TSTP Solution File: COM175^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COM175^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 07:30:13 EDT 2024
% Result : Theorem 170.21s 137.33s
% Output : Refutation 171.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 317
% Syntax : Number of formulae : 594 ( 202 unt; 42 typ; 0 def)
% Number of atoms : 1868 ( 470 equ; 4 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 8498 ( 174 ~; 76 |; 162 &;7276 @)
% ( 0 <=>; 810 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 470 ( 470 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 12 con; 0-8 aty)
% Number of variables : 2214 ( 112 ^1918 !; 148 ?;2214 :)
% ( 36 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semilattice_sup_type,type,
semilattice_sup:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comple187826305attice_type,type,
comple187826305attice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
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(coindu1259883913_llist_type,type,
coindu1259883913_llist:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > $o ) > ( TB > ( coinductive_llist @ TA ) ) > ( TB > TB ) > TB > ( 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(coindu63249387sorted_type,type,
coindu63249387sorted:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coindu1441602521_llist_type,type,
coindu1441602521_llist:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > TB ) > TB > ( coinductive_llist @ TA ) ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(koenig916195507_paths_type,type,
koenig916195507_paths:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(koenig2031690877pathsp_type,type,
koenig2031690877pathsp:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(koenig317145564le_via_type,type,
koenig317145564le_via:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > TA > ( set @ TA ) ) ).
thf(koenig1757754772e_viap_type,type,
koenig1757754772e_viap:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > TA > TA > $o ) ).
thf(sup_sup_type,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(graph_type,type,
graph: a > a > $o ).
thf(n_type,type,
n: a ).
thf(n2_type,type,
n2: a ).
thf(ns_type,type,
ns: set @ a ).
thf(x_type,type,
x: a ).
thf(xs_type,type,
xs: coinductive_llist @ a ).
thf(xs2_type,type,
xs2: coinductive_llist @ a ).
thf(122,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_lsorted_Ocases) ).
thf(645,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(238,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( koenig916195507_paths @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: TA] :
( A
= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
| ? [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
& ( B @ C @ D )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_paths_Osimps) ).
thf(1036,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( koenig916195507_paths @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: TA] :
( A
= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
| ? [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
& ( B @ C @ D )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(176,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(809,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(275,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ D ) @ ( koenig916195507_paths @ TA @ A ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) @ ( koenig916195507_paths @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_paths_OLCons) ).
thf(1168,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ D ) @ ( koenig916195507_paths @ TA @ A ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) @ ( koenig916195507_paths @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(253,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ( coindu63249387sorted @ TA @ B )
& ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_lsorted__LCons) ).
thf(1083,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ( coindu63249387sorted @ TA @ B )
& ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(71,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_set__eq__subset) ).
thf(481,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_ord__le__eq__subst) ).
thf(333,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(115,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_sup_Omono) ).
thf(628,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_subsetI) ).
thf(1158,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(228,axiom,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ns ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062LCons_An_Axs_A_092_060in_062_Apaths_Agraph_059_Ax_A_092_060in_062_Alset_Axs_059_Alset_Axs_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(994,plain,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ns ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(20,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_equalityE) ).
thf(308,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(131,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_15_llist_Oinject) ).
thf(677,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)],[131]) ).
thf(251,axiom,
! [TA: $tType] :
( ( koenig1757754772e_viap @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA,C: TA,D: TA] :
? [E: coinductive_llist @ TA,F: TA] :
( ( D = F )
& ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ E ) )
& ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_reachable__viap_Osimps) ).
thf(1078,plain,
! [TA: $tType] :
( ( koenig1757754772e_viap @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA,C: TA,D: TA] :
? [E: coinductive_llist @ TA,F: TA] :
( ( D = F )
& ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ E ) )
& ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(43,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_le__iff__sup) ).
thf(385,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(85,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_211_llexord__linear) ).
thf(533,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)],[85]) ).
thf(171,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_135_lfinite__LCons) ).
thf(797,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)],[171]) ).
thf(68,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_lfp_Oleq__antisym) ).
thf(472,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(178,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_134_lfinite__code_I2_J) ).
thf(814,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)],[178]) ).
thf(153,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_sup_Oabsorb__iff1) ).
thf(747,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(29,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_lfp_Oleq__refl) ).
thf(340,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(86,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_179_lfilter__lappend__lfinite) ).
thf(538,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)],[86]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_ord__eq__le__subst) ).
thf(670,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(166,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_inf__sup__ord_I4_J) ).
thf(782,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(144,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: coinductive_llist @ TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ B @ C ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_LCons__LCons) ).
thf(709,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: coinductive_llist @ TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ B @ C ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(59,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_sup_OcoboundedI2) ).
thf(436,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B )
= ( coinductive_LCons @ TB @ ( C @ B ) @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_unfold__llist_Octr_I2_J) ).
thf(829,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B )
= ( coinductive_LCons @ TB @ ( C @ B ) @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(50,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_lfinite__LNil) ).
thf(404,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_le__funI) ).
thf(885,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(242,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_202_UnI2) ).
thf(1046,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)],[242]) ).
thf(23,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_inf__sup__ord_I3_J) ).
thf(320,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(95,axiom,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_lappend__LNil__LNil) ).
thf(565,plain,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(40,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_98_neq__LNil__conv) ).
thf(372,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)],[40]) ).
thf(141,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_sup_OboundedI) ).
thf(702,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(64,axiom,
! [TA: $tType,A: TA > $o] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_lfilter__LNil) ).
thf(460,plain,
! [TA: $tType,A: TA > $o] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(101,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_138_lfinite__LConsI) ).
thf(587,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)],[101]) ).
thf(183,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_sup_OcoboundedI1) ).
thf(838,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_subset__Un__eq) ).
thf(559,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(55,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_130_llimit__induct) ).
thf(416,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)],[55]) ).
thf(8,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_12) ).
thf(289,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(261,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) @ ( koenig916195507_paths @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_paths_OSingle) ).
thf(1100,plain,
! [TA: $tType,A: TA,B: TA > TA > $o] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) @ ( koenig916195507_paths @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(179,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: TA] :
( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LNil @ TA ) ) )
| ? [E: TA,F: TA,G: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LCons @ TA @ F @ G ) ) )
& ( C @ E @ F )
& ( ( A @ ( coinductive_LCons @ TA @ F @ G ) )
| ( koenig2031690877pathsp @ TA @ C @ ( coinductive_LCons @ TA @ F @ G ) ) ) ) ) )
=> ( koenig2031690877pathsp @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_pathsp_Ocoinduct) ).
thf(817,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: TA] :
( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LNil @ TA ) ) )
| ? [E: TA,F: TA,G: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LCons @ TA @ F @ G ) ) )
& ( C @ E @ F )
& ( ( A @ ( coinductive_LCons @ TA @ F @ G ) )
| ( koenig2031690877pathsp @ TA @ C @ ( coinductive_LCons @ TA @ F @ G ) ) ) ) ) )
=> ( koenig2031690877pathsp @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(201,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_Singleton) ).
thf(902,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(265,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ! [C: TA] :
( A
!= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
=> ( ( B @ C @ D )
=> ~ ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_paths_Ocases) ).
thf(1115,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ! [C: TA] :
( A
!= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
=> ( ( B @ C @ D )
=> ~ ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(25,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Collect__mono) ).
thf(325,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(156,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_181_llexord__append__right) ).
thf(756,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)],[156]) ).
thf(169,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_148_llast__lappend__LCons) ).
thf(789,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)],[169]) ).
thf(35,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_lappend__LNil2) ).
thf(353,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(244,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_20_lset__intros_I1_J) ).
thf(1051,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)],[244]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__fun__def) ).
thf(475,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(205,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_168_llexord__lappend__leftD) ).
thf(924,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)],[205]) ).
thf(98,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_215_lfilter__eq__lappend__lfiniteD) ).
thf(574,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)],[98]) ).
thf(235,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_117_ldistinct_Osimps) ).
thf(1020,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)],[235]) ).
thf(32,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).
thf(348,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(106,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_order__trans) ).
thf(602,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(280,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(195,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_le__supE) ).
thf(877,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(249,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA,E: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ B ) @ E )
=> ( member @ TA @ D @ ( koenig317145564le_via @ TA @ C @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_reachable__via_Ointros) ).
thf(1072,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA,E: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ B ) @ E )
=> ( member @ TA @ D @ ( koenig317145564le_via @ TA @ C @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(53,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_182_ldistinct__lfilterI) ).
thf(411,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)],[53]) ).
thf(56,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_pathsp_OSingle) ).
thf(428,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(47,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_sup_Ocobounded2) ).
thf(397,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(135,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_lfinite__code_I1_J) ).
thf(687,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(250,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_25_lset__induct_H) ).
thf(1074,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)],[250]) ).
thf(11,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_123_llist__less__induct) ).
thf(292,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)],[11]) ).
thf(127,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_ord__eq__le__trans) ).
thf(661,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ( coindu63249387sorted @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
| ? [B: TA] :
( A
= ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) )
| ? [B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) )
& ( ord_less_eq @ TA @ B @ C )
& ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_lsorted_Osimps) ).
thf(366,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ( coindu63249387sorted @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
| ? [B: TA] :
( A
= ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) )
| ? [B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) )
& ( ord_less_eq @ TA @ B @ C )
& ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(248,axiom,
~ ! [A: a,B: coinductive_llist @ a] :
( xs2
!= ( coinductive_LCons @ a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1067,plain,
~ ! [A: a,B: coinductive_llist @ a] :
( xs2
!= ( coinductive_LCons @ a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(146,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(714,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)],[146]) ).
thf(274,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_150_split__llist__first) ).
thf(1163,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)],[274]) ).
thf(270,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_subsetCE) ).
thf(1153,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__funE) ).
thf(761,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(214,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_169_UnCI) ).
thf(957,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)],[214]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(193,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_4) ).
thf(862,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_le__cases) ).
thf(630,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(114,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( B
= ( sup_sup @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_sup_Oorder__iff) ).
thf(625,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( B
= ( sup_sup @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(128,axiom,
! [TA: $tType] :
( ( koenig2031690877pathsp @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: TA] :
( B
= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
| ? [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
& ( A @ C @ D )
& ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_pathsp_Osimps) ).
thf(665,plain,
! [TA: $tType] :
( ( koenig2031690877pathsp @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
| ? [C: TA] :
( B
= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
| ? [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
& ( A @ C @ D )
& ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(99,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_linear) ).
thf(583,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coinductive_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B )
= ( coinductive_LCons @ TB @ ( C @ B ) @ ( if @ ( coinductive_llist @ TB ) @ ( D @ B ) @ ( E @ B ) @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ ( F @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_llist_Ocorec_I2_J) ).
thf(493,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coinductive_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B )
= ( coinductive_LCons @ TB @ ( C @ B ) @ ( if @ ( coinductive_llist @ TB ) @ ( D @ B ) @ ( E @ B ) @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ ( F @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(133,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_171_lfilter__idem) ).
thf(682,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)],[133]) ).
thf(90,axiom,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_gen__lset__code_I1_J) ).
thf(551,plain,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(185,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( B
= ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_sup_OorderE) ).
thf(842,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( B
= ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ( comple187826305attice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_Ocomplete__lattice) ).
thf(285,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ( comple187826305attice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(203,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_174_lfilter__LCons) ).
thf(916,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)],[203]) ).
thf(66,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_100_llist_Odistinct_I1_J) ).
thf(467,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)],[66]) ).
thf(187,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_antisym__conv) ).
thf(847,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(72,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_dual__order_Oantisym) ).
thf(484,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(151,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Un__least) ).
thf(742,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(139,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_177_llexord__code_I1_J) ).
thf(697,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)],[139]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu1441602521_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coinductive_llist @ TB ) @ ( A @ D ) @ ( coinductive_LNil @ TB ) @ ( coinductive_LCons @ TB @ ( B @ D ) @ ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_unfold__llist_Ocode) ).
thf(317,plain,
! [TA: $tType,TB: $tType] :
( ( coindu1441602521_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coinductive_llist @ TB ) @ ( A @ D ) @ ( coinductive_LNil @ TB ) @ ( coinductive_LCons @ TB @ ( B @ D ) @ ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(212,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_22_llist_Oset__intros_I1_J) ).
thf(948,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)],[212]) ).
thf(110,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_eq__iff) ).
thf(615,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(259,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_set__rev__mp) ).
thf(1096,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(231,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_186_lfilter__id__conv) ).
thf(1006,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)],[231]) ).
thf(44,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_lsorted__LCons__LCons) ).
thf(388,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(36,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_183_lfilter__LCons__seek) ).
thf(356,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)],[36]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Un__upper2) ).
thf(499,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(226,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_subset__iff) ).
thf(989,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(26,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_209_Un__left__commute) ).
thf(328,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)],[26]) ).
thf(237,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_116_ldistinct_Ocoinduct) ).
thf(1028,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)],[237]) ).
thf(91,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_119_llast__LCons2) ).
thf(554,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)],[91]) ).
thf(121,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Collect__mono__iff) ).
thf(642,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_sup__ge1) ).
thf(637,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(239,axiom,
! [TA: $tType,A: TA > TA > $o,B: set @ TA,C: TA,D: TA] :
( ( koenig1757754772e_viap @ TA @ A @ B @ C @ D )
=> ~ ! [E: coinductive_llist @ TA] :
( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ E ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_reachable__viap_Ocases) ).
thf(1039,plain,
! [TA: $tType,A: TA > TA > $o,B: set @ TA,C: TA,D: TA] :
( ( koenig1757754772e_viap @ TA @ A @ B @ C @ D )
=> ~ ! [E: coinductive_llist @ TA] :
( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ E ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(271,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_122_ldistinct__LCons) ).
thf(1155,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)],[271]) ).
thf(143,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_sup_Oabsorb2) ).
thf(706,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(113,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_205_Un__assoc) ).
thf(622,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)],[113]) ).
thf(224,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( koenig916195507_paths @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_paths__lappendD1) ).
thf(985,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( koenig916195507_paths @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(269,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_subset__eq) ).
thf(1150,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(150,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_ord__le__eq__trans) ).
thf(738,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(124,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_176_llexord__LCons__LCons) ).
thf(654,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)],[124]) ).
thf(223,axiom,
graph @ n @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation) ).
thf(984,plain,
graph @ n @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(230,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_149_split__llist) ).
thf(1002,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)],[230]) ).
thf(165,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_160_LNil__eq__lappend__iff) ).
thf(779,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)],[165]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__funD) ).
thf(503,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(170,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_wlog__linorder__le) ).
thf(792,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(254,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_21_llist_Oset__intros_I2_J) ).
thf(1086,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)],[254]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Un__upper1) ).
thf(805,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(81,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_le__supI1) ).
thf(508,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(204,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(921,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(87,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_dual__order_Orefl) ).
thf(541,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(125,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_6) ).
thf(657,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(160,axiom,
! [TA: $tType] :
( ( coinductive_llexord @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( B = C )
| ? [D: coinductive_llist @ TA,E: coinductive_llist @ TA,F: TA,G: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
& ( B
= ( coinductive_lappend @ TA @ D @ E ) )
& ( C
= ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ F @ G ) ) )
& ( ( E
= ( coinductive_LNil @ TA ) )
| ( A @ ( coinductive_lhd @ TA @ E ) @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_llexord__conv) ).
thf(765,plain,
! [TA: $tType] :
( ( coinductive_llexord @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( B = C )
| ? [D: coinductive_llist @ TA,E: coinductive_llist @ TA,F: TA,G: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
& ( B
= ( coinductive_lappend @ TA @ D @ E ) )
& ( C
= ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ F @ G ) ) )
& ( ( E
= ( coinductive_LNil @ TA ) )
| ( A @ ( coinductive_lhd @ TA @ E ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(276,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_paths__lappendD2) ).
thf(1170,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(163,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_184_lfilter__LCons__found) ).
thf(773,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)],[163]) ).
thf(14,axiom,
comple187826305attice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7) ).
thf(298,plain,
comple187826305attice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(111,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_3) ).
thf(618,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(57,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_196_llexord__LCons__left) ).
thf(430,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)],[57]) ).
thf(263,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( A != D )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ E ) @ ( koenig916195507_paths @ TA @ C ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ ( coinductive_lset @ TA @ B ) )
& ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_path__avoid__node) ).
thf(1103,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( A != D )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ E ) @ ( koenig916195507_paths @ TA @ C ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ ( coinductive_lset @ TA @ B ) )
& ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(190,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ A ) @ ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_lset__lappend1) ).
thf(856,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ A ) @ ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(62,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_le__cases3) ).
thf(444,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(217,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_170_Un__iff) ).
thf(965,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)],[217]) ).
thf(154,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_213_lfinite__lfilterI) ).
thf(750,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)],[154]) ).
thf(136,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: TA > $o] :
( ( coindu63249387sorted @ TA @ A )
=> ( coindu63249387sorted @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_lsorted__lfilterI) ).
thf(689,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: TA > $o] :
( ( coindu63249387sorted @ TA @ A )
=> ( coindu63249387sorted @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(296,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_sup__absorb1) ).
thf(375,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(149,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_212_llexord__antisym) ).
thf(733,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)],[149]) ).
thf(138,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_161_lappend__eq__LNil__iff) ).
thf(694,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)],[138]) ).
thf(49,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_lfp_Oleq__trans) ).
thf(402,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(145,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_195_llexord__code_I3_J) ).
thf(711,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)],[145]) ).
thf(10,axiom,
semilattice_sup @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_8) ).
thf(291,plain,
semilattice_sup @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(54,axiom,
! [TA: $tType] :
( ( coinductive_llexord @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ? [D: coinductive_llist @ TA,E: coinductive_llist @ TA,F: TA] :
( ( B
= ( coinductive_LCons @ TA @ F @ D ) )
& ( C
= ( coinductive_LCons @ TA @ F @ E ) )
& ( coinductive_llexord @ TA @ A @ D @ E ) )
| ? [D: TA,E: TA,F: coinductive_llist @ TA,G: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ F ) )
& ( C
= ( coinductive_LCons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_llexord_Osimps) ).
thf(413,plain,
! [TA: $tType] :
( ( coinductive_llexord @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ? [D: coinductive_llist @ TA,E: coinductive_llist @ TA,F: TA] :
( ( B
= ( coinductive_LCons @ TA @ F @ D ) )
& ( C
= ( coinductive_LCons @ TA @ F @ E ) )
& ( coinductive_llexord @ TA @ A @ D @ E ) )
| ? [D: TA,E: TA,F: coinductive_llist @ TA,G: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ D @ F ) )
& ( C
= ( coinductive_LCons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LNil @ TA ) )
& ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(94,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_gfp_Oleq__antisym) ).
thf(562,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(202,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ( A @ B )
=> ( ! [C: coinductive_llist @ TA] :
( ( A @ C )
=> ( ( C
= ( coinductive_LNil @ TA ) )
| ? [D: TA] :
( C
= ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) )
| ? [D: TA,E: TA,F: coinductive_llist @ TA] :
( ( C
= ( coinductive_LCons @ TA @ D @ ( coinductive_LCons @ TA @ E @ F ) ) )
& ( ord_less_eq @ TA @ D @ E )
& ( ( A @ ( coinductive_LCons @ TA @ E @ F ) )
| ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ E @ F ) ) ) ) ) )
=> ( coindu63249387sorted @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_lsorted_Ocoinduct) ).
thf(904,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ( A @ B )
=> ( ! [C: coinductive_llist @ TA] :
( ( A @ C )
=> ( ( C
= ( coinductive_LNil @ TA ) )
| ? [D: TA] :
( C
= ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) )
| ? [D: TA,E: TA,F: coinductive_llist @ TA] :
( ( C
= ( coinductive_LCons @ TA @ D @ ( coinductive_LCons @ TA @ E @ F ) ) )
& ( ord_less_eq @ TA @ D @ E )
& ( ( A @ ( coinductive_LCons @ TA @ E @ F ) )
| ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ E @ F ) ) ) ) ) )
=> ( coindu63249387sorted @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(45,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_le__sup__iff) ).
thf(391,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(168,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_198_llexord__LCons__less) ).
thf(787,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)],[168]) ).
thf(257,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_subsetD) ).
thf(1092,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(256,axiom,
! [TA: $tType,A: TA > TA > $o] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( koenig916195507_paths @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_paths_OEmpty) ).
thf(1090,plain,
! [TA: $tType,A: TA > TA > $o] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( koenig916195507_paths @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(142,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_le__supI) ).
thf(704,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(33,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_9) ).
thf(350,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(51,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu351974385stinct @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( ( ( coinductive_lset @ TA @ A )
= ( coinductive_lset @ TA @ B ) )
=> ( A = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_lsorted__ldistinct__lset__unique) ).
thf(406,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu351974385stinct @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( ( ( coinductive_lset @ TA @ A )
= ( coinductive_lset @ TA @ B ) )
=> ( A = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(167,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_207_Un__commute) ).
thf(784,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)],[167]) ).
thf(243,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_203_bex__Un) ).
thf(1048,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)],[243]) ).
thf(266,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_166_lfilter__eq__LConsD) ).
thf(1122,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)],[266]) ).
thf(105,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Un__absorb) ).
thf(599,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(221,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_164_in__lset__lappend__iff) ).
thf(979,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)],[221]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_order__subst1) ).
thf(604,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(196,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_lappend__code_I1_J) ).
thf(880,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(240,axiom,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs2 ) @ ( koenig916195507_paths @ a @ graph ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_path) ).
thf(1043,plain,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs2 ) @ ( koenig916195507_paths @ a @ graph ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(177,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_99_llist_Oexhaust) ).
thf(811,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)],[177]) ).
thf(157,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( sup_sup @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_sup_OorderI) ).
thf(758,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( sup_sup @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(103,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_lsorted__code_I1_J) ).
thf(594,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(129,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( 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_221_lset__lappend) ).
thf(668,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( 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)],[129]) ).
thf(264,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_204_ball__Un) ).
thf(1112,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)],[264]) ).
thf(31,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_152_lappend__code_I2_J) ).
thf(345,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)],[31]) ).
thf(191,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_172_llexord__refl) ).
thf(858,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)],[191]) ).
thf(208,axiom,
! [TA: $tType] :
( ( koenig2031690877pathsp @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_pathsp__paths__eq) ).
thf(932,plain,
! [TA: $tType] :
( ( koenig2031690877pathsp @ TA )
= ( ^ [A: TA > TA > $o,B: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(247,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_24_lset__induct) ).
thf(1061,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)],[247]) ).
thf(134,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_199_llexord__LNil) ).
thf(685,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)],[134]) ).
thf(48,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_order__class_Oorder_Oantisym) ).
thf(399,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coinductive_llist @ TB] :
( ( ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ D )
= ( coinductive_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_unfold__llist__eq__LCons) ).
thf(768,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coinductive_llist @ TB] :
( ( ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ D )
= ( coinductive_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(241,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_paths__LConsD) ).
thf(1044,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(3,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_140_lstrict__prefix__lfinite1) ).
thf(278,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)],[3]) ).
thf(197,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ D ) )
=> ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_pathsp_OLCons) ).
thf(883,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ D ) )
=> ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(234,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_73_llist_Oset__cases) ).
thf(1015,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)],[234]) ).
thf(15,axiom,
lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_10) ).
thf(299,plain,
lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(262,axiom,
member @ a @ x @ ( koenig317145564le_via @ a @ graph @ ns @ n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062x_A_092_060in_062_Areachable__via_Agraph_Ans_An_092_060close_062) ).
thf(1102,plain,
member @ a @ x @ ( koenig317145564le_via @ a @ graph @ ns @ n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Un__absorb1) ).
thf(394,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(19,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_sup__mono) ).
thf(306,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(80,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_255_lstrict__prefix__lappend__conv) ).
thf(505,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)],[80]) ).
thf(60,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_127_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(438,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)],[60]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1441602521_llist @ TB @ TA @ A @ C @ D @ B )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_unfold__llist_Octr_I1_J) ).
thf(490,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1441602521_llist @ TB @ TA @ A @ C @ D @ B )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(102,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_147_lfinite_Ocases) ).
thf(589,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)],[102]) ).
thf(132,axiom,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_lmember__code_I1_J) ).
thf(680,plain,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(89,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Un__absorb2) ).
thf(548,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(206,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: TA,E: set @ TA] :
( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ C ) @ E )
=> ( koenig1757754772e_viap @ TA @ A @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_reachable__viap_Ointros) ).
thf(927,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: coinductive_llist @ TA,D: TA,E: set @ TA] :
( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ C ) @ E )
=> ( koenig1757754772e_viap @ TA @ A @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(73,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_lappend__assoc) ).
thf(487,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(252,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_19_lset__intros_I2_J) ).
thf(1081,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)],[252]) ).
thf(210,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_23_lset__cases) ).
thf(939,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)],[210]) ).
thf(30,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_antisym) ).
thf(342,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(268,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_178_diverge__lfilter__LNil) ).
thf(1145,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)],[268]) ).
thf(84,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_subset__refl) ).
thf(531,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(211,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ~ ! [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_reachable__via_Ocases) ).
thf(944,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ~ ! [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(218,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
= ( ? [E: coinductive_llist @ TA,F: TA] :
( ( A = F )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
& ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_reachable__via_Osimps) ).
thf(968,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
= ( ? [E: coinductive_llist @ TA,F: TA] :
( ( A = F )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
& ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(458,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(164,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_155_lfinite__lappend) ).
thf(776,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)],[164]) ).
thf(92,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_2) ).
thf(557,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_11) ).
thf(295,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1478340336prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_lstrict__prefix__code_I4_J) ).
thf(282,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1478340336prefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(199,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: TA > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( A @ E @ F )
=> ( ? [G: coinductive_llist @ TA,H: coinductive_llist @ TA,I: TA] :
( ( E
= ( coinductive_LCons @ TA @ I @ G ) )
& ( F
= ( coinductive_LCons @ TA @ I @ H ) )
& ( ( A @ G @ H )
| ( coinductive_llexord @ TA @ D @ G @ H ) ) )
| ? [G: TA,H: TA,I: coinductive_llist @ TA,J: coinductive_llist @ TA] :
( ( E
= ( coinductive_LCons @ TA @ G @ I ) )
& ( F
= ( coinductive_LCons @ TA @ H @ J ) )
& ( D @ G @ H ) )
| ? [G: coinductive_llist @ TA] :
( ( E
= ( coinductive_LNil @ TA ) )
& ( F = G ) ) ) )
=> ( coinductive_llexord @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_llexord_Ocoinduct) ).
thf(887,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: TA > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( A @ E @ F )
=> ( ? [G: coinductive_llist @ TA,H: coinductive_llist @ TA,I: TA] :
( ( E
= ( coinductive_LCons @ TA @ I @ G ) )
& ( F
= ( coinductive_LCons @ TA @ I @ H ) )
& ( ( A @ G @ H )
| ( coinductive_llexord @ TA @ D @ G @ H ) ) )
| ? [G: TA,H: TA,I: coinductive_llist @ TA,J: coinductive_llist @ TA] :
( ( E
= ( coinductive_LCons @ TA @ G @ I ) )
& ( F
= ( coinductive_LCons @ TA @ H @ J ) )
& ( D @ G @ H ) )
| ? [G: coinductive_llist @ TA] :
( ( E
= ( coinductive_LNil @ TA ) )
& ( F = G ) ) ) )
=> ( coinductive_llexord @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(219,axiom,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062) ).
thf(971,plain,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(52,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_180_llexord__lappend__leftI) ).
thf(409,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)],[52]) ).
thf(260,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_200_UnE) ).
thf(1098,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)],[260]) ).
thf(245,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(1053,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(27,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_sup__ge2) ).
thf(331,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(61,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_sup_Obounded__iff) ).
thf(441,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(100,axiom,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1) ).
thf(585,plain,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(184,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_order__refl) ).
thf(840,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(65,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_eq__refl) ).
thf(463,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(67,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_gfp_Oleq__trans) ).
thf(470,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(37,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( koenig2031690877pathsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ( ! [C: TA] :
( B
!= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
=> ~ ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_pathsp_Ocases) ).
thf(359,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( koenig2031690877pathsp @ TA @ A @ B )
=> ( ( B
!= ( coinductive_LNil @ TA ) )
=> ( ! [C: TA] :
( B
!= ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ ( coinductive_LCons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
=> ~ ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(152,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_subset__antisym) ).
thf(744,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(236,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_223_llexord__lappend__left) ).
thf(1023,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)],[236]) ).
thf(194,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_151_lfinite__rev__induct) ).
thf(864,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)],[194]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_equalityD2) ).
thf(727,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(258,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_contra__subsetD) ).
thf(1094,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(97,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Un__subset__iff) ).
thf(571,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(109,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_77_lmember__code_I2_J) ).
thf(612,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)],[109]) ).
thf(186,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_LNil) ).
thf(845,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(162,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dual__order_Otrans) ).
thf(771,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(140,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(699,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)],[140]) ).
thf(216,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_201_UnI1) ).
thf(963,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)],[216]) ).
thf(18,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_197_llexord__LCons__eq) ).
thf(304,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)],[18]) ).
thf(117,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_208_Un__left__absorb) ).
thf(632,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)],[117]) ).
thf(148,axiom,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ldistinct__LNil__code) ).
thf(731,plain,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(123,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_114_lstrict__prefix__code_I3_J) ).
thf(652,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)],[123]) ).
thf(34,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_sup__least) ).
thf(351,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(96,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_112_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(568,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)],[96]) ).
thf(207,axiom,
! [TA: $tType] :
( ( koenig1757754772e_viap @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA,C: TA,D: TA] : ( member @ TA @ D @ ( koenig317145564le_via @ TA @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_reachable__viap__reachable__via__eq) ).
thf(929,plain,
! [TA: $tType] :
( ( koenig1757754772e_viap @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA,C: TA,D: TA] : ( member @ TA @ D @ ( koenig317145564le_via @ TA @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(70,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_156_lappend__inf) ).
thf(478,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)],[70]) ).
thf(159,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_order_Otrans) ).
thf(763,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(200,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_sup__absorb2) ).
thf(899,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(181,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_sup_OboundedE) ).
thf(832,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(9,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(290,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(42,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ D @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ E @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ D )
=> ( ( ord_less_eq @ TA @ F @ D )
=> ( ord_less_eq @ TA @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_sup__unique) ).
thf(378,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ D @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ E @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ D )
=> ( ( ord_less_eq @ TA @ F @ D )
=> ( ord_less_eq @ TA @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(58,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_167_lset__lappend__lfinite) ).
thf(433,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)],[58]) ).
thf(82,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA,F: TA] :
( ( B
= ( coinductive_LCons @ TA @ F @ D ) )
=> ( ( C
= ( coinductive_LCons @ TA @ F @ E ) )
=> ~ ( coinductive_llexord @ TA @ A @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: coinductive_llist @ TA] :
( B
= ( coinductive_LCons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: coinductive_llist @ TA] :
( C
= ( coinductive_LCons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ( ( B
= ( coinductive_LNil @ TA ) )
=> ! [D: coinductive_llist @ TA] : ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_llexord_Ocases) ).
thf(510,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_llexord @ TA @ A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA,F: TA] :
( ( B
= ( coinductive_LCons @ TA @ F @ D ) )
=> ( ( C
= ( coinductive_LCons @ TA @ F @ E ) )
=> ~ ( coinductive_llexord @ TA @ A @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: coinductive_llist @ TA] :
( B
= ( coinductive_LCons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: coinductive_llist @ TA] :
( C
= ( coinductive_LCons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ( ( B
= ( coinductive_LNil @ TA ) )
=> ! [D: coinductive_llist @ TA] : ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_set__mp) ).
thf(1161,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(172,axiom,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_llast__singleton) ).
thf(800,plain,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( semilattice_sup @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(287,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( semilattice_sup @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(267,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: TA] :
( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LNil @ TA ) ) )
| ? [E: TA,F: TA,G: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LCons @ TA @ F @ G ) ) )
& ( C @ E @ F )
& ( ( A @ ( coinductive_LCons @ TA @ F @ G ) )
| ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ F @ G ) @ ( koenig916195507_paths @ TA @ C ) ) ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_paths_Ocoinduct) ).
thf(1133,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: TA] :
( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LNil @ TA ) ) )
| ? [E: TA,F: TA,G: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ ( coinductive_LCons @ TA @ F @ G ) ) )
& ( C @ E @ F )
& ( ( A @ ( coinductive_LCons @ TA @ F @ G ) )
| ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ F @ G ) @ ( koenig916195507_paths @ TA @ C ) ) ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(16,axiom,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_lstrict__prefix__code_I1_J) ).
thf(300,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(155,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_210_llexord__trans) ).
thf(752,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)],[155]) ).
thf(21,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_le__supI2) ).
thf(315,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(189,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_113_lstrict__prefix__code_I2_J) ).
thf(854,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)],[189]) ).
thf(229,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_214_lfilter__empty__conv) ).
thf(999,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)],[229]) ).
thf(112,axiom,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_ldistinct_OLNil) ).
thf(620,plain,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(213,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_129_ldistinct_Ocases) ).
thf(950,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)],[213]) ).
thf(182,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_sup_Oabsorb__iff2) ).
thf(835,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(175,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_sup_Ocobounded1) ).
thf(807,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(246,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA,E: TA > $o] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ( ! [F: coinductive_llist @ TA,G: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ F ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ G @ ( coinductive_lset @ TA @ F ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ F ) @ C )
=> ( E @ G ) ) ) )
=> ( E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_reachable__via_Oinducts) ).
thf(1056,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA,E: TA > $o] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ( ! [F: coinductive_llist @ TA,G: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ F ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ G @ ( coinductive_lset @ TA @ F ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ F ) @ C )
=> ( E @ G ) ) ) )
=> ( E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(215,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_75_lset__lmember) ).
thf(960,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)],[215]) ).
thf(118,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_lsorted__code_I2_J) ).
thf(635,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(225,axiom,
( xs2
= ( coinductive_LCons @ a @ n2 @ xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_xs) ).
thf(987,plain,
( xs2
= ( coinductive_LCons @ a @ n2 @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(192,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Un__mono) ).
thf(860,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(104,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_146_lfinite_Osimps) ).
thf(596,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)],[104]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_order__subst2) ).
thf(528,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(227,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rev__subsetD) ).
thf(992,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(188,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_equalityD1) ).
thf(850,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(222,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_125_ldistinct_OLCons) ).
thf(982,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)],[222]) ).
thf(78,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_219_llexord__code_I2_J) ).
thf(501,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)],[78]) ).
thf(1,conjecture,
member @ a @ n2 @ ns,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ a @ n2 @ ns ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(277,plain,
~ ( member @ a @ n2 @ ns ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(137,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_163_lappend__snocL1__conv__LCons2) ).
thf(691,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)],[137]) ).
thf(39,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_220_gen__lset__def) ).
thf(369,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)],[39]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_linorder__wlog) ).
thf(607,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(24,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_sup_Oabsorb1) ).
thf(322,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(173,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_subset__trans) ).
thf(803,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(126,axiom,
! [TA: $tType,A: TA > TA > $o] : ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_pathsp_OEmpty) ).
thf(659,plain,
! [TA: $tType,A: TA > TA > $o] : ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(88,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_222_lset__lappend__conv) ).
thf(543,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)],[88]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > $o,E: TB > ( coinductive_llist @ TA ),F: TB > TB] :
( ( A @ B )
=> ( ( coindu1259883913_llist @ TB @ TA @ A @ C @ D @ E @ F @ B )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_llist_Ocorec_I1_J) ).
thf(639,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > $o,E: TB > ( coinductive_llist @ TA ),F: TB > TB] :
( ( A @ B )
=> ( ( coindu1259883913_llist @ TB @ TA @ A @ C @ D @ E @ F @ B )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(255,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_in__mono) ).
thf(1088,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu1259883913_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coinductive_llist @ TB ),E: TA > TA,F: TA] : ( if @ ( coinductive_llist @ TB ) @ ( A @ F ) @ ( coinductive_LNil @ TB ) @ ( coinductive_LCons @ TB @ ( B @ F ) @ ( if @ ( coinductive_llist @ TB ) @ ( C @ F ) @ ( D @ F ) @ ( coindu1259883913_llist @ TA @ TB @ A @ B @ C @ D @ E @ ( E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_llist_Ocorec__code) ).
thf(496,plain,
! [TA: $tType,TB: $tType] :
( ( coindu1259883913_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coinductive_llist @ TB ),E: TA > TA,F: TA] : ( if @ ( coinductive_llist @ TB ) @ ( A @ F ) @ ( coinductive_LNil @ TB ) @ ( coinductive_LCons @ TB @ ( B @ F ) @ ( if @ ( coinductive_llist @ TB ) @ ( C @ F ) @ ( D @ F ) @ ( coindu1259883913_llist @ TA @ TB @ A @ B @ C @ D @ E @ ( E @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(209,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_72_llist_Oset__induct) ).
thf(935,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)],[209]) ).
thf(232,axiom,
! [TA: $tType,A: TA > TA > $o,B: set @ TA,C: TA,D: TA,E: TA > $o] :
( ( koenig1757754772e_viap @ TA @ A @ B @ C @ D )
=> ( ! [F: coinductive_llist @ TA,G: TA] :
( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ F ) )
=> ( ( member @ TA @ G @ ( coinductive_lset @ TA @ F ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ F ) @ B )
=> ( E @ G ) ) ) )
=> ( E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_reachable__viap_Oinducts) ).
thf(1009,plain,
! [TA: $tType,A: TA > TA > $o,B: set @ TA,C: TA,D: TA,E: TA > $o] :
( ( koenig1757754772e_viap @ TA @ A @ B @ C @ D )
=> ( ! [F: coinductive_llist @ TA,G: TA] :
( ( koenig2031690877pathsp @ TA @ A @ ( coinductive_LCons @ TA @ C @ F ) )
=> ( ( member @ TA @ G @ ( coinductive_lset @ TA @ F ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ F ) @ B )
=> ( E @ G ) ) ) )
=> ( E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(233,axiom,
member @ a @ x @ ( coinductive_lset @ a @ xs2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062x_A_092_060in_062_Alset_Axs_092_060close_062) ).
thf(1014,plain,
member @ a @ x @ ( coinductive_lset @ a @ xs2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(220,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_185_lfilter__cong) ).
thf(972,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)],[220]) ).
thf(1172,plain,
$false,
inference(e,[status(thm)],[645,1036,809,1168,1083,481,333,628,1158,994,308,677,1078,385,533,797,472,814,747,340,538,670,782,709,436,829,404,885,1046,320,565,372,702,460,587,838,559,416,289,1100,817,902,1115,325,756,789,353,1051,475,924,574,1020,348,602,280,877,1072,411,428,397,687,1074,292,661,366,1067,714,1163,1153,761,957,302,862,630,625,665,583,493,682,551,842,285,916,467,847,484,742,697,317,948,615,1096,1006,388,356,499,989,328,1028,554,642,637,1039,1155,706,622,985,1150,738,654,984,1002,779,503,792,1086,805,508,921,541,657,765,1170,773,298,618,430,1103,856,444,965,750,689,296,375,733,694,402,711,291,413,562,904,391,787,1092,1090,704,350,406,784,1048,1122,599,979,604,880,1043,811,758,594,668,1112,345,858,932,1061,685,399,768,1044,278,883,1015,299,1102,394,306,505,438,490,589,680,548,927,487,1081,939,342,1145,531,944,968,458,776,557,295,282,887,971,409,1098,1053,331,441,585,840,463,470,359,744,1023,864,727,1094,571,612,845,771,699,963,304,632,731,652,351,568,929,478,763,899,832,290,378,433,510,1161,800,287,1133,300,752,315,854,999,620,950,835,807,1056,960,635,987,860,596,528,992,850,982,501,277,691,369,607,322,803,659,543,639,1088,496,935,1009,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM175^1 : TPTP v8.1.2. Released v7.0.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 16:46:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.09/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.97/1.22 % [INFO] Parsing done (278ms).
% 1.97/1.23 % [INFO] Running in sequential loop mode.
% 2.59/1.46 % [INFO] eprover registered as external prover.
% 2.90/1.46 % [INFO] cvc4 registered as external prover.
% 2.90/1.46 % [INFO] Scanning for conjecture ...
% 3.07/1.56 % [INFO] Found a conjecture and 278 axioms. Running axiom selection ...
% 3.31/1.65 % [INFO] Axiom selection finished. Selected 274 axioms (removed 4 axioms).
% 4.01/1.85 % [INFO] Problem is higher-order (TPTP THF).
% 4.01/1.87 % [INFO] Type checking passed.
% 4.01/1.87 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 170.21/137.32 % External prover 'e' found a proof!
% 170.21/137.32 % [INFO] Killing All external provers ...
% 170.21/137.32 % Time passed: 136790ms (effective reasoning time: 136086ms)
% 170.21/137.32 % 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)>
% 170.21/137.33 % Axioms used in derivation (274): fact_122_ldistinct__LCons, fact_220_gen__lset__def, fact_247_sup_OboundedI, fact_128_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, fact_67_equalityE, fact_94_pathsp_Osimps, fact_54_le__funD, fact_78_lfp_Oleq__antisym, fact_99_llist_Oexhaust, fact_161_lappend__eq__LNil__iff, fact_208_Un__left__absorb, fact_194_lsorted__lfilterI, fact_113_lstrict__prefix__code_I2_J, fact_206_Un__absorb, fact_199_llexord__LNil, fact_21_llist_Oset__intros_I2_J, fact_73_llist_Oset__cases, fact_219_llexord__code_I2_J, fact_140_lstrict__prefix__lfinite1, fact_117_ldistinct_Osimps, fact_156_lappend__inf, fact_201_UnI1, fact_145_lfinite_Oinducts, fact_170_Un__iff, fact_152_lappend__code_I2_J, fact_187_Un__mono, fact_23_lset__cases, fact_13_reachable__via_Ointros, fact_3__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062, fact_250_sup_Ocobounded2, fact_56_contra__subsetD, fact_160_LNil__eq__lappend__iff, fact_107_paths_Ocoinduct, fact_150_split__llist__first, fact_32_ord__le__eq__trans, fact_213_lfinite__lfilterI, fact_174_lfilter__LCons, fact_49_order__subst2, fact_216_llexord_Ocoinduct, fact_134_lfinite__code_I2_J, fact_182_ldistinct__lfilterI, fact_29_dual__order_Orefl, fact_39_eq__refl, fact_125_ldistinct_OLCons, fact_31_order__class_Oorder_Oantisym, fact_233_le__supI1, fact_138_lfinite__LConsI, fact_14_reachable__via_Oinducts, fact_51_le__fun__def, fact_71_set__mp, fact_121_lstrict__prefix__code_I1_J, fact_79_gfp_Oleq__antisym, fact_72_llist_Oset__induct, fact_18_order__refl, fact_191_Un__absorb1, fact_181_llexord__append__right, fact_16_subsetI, fact_55_Collect__mono__iff, fact_249_sup_Ocobounded1, tcon_fun___Orderings_Oord, fact_149_split__llist, fact_211_llexord__linear, fact_111_lsorted_Ocoinduct, fact_22_llist_Oset__intros_I1_J, fact_10_path__avoid__node, fact_27_dual__order_Otrans, fact_60_subset__refl, fact_65_equalityD1, fact_50_order__subst1, tcon_HOL_Obool___Orderings_Olinorder, fact_77_lmember__code_I2_J, fact_59_Collect__mono, fact_180_llexord__lappend__leftI, fact_133_unfold__llist_Ocode, fact_100_llist_Odistinct_I1_J, fact_26_dual__order_Oantisym, fact_185_lfilter__cong, fact_127_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, fact_15_llist_Oinject, fact_52_le__funI, fact_110_paths_Ocases, fact_248_sup_Oorder__iff, fact_86_reachable__viap_Osimps, fact_62_subset__iff, fact_112_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, fact_43_ord__le__eq__subst, fact_89_lsorted_Ocases, fact_154_lappend__LNil2, fact_88_reachable__viap_Oinducts, fact_126_lsorted__ldistinct__lset__unique, fact_231_sup__ge1, fact_104_lmember__code_I1_J, fact_166_lfilter__eq__LConsD, tcon_HOL_Obool___Lattices_Olattice_10, fact_46_Collect__mem__eq, fact_238_le__iff__sup, fact_68_subsetCE, fact_66_subset__eq, fact_7_path, fact_137_unfold__llist__eq__LCons, fact_69_subsetD, fact_188_Un__least, fact_197_llexord__LCons__eq, tcon_HOL_Obool___Orderings_Oorder_11, fact_142_unfold__llist_Octr_I1_J, fact_179_lfilter__lappend__lfinite, fact_178_diverge__lfilter__LNil, fact_214_lfilter__empty__conv, fact_190_Un__upper2, fact_106_Singleton, fact_218_llexord_Ocases, tcon_fun___Lattices_Osemilattice__sup, fact_41_antisym, fact_205_Un__assoc, fact_34_antisym__conv, fact_236_sup__mono, fact_162_lset__lappend1, fact_2_xs, fact_175_lfilter__LNil, fact_92_lsorted__code_I2_J, fact_130_llimit__induct, fact_226_sup_OcoboundedI2, fact_163_lappend__snocL1__conv__LCons2, fact_58_subset__trans, fact_4_calculation, tcon_Set_Oset___Orderings_Oord_6, fact_40_linear, fact_139_lfinite__LNil, fact_242_sup_Oabsorb1, fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062LCons_An_Axs_A_092_060in_062_Apaths_Agraph_059_Ax_A_092_060in_062_Alset_Axs_059_Alset_Axs_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_91_lsorted__code_I1_J, fact_42_eq__iff, fact_251_sup_Oabsorb__iff1, fact_19_lset__intros_I2_J, fact_157_lappend__assoc, fact_116_ldistinct_Ocoinduct, fact_196_llexord__LCons__left, fact_136_lfinite__code_I1_J, fact_37_le__cases, fact_36_order_Otrans, fact_234_le__supI2, fact_159_lappend__LNil__LNil, fact_252_sup_Oabsorb__iff2, fact_103_pathsp_OLCons, fact_225_sup_Obounded__iff, fact_45_mem__Collect__eq, fact_195_llexord__code_I3_J, fact_237_sup__least, fact_146_lfinite_Osimps, fact_144_llist_Ocorec_I1_J, fact_240_sup_OorderI, fact_131_gen__lset__code_I1_J, fact_222_lset__lappend__conv, fact_85_reachable__viap_Ocases, fact_169_UnCI, fact_151_lfinite__rev__induct, tcon_Set_Oset___Lattices_Olattice_4, tcon_HOL_Obool___Orderings_Opreorder_9, tcon_Set_Oset___Orderings_Opreorder_3, fact_129_ldistinct_Ocases, fact_124_ldistinct_OLNil, fact_255_lstrict__prefix__lappend__conv, fact_57_set__eq__subset, fact_114_lstrict__prefix__code_I3_J, fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_148_llast__lappend__LCons, fact_232_sup__ge2, fact_244_sup__absorb1, fact_253_sup_OcoboundedI1, fact_115_llast__singleton, fact_47_Collect__cong, fact_12_reachable__via_Osimps, fact_105_pathsp__paths__eq, fact_53_le__funE, fact_228_inf__sup__ord_I3_J, fact_93_pathsp_Ocases, fact_241_sup__unique, fact_44_ord__eq__le__subst, fact_90_lsorted_Osimps, fact_80_lfp_Oleq__trans, fact_108_paths_OSingle, fact_223_llexord__lappend__left, fact_120_lstrict__prefix__code_I4_J, fact_119_llast__LCons2, fact_172_llexord__refl, fact_200_UnE, fact_9_paths__LConsD, fact_209_Un__left__commute, fact_35_le__cases3, fact_0__092_060open_062x_A_092_060in_062_Alset_Axs_092_060close_062, fact_33_ord__eq__le__trans, fact_135_lfinite__LCons, fact_132_llist_Ocorec__code, fact_198_llexord__LCons__less, fact_30_order__trans, fact_167_lset__lappend__lfinite, fact_143_llist_Ocorec_I2_J, fact_98_neq__LNil__conv, fact_70_in__mono, fact_87_reachable__viap_Ointros, fact_82_lfp_Oleq__refl, tcon_fun___Orderings_Opreorder, fact_81_gfp_Oleq__trans, tcon_Set_Oset___Orderings_Oorder_5, fact_8_paths_OLCons, fact_25_lset__induct_H, fact_76_lsorted__LCons, fact_221_lset__lappend, fact_177_llexord__code_I1_J, fact_235_sup_Omono, fact_165_paths__lappendD2, fact_246_sup_OboundedE, tcon_fun___Complete__Lattices_Ocomplete__lattice, tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7, fact_5__092_060open_062x_A_092_060in_062_Areachable__via_Agraph_Ans_An_092_060close_062, fact_215_lfilter__eq__lappend__lfiniteD, fact_193_subset__Un__eq, fact_74_reachable__viap__reachable__via__eq, fact_153_lappend__code_I1_J, fact_204_ball__Un, fact_75_lset__lmember, tcon_HOL_Obool___Lattices_Osemilattice__sup_8, fact_230_le__supI, fact_192_Un__absorb2, tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1, fact_38_wlog__linorder__le, fact_109_paths_Osimps, fact_203_bex__Un, fact_97_pathsp_OEmpty, fact_183_lfilter__LCons__seek, tcon_fun___Orderings_Oorder, fact_164_in__lset__lappend__iff, fact_123_llist__less__induct, fact_102_paths_OEmpty, fact_202_UnI2, fact_207_Un__commute, fact_176_llexord__LCons__LCons, fact_118_ldistinct__LNil__code, fact_229_le__supE, fact_141_unfold__llist_Octr_I2_J, fact_61_rev__subsetD, fact_17_subset__antisym, fact_254_llexord__conv, tcon_HOL_Obool___Orderings_Oord_12, fact_83_lsorted__LCons__LCons, fact_28_linorder__wlog, fact_243_sup_Oabsorb2, fact_63_set__rev__mp, fact_212_llexord__antisym, fact_239_sup_OorderE, fact_186_lfilter__id__conv, fact_224_le__sup__iff, fact_184_lfilter__LCons__found, fact_95_pathsp_OSingle, fact_155_lfinite__lappend, fact_210_llexord__trans, fact_227_inf__sup__ord_I4_J, fact_171_lfilter__idem, fact_173_Un__subset__iff, fact_168_llexord__lappend__leftD, fact_189_Un__upper1, fact_96_pathsp_Ocoinduct, fact_217_llexord_Osimps, tcon_Set_Oset___Lattices_Osemilattice__sup_2, fact_20_lset__intros_I1_J, fact_245_sup__absorb2, fact_84_LCons__LCons, fact_147_lfinite_Ocases, fact_64_equalityD2, fact_24_lset__induct, fact_11_reachable__via_Ocases, tcon_fun___Lattices_Olattice, fact_158_paths__lappendD1, fact_101_LNil
% 170.21/137.33 % No. of inferences in proof: 552
% 170.21/137.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 136790 ms resp. 136086 ms w/o parsing
% 171.01/137.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 171.01/137.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------