TSTP Solution File: DAT189^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT189^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:43 EDT 2024
% Result : Theorem 25.63s 8.91s
% Output : Refutation 26.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 264
% Syntax : Number of formulae : 499 ( 219 unt; 31 typ; 0 def)
% Number of atoms : 1398 ( 467 equ; 4 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 6599 ( 250 ~; 87 |; 139 &;5519 @)
% ( 0 <=>; 604 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 412 ( 412 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 8 con; 0-8 aty)
% Number of variables : 1827 ( 70 ^1625 !; 102 ?;1827 :)
% ( 30 !>; 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(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[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(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_lhd_type,type,
coinductive_lhd:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(coinductive_lnull_type,type,
coinductive_lnull:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_ltl_type,type,
coinductive_ltl:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lmember_type,type,
coinductive_lmember:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lprefix_type,type,
coinductive_lprefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coindu1478340336prefix_type,type,
coindu1478340336prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coindu501562517eWhile_type,type,
coindu501562517eWhile:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
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(undefined_type,type,
undefined:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(lMirro427583474mirror_type,type,
lMirro427583474mirror:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lMirro999291890or_aux_type,type,
lMirro999291890or_aux:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ 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(acc_type,type,
acc: coinductive_llist @ a ).
thf(xs_type,type,
xs: coinductive_llist @ a ).
thf(95,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coinductive_llist @ TA] :
( ( C
= ( coinductive_LCons @ TA @ A @ D ) )
& ( coinductive_lprefix @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_LCons__lprefix__conv) ).
thf(500,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coinductive_llist @ TA] :
( ( C
= ( coinductive_LCons @ TA @ A @ D ) )
& ( coinductive_lprefix @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coinductive_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_ltl__unfold__llist) ).
thf(645,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coinductive_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(127,axiom,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_gen__lset__code_I1_J) ).
thf(629,plain,
! [TA: $tType,A: set @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(46,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_lprefix__lfiniteD) ).
thf(365,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(88,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_eq__refl) ).
thf(479,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)],[88]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_le__fun__def) ).
thf(347,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)],[40]) ).
thf(42,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_order__refl) ).
thf(352,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_lprefix__ltakeWhile) ).
thf(276,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_order__subst1) ).
thf(308,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)],[27]) ).
thf(156,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ D @ E )
=> ( ? [F: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
& ( E = F ) )
| ? [F: coinductive_llist @ TA,G: coinductive_llist @ TA,H: TA] :
( ( D
= ( coinductive_LCons @ TA @ H @ F ) )
& ( E
= ( coinductive_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coinductive_lprefix @ TA @ F @ G ) ) ) ) )
=> ( coinductive_lprefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_lprefix_Ocoinduct) ).
thf(741,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ D @ E )
=> ( ? [F: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
& ( E = F ) )
| ? [F: coinductive_llist @ TA,G: coinductive_llist @ TA,H: TA] :
( ( D
= ( coinductive_LCons @ TA @ H @ F ) )
& ( E
= ( coinductive_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coinductive_lprefix @ TA @ F @ G ) ) ) ) )
=> ( coinductive_lprefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_239_llexord__antisym) ).
thf(677,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)],[143]) ).
thf(135,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coindu501562517eWhile @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_ltakeWhile__eq__LNil__iff) ).
thf(655,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coindu501562517eWhile @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( B
!= ( coinductive_LNil @ TA ) )
=> ~ ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(99,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_3) ).
thf(511,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(178,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_lappend_Odisc__iff_I2_J) ).
thf(829,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',fact_24_llist_Ocorec__code) ).
thf(782,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)],[164]) ).
thf(153,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ( A @ ( coinductive_LNil @ TA ) )
=> ( ! [C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
=> ( ( A @ D )
=> ( A @ ( coinductive_LCons @ TA @ C @ D ) ) ) )
=> ( ( ! [C: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ C @ B )
=> ( A @ C ) )
=> ( A @ B ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_llimit__induct) ).
thf(709,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)],[153]) ).
thf(182,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_lappend_Octr_I1_J) ).
thf(841,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(24,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( B @ ( coinductive_LNil @ TA ) )
=> ( ! [C: coinductive_llist @ TA,D: TA] :
( ( coinductive_lfinite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coinductive_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_lfinite_Oinducts) ).
thf(288,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)],[24]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_20_unfold__llist_Octr_I2_J) ).
thf(301,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)],[25]) ).
thf(219,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_lappend__lnull2) ).
thf(973,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(198,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ B )
& ( coinductive_lnull @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_lmirror__aux_Odisc__iff_I1_J) ).
thf(885,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ B )
& ( coinductive_lnull @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(110,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ ( coinductive_lappend @ TA @ A @ C ) )
= ( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lprefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_lprefix__lappend__same) ).
thf(570,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ ( coinductive_lappend @ TA @ A @ C ) )
= ( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lprefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(165,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ D ) )
& ( coindu328551480prefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(785,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)],[165]) ).
thf(49,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ( coinductive_lfinite @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_lfinite__lappend) ).
thf(372,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)],[49]) ).
thf(211,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ~ ( coinductive_lnull @ TA @ B )
=> ( ( ord_less_eq @ TA @ A @ ( coinductive_lhd @ TA @ B ) )
& ( coindu63249387sorted @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_lsorted__LCons_H) ).
thf(934,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ~ ( coinductive_lnull @ TA @ B )
=> ( ( ord_less_eq @ TA @ A @ ( coinductive_lhd @ TA @ B ) )
& ( coindu63249387sorted @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(214,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_ltl @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_ltl @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_ltl @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( coinductive_ltl @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ltl__lappend) ).
thf(949,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_ltl @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_ltl @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_ltl @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( coinductive_ltl @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(107,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Singleton) ).
thf(542,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)],[107]) ).
thf(115,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_ord__le__eq__trans) ).
thf(587,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)],[115]) ).
thf(123,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_dual__order_Orefl) ).
thf(619,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_lzip_Oexhaust) ).
thf(838,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(206,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lhd @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lhd @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lhd @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_lhd__lappend) ).
thf(917,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lhd @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lhd @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lhd @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(150,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( coindu63249387sorted @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_lsorted__code_I2_J) ).
thf(702,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)],[150]) ).
thf(171,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_lnull__ltakeWhile) ).
thf(802,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(39,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_llast__lappend__LCons) ).
thf(344,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)],[39]) ).
thf(203,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_llist_Ocollapse_I1_J) ).
thf(902,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(130,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_llexord @ TA @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_lprefix__imp__llexord) ).
thf(638,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_llexord @ TA @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_223_llexord__append__right) ).
thf(448,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)],[78]) ).
thf(30,axiom,
! [TA: $tType] :
( ( coinductive_lfinite @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
| ? [B: coinductive_llist @ TA,C: TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ B ) )
& ( coinductive_lfinite @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_lfinite_Osimps) ).
thf(316,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)],[30]) ).
thf(208,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ~ ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_llist_OdiscI_I2_J) ).
thf(924,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ C ) )
=> ~ ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_ltl @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_ltl__simps_I2_J) ).
thf(492,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_ltl @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(116,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(591,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)],[116]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_linear) ).
thf(443,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)],[75]) ).
thf(32,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_antisym__conv) ).
thf(321,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)],[32]) ).
thf(125,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ D ) )
& ( coinductive_lprefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_lprefix__LCons__conv) ).
thf(623,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ D ) )
& ( coinductive_lprefix @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(212,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 )
=> ( ~ ( coinductive_lnull @ TA @ E )
=> ( ~ ( coinductive_lnull @ TA @ F )
& ( ~ ( coinductive_lnull @ TA @ F )
=> ( ( D @ ( coinductive_lhd @ TA @ E ) @ ( coinductive_lhd @ TA @ F ) )
| ( ( ( coinductive_lhd @ TA @ E )
= ( coinductive_lhd @ TA @ F ) )
& ( ( A @ ( coinductive_ltl @ TA @ E ) @ ( coinductive_ltl @ TA @ F ) )
| ( coinductive_llexord @ TA @ D @ ( coinductive_ltl @ TA @ E ) @ ( coinductive_ltl @ TA @ F ) ) ) ) ) ) ) ) )
=> ( coinductive_llexord @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_llexord__coinduct) ).
thf(937,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 )
=> ( ~ ( coinductive_lnull @ TA @ E )
=> ( ~ ( coinductive_lnull @ TA @ F )
& ( ~ ( coinductive_lnull @ TA @ F )
=> ( ( D @ ( coinductive_lhd @ TA @ E ) @ ( coinductive_lhd @ TA @ F ) )
| ( ( ( coinductive_lhd @ TA @ E )
= ( coinductive_lhd @ TA @ F ) )
& ( ( A @ ( coinductive_ltl @ TA @ E ) @ ( coinductive_ltl @ TA @ F ) )
| ( coinductive_llexord @ TA @ D @ ( coinductive_ltl @ TA @ E ) @ ( coinductive_ltl @ TA @ F ) ) ) ) ) ) ) ) )
=> ( coinductive_llexord @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(204,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) )
& ( ~ ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( undefined @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_llast__lappend) ).
thf(905,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ B ) ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) )
& ( ~ ( coinductive_lfinite @ TA @ B )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ B @ A ) )
= ( undefined @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(222,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lprefix @ TA @ B @ A )
= ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_lprefix__lnull) ).
thf(981,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lprefix @ TA @ B @ A )
= ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_61_lsorted_Ocases) ).
thf(687,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)],[146]) ).
thf(21,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ C )
=> ( coinductive_lprefix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_lprefix__trans) ).
thf(280,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ C )
=> ( coinductive_lprefix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(195,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_lprefix__LNil) ).
thf(877,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(80,axiom,
! [TA: $tType] :
( ( coindu328551480prefix @ TA )
= ( coinductive_lprefix @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Coinductive__List_Ofinite__lprefix__def) ).
thf(453,plain,
! [TA: $tType] :
( ( coindu328551480prefix @ TA )
= ( coinductive_lprefix @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(57,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ ( coinductive_LNil @ TA ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_llexord__LNil) ).
thf(396,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)],[57]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',fact_248_llexord__code_I2_J) ).
thf(428,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)],[69]) ).
thf(185,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_lappend__lnull1) ).
thf(849,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_equalityE) ).
thf(248,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)],[8]) ).
thf(16,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_subset__refl) ).
thf(270,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(137,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_LNil__lprefix) ).
thf(661,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(168,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_order__class_Oorder_Oantisym) ).
thf(793,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)],[168]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_lfinite__code_I2_J) ).
thf(534,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)],[104]) ).
thf(35,axiom,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_lstrict__prefix__code_I1_J) ).
thf(334,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(200,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_lappend_Odisc_I2_J) ).
thf(894,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
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/sandbox/benchmark/theBenchmark.p',fact_173_dual__order_Otrans) ).
thf(778,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(61,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_LNil__eq__lappend__iff) ).
thf(407,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)],[61]) ).
thf(166,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_lfinite__LConsI) ).
thf(788,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)],[166]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(260,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(190,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_lmirror__aux_Oexhaust) ).
thf(862,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(85,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_antisym) ).
thf(467,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)],[85]) ).
thf(184,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 )
=> ~ ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_llist_Ocorec__disc_I2_J) ).
thf(847,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 )
=> ~ ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(139,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_lappend__snocL1__conv__LCons2) ).
thf(665,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)],[139]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',fact_251_llexord_Ocoinduct) ).
thf(522,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)],[103]) ).
thf(144,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_LNil) ).
thf(682,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_63_lsorted__LCons__LCons) ).
thf(456,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)],[81]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ord__le__eq__subst) ).
thf(324,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)],[33]) ).
thf(232,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coinductive_lnull @ TA @ D )
= ( coinductive_lnull @ TA @ E ) )
& ( ~ ( coinductive_lnull @ TA @ D )
=> ( ~ ( coinductive_lnull @ TA @ E )
=> ( ( ( coinductive_lhd @ TA @ D )
= ( coinductive_lhd @ TA @ E ) )
& ( ( A @ ( coinductive_ltl @ TA @ D ) @ ( coinductive_ltl @ TA @ E ) )
| ( ( coinductive_ltl @ TA @ D )
= ( coinductive_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_llist_Ocoinduct__strong) ).
thf(1012,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coinductive_lnull @ TA @ D )
= ( coinductive_lnull @ TA @ E ) )
& ( ~ ( coinductive_lnull @ TA @ D )
=> ( ~ ( coinductive_lnull @ TA @ E )
=> ( ( ( coinductive_lhd @ TA @ D )
= ( coinductive_lhd @ TA @ E ) )
& ( ( A @ ( coinductive_ltl @ TA @ D ) @ ( coinductive_ltl @ TA @ E ) )
| ( ( coinductive_ltl @ TA @ D )
= ( coinductive_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(23,axiom,
! [TA: $tType] :
( ( coindu1478340336prefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_lstrict__prefix__def) ).
thf(285,plain,
! [TA: $tType] :
( ( coindu1478340336prefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_unfold__llist_Odisc_I2_J) ).
thf(852,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(72,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_lappend__assoc) ).
thf(435,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)],[72]) ).
thf(102,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_dual__order_Oantisym) ).
thf(519,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)],[102]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( coinductive_LCons @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_lappend__code_I2_J) ).
thf(697,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)],[148]) ).
thf(194,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lhd @ TA @ A )
= ( coinductive_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_lprefix__lhdD) ).
thf(874,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lhd @ TA @ A )
= ( coinductive_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_le__funD) ).
thf(650,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)],[133]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( coindu63249387sorted @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_lsorted__lprefixD) ).
thf(403,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( coindu63249387sorted @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(229,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( B @ ( coinductive_lhd @ TA @ A ) )
=> ~ ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_ltakeWhile_Odisc_I2_J) ).
thf(1006,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( B @ ( coinductive_lhd @ TA @ A ) )
=> ~ ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(54,axiom,
! [TA: $tType] :
( ( coinductive_lprefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
? [C: coinductive_llist @ TA] :
( B
= ( coinductive_lappend @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_lprefix__conv__lappend) ).
thf(388,plain,
! [TA: $tType] :
( ( coinductive_lprefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
? [C: coinductive_llist @ TA] :
( B
= ( coinductive_lappend @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(192,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_lstrict__prefix__lappend__conv) ).
thf(869,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)],[192]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_lstrict__prefix__code_I2_J) ).
thf(420,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)],[66]) ).
thf(37,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(339,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(105,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_llist_Oleq__refl) ).
thf(537,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_216_llexord__LCons__LCons) ).
thf(489,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)],[91]) ).
thf(218,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ~ ( B @ ( coinductive_lhd @ TA @ A ) ) )
=> ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ltakeWhile_Odisc_I1_J) ).
thf(970,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ~ ( B @ ( coinductive_lhd @ TA @ A ) ) )
=> ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_250_llexord_Osimps) ).
thf(706,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)],[152]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmember @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coinductive_lmember @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lmember__code_I2_J) ).
thf(393,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)],[56]) ).
thf(226,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( lMirro999291890or_aux @ TA @ B @ A )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_lmirror__aux_Octr_I1_J) ).
thf(997,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( ( lMirro999291890or_aux @ TA @ B @ A )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(223,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ ( coinductive_ltl @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_lnull__ltlI) ).
thf(984,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ ( coinductive_ltl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(154,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_llexord__refl) ).
thf(721,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)],[154]) ).
thf(96,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ A @ B )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_lstrict__prefix__lfinite1) ).
thf(503,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)],[96]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(237,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_equalityD2) ).
thf(266,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)],[15]) ).
thf(172,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ B )
| ~ ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_ltakeWhile_Odisc__iff_I1_J) ).
thf(805,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ B )
| ~ ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(98,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_lappend__LNil2) ).
thf(508,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_lsorted__code_I1_J) ).
thf(311,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(158,axiom,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_llast__LCons2) ).
thf(765,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)],[158]) ).
thf(58,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: coinductive_llist @ TA] :
( ? [C: TA] :
( A
= ( coinductive_LCons @ TA @ C @ B ) )
=> ~ ( coinductive_lfinite @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_lfinite_Ocases) ).
thf(398,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)],[58]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_233_llexord__LCons__left) ).
thf(674,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)],[142]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_21_unfold__llist_Octr_I1_J) ).
thf(773,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)],[160]) ).
thf(199,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ~ ( B @ ( coinductive_lhd @ TA @ A ) ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ~ ( B @ ( coinductive_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_ltakeWhile_Oexhaust) ).
thf(888,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ~ ( B @ ( coinductive_lhd @ TA @ A ) ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ~ ( B @ ( coinductive_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',fact_18_llist_Ocorec_I1_J) ).
thf(412,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)],[63]) ).
thf(68,axiom,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_lappend__LNil__LNil) ).
thf(425,plain,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(14,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_2) ).
thf(264,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(188,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_llist_OdiscI_I1_J) ).
thf(856,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(111,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_order__trans) ).
thf(573,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)],[111]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_16_unfold__llist__eq__LCons) ).
thf(375,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)],[50]) ).
thf(100,axiom,
! [TA: $tType] :
( ( coinductive_ltl @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_ltl__simps_I1_J) ).
thf(513,plain,
! [TA: $tType] :
( ( coinductive_ltl @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(70,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_lfinite__code_I1_J) ).
thf(430,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_17_llist_Ocorec_I2_J) ).
thf(584,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)],[114]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_211_llexord__conv) ).
thf(694,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)],[147]) ).
thf(177,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_not__lnull__conv) ).
thf(826,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(113,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coindu501562517eWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coindu501562517eWhile @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coindu501562517eWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_ltakeWhile__LCons) ).
thf(579,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coindu501562517eWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coindu501562517eWhile @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coindu501562517eWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(10,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(259,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(55,axiom,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_lmember__code_I1_J) ).
thf(391,plain,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(76,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_6) ).
thf(445,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(29,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lprefix @ TA @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_not__lfinite__lprefix__conv__eq) ).
thf(313,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lprefix @ TA @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(120,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_lprefix__refl) ).
thf(611,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(94,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ C )
=> ( coinductive_lprefix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_llist_Oleq__trans) ).
thf(498,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ C )
=> ( coinductive_lprefix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(151,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_ltl @ TA @ A ) @ ( coinductive_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_lprefix__ltlI) ).
thf(704,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_ltl @ TA @ A ) @ ( coinductive_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_le__funI) ).
thf(350,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)],[41]) ).
thf(221,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lprefix @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_lnull__lprefix) ).
thf(979,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lprefix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(18,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_lfinite__LNil) ).
thf(274,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_llist_Oleq__antisym) ).
thf(362,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(6,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(245,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(196,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
| ~ ( coinductive_lnull @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lmirror__aux_Odisc__iff_I2_J) ).
thf(880,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
| ~ ( coinductive_lnull @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(122,axiom,
! [TA: $tType] :
( ( coinductive_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_llast__LNil) ).
thf(616,plain,
! [TA: $tType] :
( ( coinductive_llast @ TA @ ( coinductive_LNil @ TA ) )
= ( undefined @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(87,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_order_Otrans) ).
thf(477,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)],[87]) ).
thf(174,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
= ( coinductive_lnull @ TA @ B ) )
=> ( ( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ( ( ( coinductive_lhd @ TA @ A )
= ( coinductive_lhd @ TA @ B ) )
& ( ( coinductive_ltl @ TA @ A )
= ( coinductive_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_llist_Oexpand) ).
thf(811,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
= ( coinductive_lnull @ TA @ B ) )
=> ( ( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ( ( ( coinductive_lhd @ TA @ A )
= ( coinductive_lhd @ TA @ B ) )
& ( ( coinductive_ltl @ TA @ A )
= ( coinductive_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',fact_232_llexord__LCons__eq) ).
thf(367,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)],[47]) ).
thf(119,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_lappend @ TA @ C @ A ) @ ( coinductive_lappend @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_lprefix__lappend__sameI) ).
thf(609,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_lappend @ TA @ C @ A ) @ ( coinductive_lappend @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_le__cases) ).
thf(594,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)],[117]) ).
thf(170,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llexord @ TA @ B @ C @ A )
= ( coinductive_lnull @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_llexord__LNil__right) ).
thf(799,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llexord @ TA @ B @ C @ A )
= ( coinductive_lnull @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_231_llexord__LCons__less) ).
thf(621,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)],[124]) ).
thf(89,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 )
=> ( ( coinductive_lhd @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_llist_Ocorec__sel_I1_J) ).
thf(483,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 )
=> ( ( coinductive_lhd @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(700,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(126,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( A
!= ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_llist_Oexhaust) ).
thf(626,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)],[126]) ).
thf(140,axiom,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_llast__singleton) ).
thf(668,plain,
! [TA: $tType,A: TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LNil @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(83,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ C @ B )
=> ( ( coinductive_lprefix @ TA @ A @ C )
| ( coinductive_lprefix @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_lprefix__down__linear) ).
thf(462,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ C @ B )
=> ( ( coinductive_lprefix @ TA @ A @ C )
| ( coinductive_lprefix @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(205,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_llast__LCons) ).
thf(912,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= B ) )
& ( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ A ) )
= ( coinductive_llast @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(159,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_linorder__wlog) ).
thf(768,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)],[159]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_224_llexord__lappend__leftI) ).
thf(278,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)],[20]) ).
thf(163,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ C @ A ) @ ( coinductive_LCons @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Le__LCons) ).
thf(780,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ C @ A ) @ ( coinductive_LCons @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(197,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lnull @ TA @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_llist_Odisc_I2_J) ).
thf(883,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lnull @ TA @ ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(224,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ C )
=> ( ~ ( coinductive_lnull @ TA @ C )
=> ( ( B @ ( coinductive_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_lfinite__induct) ).
thf(986,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ C )
=> ( ~ ( coinductive_lnull @ TA @ C )
=> ( ( B @ ( coinductive_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coinductive_llist @ TB ),E: TA > TA,F: TA] :
( ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) )
= ( A @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_llist_Ocorec__disc__iff_I1_J) ).
thf(1000,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coinductive_llist @ TB ),E: TA > TA,F: TA] :
( ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) )
= ( A @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(207,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 )
=> ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_llist_Ocorec__disc_I1_J) ).
thf(922,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 )
=> ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coinductive_lhd @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_unfold__llist_Osimps_I3_J) ).
thf(658,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coinductive_lhd @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(97,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_lfinite__LCons) ).
thf(505,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)],[97]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_25_unfold__llist_Ocode) ).
thf(438,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)],[73]) ).
thf(138,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_lprefix__lappend) ).
thf(663,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(9,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_equalityD1) ).
thf(255,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)],[9]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_llist_Oinject) ).
thf(516,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)],[101]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( coindu63249387sorted @ TA @ ( coinductive_ltl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_lsorted__ltlI) ).
thf(342,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( coindu63249387sorted @ TA @ ( coinductive_ltl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(176,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_lappend_Oexhaust) ).
thf(823,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_le__funE) ).
thf(776,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)],[161]) ).
thf(228,axiom,
! [TA: $tType] :
( ( coindu501562517eWhile @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( if @ ( coinductive_llist @ TA )
@ ( ( coinductive_lnull @ TA @ B )
| ~ ( A @ ( coinductive_lhd @ TA @ B ) ) )
@ ( coinductive_LNil @ TA )
@ ( coinductive_LCons @ TA @ ( coinductive_lhd @ TA @ B ) @ ( coindu501562517eWhile @ TA @ A @ ( coinductive_ltl @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ltakeWhile_Ocode) ).
thf(1003,plain,
! [TA: $tType] :
( ( coindu501562517eWhile @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] :
( if @ ( coinductive_llist @ TA )
@ ( ( coinductive_lnull @ TA @ B )
| ~ ( A @ ( coinductive_lhd @ TA @ B ) ) )
@ ( coinductive_LNil @ TA )
@ ( coinductive_LCons @ TA @ ( coinductive_lhd @ TA @ B ) @ ( coindu501562517eWhile @ TA @ A @ ( coinductive_ltl @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',fact_240_llexord__linear) ).
thf(640,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)],[131]) ).
thf(234,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_lmirror__aux_Odisc_I2_J) ).
thf(1025,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) )
=> ~ ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(193,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lmirror__aux_Odisc_I1_J) ).
thf(872,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( lMirro999291890or_aux @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coinductive_lprefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_LCons__lprefix__LCons) ).
thf(282,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coinductive_lprefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(215,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coinductive_lnull @ TA @ D )
= ( coinductive_lnull @ TA @ E ) )
& ( ~ ( coinductive_lnull @ TA @ D )
=> ( ~ ( coinductive_lnull @ TA @ E )
=> ( ( ( coinductive_lhd @ TA @ D )
= ( coinductive_lhd @ TA @ E ) )
& ( A @ ( coinductive_ltl @ TA @ D ) @ ( coinductive_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_llist_Ocoinduct) ).
thf(954,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coinductive_lnull @ TA @ D )
= ( coinductive_lnull @ TA @ E ) )
& ( ~ ( coinductive_lnull @ TA @ D )
=> ( ~ ( coinductive_lnull @ TA @ E )
=> ( ( ( coinductive_lhd @ TA @ D )
= ( coinductive_lhd @ TA @ E ) )
& ( A @ ( coinductive_ltl @ TA @ D ) @ ( coinductive_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(13,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_5) ).
thf(263,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(34,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ A )
= ( undefined @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_llast__linfinite) ).
thf(331,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ A )
= ( undefined @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(74,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_lprefix__code_I1_J) ).
thf(441,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_ord__eq__le__subst) ).
thf(470,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)],[86]) ).
thf(173,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( B @ ( coinductive_lhd @ TA @ A ) )
=> ( ( coinductive_lhd @ TA @ ( coindu501562517eWhile @ TA @ B @ A ) )
= ( coinductive_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_lhd__ltakeWhile) ).
thf(808,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( B @ ( coinductive_lhd @ TA @ A ) )
=> ( ( coinductive_lhd @ TA @ ( coindu501562517eWhile @ TA @ B @ A ) )
= ( coinductive_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(44,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_ltl @ TA @ A ) )
= ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_lfinite__ltl) ).
thf(359,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_ltl @ TA @ A ) )
= ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_59_lsorted_Ocoinduct) ).
thf(544,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)],[108]) ).
thf(36,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_lappend__code_I1_J) ).
thf(336,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(233,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_lprefix__lnullD) ).
thf(1023,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1478340336prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_lstrict__prefix__code_I4_J) ).
thf(613,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)],[121]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_lprefix__code_I2_J) ).
thf(386,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coinductive_lprefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_unfold__llist_Odisc_I1_J) ).
thf(1008,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(77,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] : ( coinductive_llexord @ TA @ A @ ( coinductive_LNil @ TA ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_llexord__code_I1_J) ).
thf(446,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)],[77]) ).
thf(79,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_lappend__inf) ).
thf(450,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)],[79]) ).
thf(109,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_le__cases3) ).
thf(556,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)],[109]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_order__subst2) ).
thf(671,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)],[141]) ).
thf(220,axiom,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_lnull__def) ).
thf(976,plain,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(93,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_eq__iff) ).
thf(495,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)],[93]) ).
thf(231,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_lappend_Odisc_I1_J) ).
thf(1010,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lnull @ TA @ B )
=> ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_unfold__llist_Odisc__iff_I1_J) ).
thf(844,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(210,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_LCons @ TA @ ( coinductive_lhd @ TA @ A ) @ ( coinductive_ltl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_lhd__LCons__ltl) ).
thf(931,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_LCons @ TA @ ( coinductive_lhd @ TA @ A ) @ ( coinductive_ltl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(106,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(539,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_unfold__llist_Odisc__iff_I2_J) ).
thf(963,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coinductive_lnull @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(31,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) )
=> ( ( coinductive_lprefix @ TA @ A @ B )
| ( coinductive_lprefix @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_lprefix__lappendD) ).
thf(319,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) )
=> ( ( coinductive_lprefix @ TA @ A @ B )
| ( coinductive_lprefix @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ord__eq__le__trans) ).
thf(304,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)],[26]) ).
thf(213,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
& ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_ltakeWhile_Odisc__iff_I2_J) ).
thf(946,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
& ( A @ ( coinductive_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(134,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ! [C: coinductive_llist @ TA] :
( ! [D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_llist__less__induct) ).
thf(652,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)],[134]) ).
thf(128,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_lprefix__antisym) ).
thf(632,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_lprefix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',fact_107_LCons__LCons) ).
thf(418,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)],[65]) ).
thf(225,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ~ ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_lprefix__not__lnullD) ).
thf(995,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ~ ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(51,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_wlog__linorder__le) ).
thf(378,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)],[51]) ).
thf(17,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_subset__trans) ).
thf(272,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)],[17]) ).
thf(52,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_lappend__eq__LNil__iff) ).
thf(383,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)],[52]) ).
thf(202,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
& ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_lnull__lappend) ).
thf(899,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
& ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1,conjecture,
( ( coinductive_lnull @ a @ ( lMirro999291890or_aux @ a @ acc @ xs ) )
= ( ( coinductive_lnull @ a @ xs )
& ( coinductive_lnull @ a @ acc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( coinductive_lnull @ a @ ( lMirro999291890or_aux @ a @ acc @ xs ) )
!= ( ( coinductive_lnull @ a @ xs )
& ( coinductive_lnull @ a @ acc ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(235,plain,
( ( coinductive_lnull @ a @ ( lMirro999291890or_aux @ a @ acc @ xs ) )
!= ( ( coinductive_lnull @ a @ xs )
& ( coinductive_lnull @ a @ acc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_1) ).
thf(246,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(179,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( lMirro999291890or_aux @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_lmirror__aux__simps_I1_J) ).
thf(832,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( lMirro999291890or_aux @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(145,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_neq__LNil__conv) ).
thf(684,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)],[145]) ).
thf(157,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( B @ ( coinductive_LNil @ TA ) )
=> ( ! [C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ D )
=> ( ( B @ D )
=> ( B @ ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_lfinite__rev__induct) ).
thf(752,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)],[157]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_234_llexord__code_I3_J) ).
thf(432,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)],[71]) ).
thf(175,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ~ ( B @ ( coinductive_lhd @ TA @ A ) ) )
=> ( ( coindu501562517eWhile @ TA @ B @ A )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_ltakeWhile_Octr_I1_J) ).
thf(818,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ~ ( B @ ( coinductive_lhd @ TA @ A ) ) )
=> ( ( coindu501562517eWhile @ TA @ B @ A )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(60,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(405,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(187,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_lnull__imp__lfinite) ).
thf(854,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coinductive_llist @ TB ),E: TA > TA,F: TA] :
( ( ~ ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) )
= ( ~ ( A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_llist_Ocorec__disc__iff_I2_J) ).
thf(865,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coinductive_llist @ TB ),E: TA > TA,F: TA] :
( ( ~ ( coinductive_lnull @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) )
= ( ~ ( A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(62,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_lstrict__prefix__code_I3_J) ).
thf(410,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)],[62]) ).
thf(217,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ ( coinductive_ltl @ TA @ A ) @ B )
= ( coinductive_ltl @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_lappend__ltl) ).
thf(967,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ( coinductive_lappend @ TA @ ( coinductive_ltl @ TA @ A ) @ B )
= ( coinductive_ltl @ TA @ ( coinductive_lappend @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(180,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu1441602521_llist @ ( coinductive_llist @ TA ) @ TA @ ( coinductive_lnull @ TA ) @ ( coinductive_lhd @ TA ) @ ( coinductive_ltl @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_unfold__llist__id) ).
thf(835,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu1441602521_llist @ ( coinductive_llist @ TA ) @ TA @ ( coinductive_lnull @ TA ) @ ( coinductive_lhd @ TA ) @ ( coinductive_ltl @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(12,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_4) ).
thf(262,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
=> ~ ! [D: coinductive_llist @ TA] :
( C
!= ( coinductive_lappend @ TA @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_lappend__lprefixE) ).
thf(422,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
=> ~ ! [D: coinductive_llist @ TA] :
( C
!= ( coinductive_lappend @ TA @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(167,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lhd @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_lhd__LCons) ).
thf(790,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lhd @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(201,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_llexord @ TA @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_lnull__llexord) ).
thf(897,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_llexord @ TA @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_unfold__llist_Osimps_I4_J) ).
thf(635,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(169,axiom,
! [TA: $tType] :
( ( lMirro427583474mirror @ TA )
= ( lMirro999291890or_aux @ TA @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lmirror__def) ).
thf(796,plain,
! [TA: $tType] :
( ( lMirro427583474mirror @ TA )
= ( lMirro999291890or_aux @ TA @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(4,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_set__eq__subset) ).
thf(239,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)],[4]) ).
thf(5,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_subset__antisym) ).
thf(242,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)],[5]) ).
thf(209,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( lMirro999291890or_aux @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( lMirro999291890or_aux @ TA @ ( coinductive_LCons @ TA @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_lmirror__aux__simps_I2_J) ).
thf(928,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( lMirro999291890or_aux @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( lMirro999291890or_aux @ TA @ ( coinductive_LCons @ TA @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',fact_60_lsorted_Osimps) ).
thf(415,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)],[64]) ).
thf(84,axiom,
! [TA: $tType] :
( ( coinductive_lprefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ? [C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
& ( B = C ) )
| ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA,E: TA] :
( ( A
= ( coinductive_LCons @ TA @ E @ C ) )
& ( B
= ( coinductive_LCons @ TA @ E @ D ) )
& ( coinductive_lprefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_lprefix_Osimps) ).
thf(464,plain,
! [TA: $tType] :
( ( coinductive_lprefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ? [C: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
& ( B = C ) )
| ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA,E: TA] :
( ( A
= ( coinductive_LCons @ TA @ E @ C ) )
& ( B
= ( coinductive_LCons @ TA @ E @ D ) )
& ( coinductive_lprefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',fact_241_llexord__trans) ).
thf(575,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)],[112]) ).
thf(189,axiom,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_llist_Odisc_I1_J) ).
thf(860,plain,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(118,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ! [C: coinductive_llist @ TA] : ( B != C ) )
=> ~ ! [C: coinductive_llist @ TA,D: coinductive_llist @ TA,E: TA] :
( ( A
= ( coinductive_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coinductive_LCons @ TA @ E @ D ) )
=> ~ ( coinductive_lprefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_lprefix_Ocases) ).
thf(596,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ! [C: coinductive_llist @ TA] : ( B != C ) )
=> ~ ! [C: coinductive_llist @ TA,D: coinductive_llist @ TA,E: TA] :
( ( A
= ( coinductive_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coinductive_LCons @ TA @ E @ D ) )
=> ~ ( coinductive_lprefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(82,axiom,
! [TA: $tType] :
( ( coinductive_lprefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lfinite @ TA @ A )
=> ( coindu328551480prefix @ TA @ A @ B ) )
& ( ~ ( coinductive_lfinite @ TA @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Coinductive__List_Olprefix__nitpick__simps) ).
thf(459,plain,
! [TA: $tType] :
( ( coinductive_lprefix @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lfinite @ TA @ A )
=> ( coindu328551480prefix @ TA @ A @ B ) )
& ( ~ ( coinductive_lfinite @ TA @ A )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',fact_249_llexord_Ocases) ).
thf(723,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)],[155]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_llist_Odistinct_I1_J) ).
thf(369,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)],[48]) ).
thf(90,axiom,
! [TA: $tType,A: TA > $o] :
( ( coindu501562517eWhile @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ltakeWhile__LNil) ).
thf(486,plain,
! [TA: $tType,A: TA > $o] :
( ( coindu501562517eWhile @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > ( coinductive_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( E @ B ) ) )
& ( ~ ( C @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( coindu1259883913_llist @ TA @ TB @ A @ D @ C @ E @ F @ ( F @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_llist_Ocorec__sel_I2_J) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > ( coinductive_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( E @ B ) ) )
& ( ~ ( C @ B )
=> ( ( coinductive_ltl @ TB @ ( coindu1259883913_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( coindu1259883913_llist @ TA @ TB @ A @ D @ C @ E @ F @ ( F @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1028,plain,
$false,
inference(e,[status(thm)],[500,645,629,365,479,347,352,276,308,741,677,655,511,829,782,709,841,288,301,973,885,570,785,372,934,949,542,587,619,838,917,702,802,344,902,638,448,316,924,492,591,443,321,623,937,905,981,687,280,877,453,396,428,849,248,270,661,793,534,334,894,778,407,788,260,862,467,847,665,522,682,456,324,1012,285,852,435,519,697,874,650,403,1006,388,869,420,339,537,489,970,706,393,997,984,721,503,237,266,805,508,311,765,398,674,773,888,412,425,264,856,573,375,513,430,584,694,826,579,259,391,445,313,611,498,704,350,979,274,362,245,880,616,477,811,367,609,594,799,621,483,700,626,668,462,912,768,278,780,883,986,1000,922,658,505,438,663,255,516,342,823,776,1003,640,1025,872,282,954,263,331,441,470,808,359,544,336,1023,613,386,1008,446,450,556,671,976,495,1010,844,931,539,963,319,304,946,652,632,418,995,378,272,383,899,235,246,832,684,752,432,818,405,854,865,410,967,835,262,422,790,897,635,796,239,242,928,415,464,575,860,596,459,723,369,486,354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : DAT189^1 : TPTP v8.1.2. Released v7.0.0.
% 0.09/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n020.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 11:35:39 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.94/1.14 % [INFO] Parsing done (266ms).
% 1.94/1.15 % [INFO] Running in sequential loop mode.
% 2.91/1.44 % [INFO] eprover registered as external prover.
% 2.91/1.45 % [INFO] cvc4 registered as external prover.
% 2.91/1.45 % [INFO] Scanning for conjecture ...
% 3.16/1.55 % [INFO] Found a conjecture and 267 axioms. Running axiom selection ...
% 3.52/1.66 % [INFO] Axiom selection finished. Selected 232 axioms (removed 35 axioms).
% 4.07/1.92 % [INFO] Problem is higher-order (TPTP THF).
% 4.35/1.95 % [INFO] Type checking passed.
% 4.35/1.95 % [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 ...
% 25.63/8.90 % External prover 'e' found a proof!
% 25.63/8.90 % [INFO] Killing All external provers ...
% 25.63/8.90 % Time passed: 8362ms (effective reasoning time: 7749ms)
% 25.63/8.90 % 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)>
% 25.63/8.91 % Axioms used in derivation (232): fact_90_lprefix__not__lnullD, fact_50_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, fact_152_ltakeWhile_Oexhaust, fact_172_dual__order_Oantisym, fact_98_Coinductive__List_Ofinite__lprefix__def, fact_222_llexord__coinduct, tcon_HOL_Obool___Orderings_Opreorder_4, fact_168_lhd__ltakeWhile, fact_57_Singleton, fact_13_unfold__llist_Odisc__iff_I2_J, fact_4_lmirror__aux_Oexhaust, fact_83_llist_Oleq__trans, fact_190_order__subst2, fact_123_lprefix__lappend__same, fact_10_lmirror__def, fact_0_lmirror__aux_Odisc__iff_I2_J, fact_125_ltakeWhile_Odisc__iff_I2_J, fact_183_le__cases, fact_37_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, fact_250_llexord_Osimps, fact_77_lprefix__down__linear, fact_88_Le__LCons, fact_177_order__class_Oorder_Oantisym, fact_150_lprefix__lappend__sameI, fact_186_antisym, fact_155_lappend__lnull1, fact_175_dual__order_Orefl, fact_223_llexord__append__right, fact_18_llist_Ocorec_I1_J, tcon_fun___Orderings_Oord, tcon_HOL_Obool___Orderings_Oorder_5, fact_166_ltakeWhile_Odisc_I2_J, fact_19_llist_Odistinct_I1_J, fact_185_linear, fact_112_order__refl, fact_221_lhd__LCons__ltl, fact_244_llist_Oexpand, tcon_HOL_Obool___Orderings_Olinorder, fact_81_lprefix__lfiniteD, fact_184_eq__refl, fact_42_lmember__code_I2_J, fact_79_llist_Oleq__antisym, fact_253_llast__linfinite, fact_122_lfinite__lappend, fact_103_lprefix_Ocases, fact_241_llexord__trans, fact_126_ltakeWhile_Odisc__iff_I1_J, fact_30_llist_Ocollapse_I1_J, fact_227_lnull__ltlI, fact_97_lstrict__prefix__def, fact_40_llast__singleton, fact_15_llist_Oinject, fact_25_unfold__llist_Ocode, fact_26_not__lnull__conv, fact_52_llast__LCons2, fact_141_subset__trans, fact_102_lprefix__code_I2_J, fact_251_llexord_Ocoinduct, fact_117_lappend__code_I2_J, fact_214_llexord__refl, fact_55_llist__less__induct, fact_179_ord__eq__le__trans, fact_213_llast__lappend, fact_231_llexord__LCons__less, fact_147_lappend__lprefixE, fact_48_llast__LCons, fact_188_ord__le__eq__subst, fact_6_lappend_Oexhaust, fact_12_llist_Ocorec__disc__iff_I1_J, fact_41_lmember__code_I1_J, fact_73_lfinite__code_I1_J, fact_76_not__lfinite__lprefix__conv__eq, fact_135_equalityD2, fact_225_lprefix__ltlI, fact_239_llexord__antisym, fact_170_lfinite__rev__induct, help_If_1_1_T, fact_14_unfold__llist_Odisc__iff_I1_J, fact_22_llist_Oexhaust, fact_72_lfinite__LCons, fact_67_llist_Oleq__refl, fact_106_lprefix__LCons__conv, fact_94_LNil__lprefix, fact_139_subset__refl, fact_224_llexord__lappend__leftI, fact_49_lsorted__code_I2_J, fact_63_lsorted__LCons__LCons, fact_212_ltakeWhile_Ocode, fact_119_lnull__lappend, fact_62_llimit__induct, fact_104_lprefix_Osimps, fact_146_lprefix__lappend, fact_38_lstrict__prefix__code_I3_J, fact_191_order__subst1, fact_187_eq__iff, fact_29_lnull__def, fact_54_lstrict__prefix__code_I1_J, fact_195_le__funD, fact_32_llist_Odisc_I1_J, fact_216_llexord__LCons__LCons, fact_211_llexord__conv, fact_5_lzip_Oexhaust, fact_242_llist_Ocoinduct__strong, fact_80_wlog__linorder__le, fact_218_llexord__code_I1_J, fact_69_LCons__lprefix__LCons, fact_194_le__funE, fact_58_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, fact_174_linorder__wlog, fact_75_Coinductive__List_Olprefix__nitpick__simps, fact_238_llist_Ocorec__sel_I2_J, fact_56_LNil, fact_60_lsorted_Osimps, fact_159_lappend__LNil__LNil, fact_167_ltakeWhile_Odisc_I1_J, fact_156_lappend__lnull2, fact_23_neq__LNil__conv, fact_89_LCons__lprefix__conv, fact_27_llist_OdiscI_I2_J, fact_47_gen__lset__code_I1_J, fact_142_set__eq__subset, fact_252_llast__LNil, fact_162_llist_Ocorec__sel_I1_J, fact_93_lnull__lprefix, fact_78_lprefix__ltakeWhile, fact_34_unfold__llist_Odisc_I2_J, fact_127_lnull__ltakeWhile, fact_11_llist_Ocorec__disc__iff_I2_J, fact_243_llist_Ocoinduct, fact_124_lhd__lappend, fact_118_lappend_Odisc__iff_I2_J, fact_99_lfinite_Ocases, fact_84_lprefix__trans, fact_217_llexord__LNil__right, fact_180_antisym__conv, fact_65_lprefix__LNil, fact_193_le__funI, fact_2_lmirror__aux_Odisc_I2_J, fact_154_lappend_Odisc_I1_J, fact_28_llist_Odisc_I2_J, fact_149_lprefix__conv__lappend, fact_178_ord__le__eq__trans, fact_59_lsorted_Ocoinduct, fact_145_lappend__assoc, fact_9_lmirror__aux__simps_I2_J, fact_232_llexord__LCons__eq, fact_3_lmirror__aux_Odisc_I1_J, fact_230_lprefix__imp__llexord, fact_35_llist_Ocorec__disc_I1_J, help_If_3_1_T, fact_31_llist_OdiscI_I1_J, fact_8_lmirror__aux__simps_I1_J, help_If_2_1_T, fact_151_lhd__LCons, fact_24_llist_Ocorec__code, fact_1_lmirror__aux_Odisc__iff_I1_J, fact_114_llast__lappend__LCons, fact_237_unfold__llist_Osimps_I4_J, fact_121_lappend__code_I1_J, fact_39_lstrict__prefix__code_I2_J, fact_16_unfold__llist__eq__LCons, fact_165_lappend_Octr_I1_J, tcon_Set_Oset___Orderings_Oord_3, fact_164_lappend__snocL1__conv__LCons2, fact_233_llexord__LCons__left, tcon_fun___Orderings_Opreorder, tcon_Set_Oset___Orderings_Oorder_2, fact_68_lprefix__refl, fact_71_lfinite__code_I2_J, fact_95_lsorted__lprefixD, fact_116_subset__antisym, fact_226_ltl__simps_I2_J, fact_85_lfinite__LConsI, fact_21_unfold__llist_Octr_I1_J, fact_132_equalityE, fact_17_llist_Ocorec_I2_J, fact_220_ltl__lappend, fact_120_lappend__LNil2, fact_36_llist_Ocorec__disc_I2_J, fact_229_lsorted__ltlI, fact_181_le__cases3, fact_158_LNil__eq__lappend__iff, fact_245_lappend__ltl, fact_82_lprefix__antisym, fact_215_lfinite__ltl, fact_182_order_Otrans, fact_33_unfold__llist_Odisc_I1_J, fact_105_lprefix_Ocoinduct, fact_219_unfold__llist__id, fact_86_lnull__imp__lfinite, tcon_fun___Orderings_Oorder, fact_196_lstrict__prefix__lappend__conv, fact_173_dual__order_Otrans, fact_234_llexord__code_I3_J, fact_169_ltakeWhile__eq__LNil__iff, fact_51_lsorted__code_I1_J, fact_134_equalityD1, fact_153_lappend_Odisc_I2_J, fact_101_lfinite_Oinducts, fact_148_lprefix__lappendD, fact_247_ltl__unfold__llist, fact_176_order__trans, fact_53_lstrict__prefix__code_I4_J, fact_66_ltakeWhile__LCons, fact_192_le__fun__def, fact_157_lappend__eq__LNil__iff, fact_163_lprefix__lhdD, tcon_HOL_Obool___Orderings_Oord_6, fact_246_lfinite__induct, fact_113_lsorted__LCons_H, fact_74_ltakeWhile__LNil, fact_87_lfinite__LNil, fact_20_unfold__llist_Octr_I2_J, fact_248_llexord__code_I2_J, fact_160_lappend__inf, fact_91_lprefix__lnullD, fact_249_llexord_Ocases, fact_100_lfinite_Osimps, fact_161_unfold__llist_Osimps_I3_J, fact_7_lmirror__aux_Octr_I1_J, fact_240_llexord__linear, fact_70_lprefix__code_I1_J, fact_96_lstrict__prefix__lfinite1, fact_61_lsorted_Ocases, tcon_Set_Oset___Orderings_Opreorder_1, fact_236_llexord__LNil, fact_107_LCons__LCons, fact_228_ltl__simps_I1_J, fact_171_ltakeWhile_Octr_I1_J, fact_92_lprefix__lnull, fact_235_lnull__llexord, fact_189_ord__eq__le__subst
% 25.63/8.91 % No. of inferences in proof: 468
% 25.63/8.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8362 ms resp. 7749 ms w/o parsing
% 26.65/9.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.65/9.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------