def, fact_207_lmember__code_I2_J, fact_233_ldistinct_OLCons, fact_74_notfin__inf, fact_205_split__llist, fact_68_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, fact_232_ldistinct__lfilterI, fact_73_llast__singleton, fact_175_lnull__lappend, fact_78_lapp__inf, fact_206_split__llist__first, fact_130_UnI2, fact_137_Un__UNIV__right, fact_53_fpslsts__iff, fact_242_lnull__llexord, fact_92_finsubsetall, fact_22_fin__finite, fact_177_lappend_Oexhaust, fact_200_lnull__imp__lfinite, fact_100_lapp__infT, fact_77_LConsE, fact_123_Un__assoc, fact_241_llexord__LNil__right, fact_84_lapp__allT__iff, fact_193_lset__induct_H, fact_148_alllstsp_Ocases, fact_105_alllstsp_Ocoinduct, fact_99_lapp__inv2T, fact_20_llistE, fact_40_iso__tuple__UNIV__I, fact_184_lnull__def, fact_103_llast__lappend__LCons, fact_109_UnCI, fact_104_fin__Un__inf, fact_56_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, fact_83_inflstsE, fact_135_lappend__inf, fact_15_lappend__is__LNil__conv, fact_58_lstrict__prefix__code_I3_J, fact_66_finlsts__rec__LNil__def, fact_86_alllsts_OLCons__all, fact_234_ldistinct_OLNil, fact_89_inflstsI2, fact_28_finlsts_OLNil__fin, fact_11_lrev__lappend, fact_138_lstrict__prefix__lfinite1, fact_46_Collect__mem__eq, fact_118_lfinite__lappend, fact_178_lzip_Oexhaust, fact_202_lappend_Octr_I1_J, fact_59_finlsts__rec__LCons__def, fact_223_lfilter__empty__conv, fact_43_UNIV__witness, fact_5_local_Ostep, fact_226_llast__linfinite, fact_227_gen__lset__code_I1_J, fact_51_llist_Odistinct_I1_J, fact_61_top1I, fact_18_lbutlast__LCons, fact_141_alllstsp_OLNil__all, fact_180_lappend__lnull2, fact_10_lbutlast__LNil, fact_216_lfilter__lappend__lfinite, fact_139_alllstsp_OLCons__all, fact_245_llexord__antisym, fact_225_Coinductive__List_Ollast__LNil, fact_49_lappend__assoc, fact_215_lnull__lfilter, fact_29_finlsts_OLCons__fin, fact_228_ldistinct_Ocases, fact_90_lapp__all__invT, fact_23_lappfin__finT, fact_13__092_060open_062l_A_092_060in_062_AA_092_060_094sup_062_092_060star_062_092_060close_062, fact_25_finlsts_Osimps, fact_44_UNIV__eq__I, fact_246_llexord__append__right, fact_115_lfinite__code_I2_J, fact_185_llist_Ocollapse_I1_J, fact_119_Un__left__commute, fact_122_Un__absorb, fact_33_LNil__eq__lappend__iff, fact_150_finlstsp_Ocases, fact_113_Un__Diff__cancel2, fact_116_lfinite__LCons, fact_252_llexord__LCons__less, fact_189_llist_OdiscI_I2_J, fact_38_llist_Oinject, fact_247_llexord__lappend__leftI, fact_45_mem__Collect__eq, fact_251_llexord__LCons__eq, fact_80_inflstsI, fact_249_llexord__code_I3_J, fact_81_alllstsE, fact_181_lappend__lnull1, fact_21_finT__simp, fact_209_llast__lappend, fact_186_llist_OdiscI_I1_J, fact_79_llast__LCons2, fact_95_alllsts_Osimps, fact_39_UNIV__I, fact_134_lfinite__LNil, fact_191_llist_Oset__induct, fact_218_lfilter__id__conv, fact_32_lappend__LNil2, fact_129_DiffE, fact_236_llexord__lappend__leftD, fact_31_lappend__code_I1_J, fact_143_lfinite_Ocases, fact_194_lset__induct, fact_132_UnE, fact_47_Collect__cong, fact_110_Diff__idemp, fact_146_lfinite__rev__induct, fact_72_poslsts__iff, fact_3_lrev__LNil, fact_244_llexord__linear, fact_36_LList2__Mirabelle__hamjzmohle_Ollast__LCons, fact_67_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, fact_7_lrev__is__lrev__conv, fact_96_alllsts_Ocases, fact_9_lrev__is__LNil__conv, fact_62_lstrict__prefix__code_I4_J, fact_243_llexord__trans, fact_8_LNil__is__lrev__conv, fact_93_finite__lemma, fact_133_lfinite__LConsI, fact_239_llexord__LCons__LCons, fact_237_llexord__lappend__left, fact_127_DiffD2, fact_179_lset__lmember, fact_196_llist_Oset__intros_I1_J, fact_120_Un__left__absorb, fact_4_lrevT, fact_97_fin__inf__cases, fact_221_lfilter__LCons__seek, fact_12_fin, fact_197_llist_Oset__intros_I2_J, fact_195_lset__cases, fact_87_alllsts_OLNil__all, fact_211_lfilter__idem, fact_144_lfinite_Osimps, fact_24_finlsts_Ocases, fact_108_Un__iff, fact_60_finlsts__rec__LCons, fact_71_top__conj_I1_J, fact_136_Un__UNIV__left, fact_250_llexord__LCons__left, fact_188_not__lnull__conv, fact_201_in__lset__lappend__iff, fact_64_llist__less__induct, fact_176_lappend_Odisc__iff_I2_J, fact_107_finlstsp_Osimps, fact_126_bex__Un, fact_19_lrev__LCons, fact_199_lset__intros_I2_J, fact_55_fpslsts__cases, fact_34_lappend__eq__LNil__iff, fact_203_Coinductive__List_Ollast__LCons, fact_98_lapp__fin__infT, fact_248_llexord__LNil, fact_30_lapp__fin__fin__lemma, fact_174_lmember__code_I1_J, fact_183_lappend_Odisc_I2_J, fact_35_lappend__code_I2_J, fact_91_lappT, fact_114_Un__Diff__cancel, fact_220_lfinite__lfilterI, fact_27_finlsts_Oinducts, fact_0_init, fact_26_finlsts__induct, fact_229_ldistinct_Osimps, fact_57_lstrict__prefix__code_I2_J, fact_82_infsubsetall, fact_147_llimit__induct, fact_182_lappend_Odisc_I1_J, fact_240_llexord__code_I1_J, fact_173_lstrict__prefix__lappend__conv, fact_85_infT__simp, fact_208_gen__lset__def, fact_17_lapp__fin__fin__iff, fact_65_finlsts__rec__LNil, fact_76_alllsts__UNIV, fact_128_DiffD1, fact_235_ldistinct_Ocoinduct, fact_125_Un__Diff, fact_187_llist_Odisc_I1_J, fact_37_lappend__snocL1__conv__LCons2, fact_50_neq__LNil__conv, fact_253_llexord__code_I2_J, fact_140_finlstsp_OLCons__fin, fact_63_lstrict__prefix__code_I1_J, fact_190_llist_Odisc_I2_J, fact_131_UnI1, fact_1_LNil__fin_Ohyps, fact_204_lset__lappend__conv, fact_124_ball__Un, fact_69_top__empty__eq, fact_14_LNil__is__lappend__conv, fact_75_notinf__fin, fact_213_lfilter__LNil, fact_149_alllstsp_Osimps, fact_42_top__set__def
% 17.05/5.17 % No. of inferences in proof: 466
% 17.05/5.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4648 ms resp. 4067 ms w/o parsing
% 17.64/5.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.64/5.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------