TSTP Solution File: DAT197^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT197^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 07:39:44 EDT 2024
% Result : Theorem 149.63s 123.57s
% Output : Refutation 150.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 256
% Syntax : Number of formulae : 464 ( 188 unt; 50 typ; 0 def)
% Number of atoms : 1656 ( 464 equ; 80 cnn)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 7657 ( 52 ~; 8 |; 74 &;7135 @)
% ( 0 <=>; 388 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 1394 (1394 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 10 con; 0-8 aty)
% Number of variables : 1918 ( 48 ^1780 !; 40 ?;1918 :)
% ( 50 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(code_natural_type,type,
code_natural: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bNF_rel_fun_type,type,
bNF_rel_fun:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC > $o ) > ( TB > TA > $o ) > ( TD > TB ) > ( TC > TA ) > $o ) ).
thf(code_case_natural_type,type,
code_case_natural:
!>[TA: $tType] : ( TA > ( code_natural > TA ) > code_natural > TA ) ).
thf(code_rec_natural_type,type,
code_rec_natural:
!>[TA: $tType] : ( TA > ( code_natural > TA > TA ) > code_natural > TA ) ).
thf(code_size_natural_type,type,
code_size_natural: code_natural > nat ).
thf(coindu328551480prefix_type,type,
coindu328551480prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coindu246717305length_type,type,
coindu246717305length:
!>[TA: $tType] : ( nat > ( coinductive_llist @ TA ) > extended_enat ) ).
thf(coinductive_iterates_type,type,
coinductive_iterates:
!>[TA: $tType] : ( ( TA > TA ) > TA > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lappend_type,type,
coinductive_lappend:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_ldrop_type,type,
coinductive_ldrop:
!>[TA: $tType] : ( extended_enat > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coindu218763757pWhile_type,type,
coindu218763757pWhile:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lfilter_type,type,
coinductive_lfilter:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lfinite_type,type,
coinductive_lfinite:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_llast_type,type,
coinductive_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(coinductive_llcp_type,type,
coinductive_llcp:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > extended_enat ) ).
thf(coinductive_llength_type,type,
coinductive_llength:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > extended_enat ) ).
thf(coinductive_LCons_type,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coindu1381640503_llist_type,type,
coindu1381640503_llist:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coinductive_llist @ TA ) > TB ) > ( coinductive_llist @ TA ) > TB ) ).
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(coindu1486289336t_all2_type,type,
coindu1486289336t_all2:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( coinductive_llist @ TB ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lmap_type,type,
coinductive_lmap:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( coinductive_llist @ TB ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lset_type,type,
coinductive_lset:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coindu543516966_llist_type,type,
coindu543516966_llist:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lprefix_type,type,
coinductive_lprefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_ltake_type,type,
coinductive_ltake:
!>[TA: $tType] : ( extended_enat > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coindu501562517eWhile_type,type,
coindu501562517eWhile:
!>[TA: $tType] : ( ( TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coindu1441602521_llist_type,type,
coindu1441602521_llist:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > TB ) > TB > ( coinductive_llist @ TA ) ) ).
thf(map_fun_type,type,
map_fun:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC ) > ( TB > TA ) > ( TC > TB ) > TD > TA ) ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(lMirro999291890or_aux_type,type,
lMirro999291890or_aux:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(case_nat_type,type,
case_nat:
!>[TA: $tType] : ( TA > ( nat > TA ) > nat > TA ) ).
thf(rec_nat_type,type,
rec_nat:
!>[TA: $tType] : ( TA > ( nat > TA > TA ) > nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(type_type,type,
type:
!>[TA: $tType] : ( itself @ TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: a > b > $o ).
thf(acc_a_type,type,
acc_a: coinductive_llist @ b ).
thf(acca_type,type,
acca: coinductive_llist @ a ).
thf(xs_a_type,type,
xs_a: coinductive_llist @ b ).
thf(xsa_type,type,
xsa: coinductive_llist @ a ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_26_lprefix__lfiniteD) ).
thf(645,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)],[133]) ).
thf(195,axiom,
! [TA: $tType] :
( ( coindu218763757pWhile @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] : ( coinductive_ldrop @ TA @ ( coinductive_llength @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ldropWhile__eq__ldrop) ).
thf(809,plain,
! [TA: $tType] :
( ( coindu218763757pWhile @ TA )
= ( ^ [A: TA > $o,B: coinductive_llist @ TA] : ( coinductive_ldrop @ TA @ ( coinductive_llength @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ B @ C ) ) )
= ( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
| ( ( coinductive_lfinite @ TA @ B )
& ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_in__lset__lappend__iff) ).
thf(365,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ B @ C ) ) )
= ( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
| ( ( coinductive_lfinite @ TA @ B )
& ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: extended_enat] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_ldrop @ TB @ D @ B ) @ ( coinductive_ldrop @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_llist__all2__ldropI) ).
thf(760,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: extended_enat] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_ldrop @ TB @ D @ B ) @ ( coinductive_ldrop @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TB @ ( A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_llist_Osimps_I13_J) ).
thf(479,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TB @ ( A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_llist_Oset__cases) ).
thf(249,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(52,axiom,
semiri456707255roduct @ nat @ ( type @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(408,plain,
semiri456707255roduct @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,A: extended_enat,B: TA > TB,C: coinductive_llist @ TA] :
( ( coinductive_ldrop @ TB @ A @ ( coinductive_lmap @ TA @ TB @ B @ C ) )
= ( coinductive_lmap @ TA @ TB @ B @ ( coinductive_ldrop @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_ldrop__lmap) ).
thf(762,plain,
! [TA: $tType,TB: $tType,A: extended_enat,B: TA > TB,C: coinductive_llist @ TA] :
( ( coinductive_ldrop @ TB @ A @ ( coinductive_lmap @ TA @ TB @ B @ C ) )
= ( coinductive_lmap @ TA @ TB @ B @ ( coinductive_ldrop @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',fact_39_Coinductive__List_Olprefix__nitpick__simps) ).
thf(655,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)],[137]) ).
thf(18,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ B )
| ? [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
& ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_lfinite__ltakeWhile) ).
thf(269,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ B )
| ? [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
& ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_add__eq__self__zero) ).
thf(677,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(190,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_llength @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( plus_plus @ extended_enat @ ( coinductive_llength @ TA @ A ) @ ( coinductive_llength @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_llength__lappend) ).
thf(797,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_llength @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( plus_plus @ extended_enat @ ( coinductive_llength @ TA @ A ) @ ( coinductive_llength @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_split__llist) ).
thf(472,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: coinductive_llist @ TB,E: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( ( coinductive_lfinite @ TB @ B )
=> ( ( coinductive_lfinite @ TA @ C )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lappend @ TB @ B @ D ) @ ( coinductive_lappend @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_llist__all2__lappendI) ).
thf(698,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: coinductive_llist @ TB,E: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( ( coinductive_lfinite @ TB @ B )
=> ( ( coinductive_lfinite @ TA @ C )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lappend @ TB @ B @ D ) @ ( coinductive_lappend @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',fact_25_lprefix__antisym) ).
thf(782,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)],[185]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TB,D: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lappend @ TB @ B @ C ) @ D )
=> ( ( coinductive_lfinite @ TB @ B )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ C @ ( coinductive_ldrop @ TA @ ( coinductive_llength @ TB @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_llist__all2__lappend1D_I2_J) ).
thf(841,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TB,D: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lappend @ TB @ B @ C ) @ D )
=> ( ( coinductive_lfinite @ TB @ B )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ C @ ( coinductive_ldrop @ TA @ ( coinductive_llength @ TB @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: coinductive_llist @ TA,E: TB > TA > $o,F: TB > TA > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ ( coinductive_lset @ TB @ B ) )
=> ( ( member @ TA @ H @ ( coinductive_lset @ TA @ D ) )
=> ( ( E @ G @ H )
= ( F @ G @ H ) ) ) )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ E @ A @ C )
= ( coindu1486289336t_all2 @ TB @ TA @ F @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_llist_Orel__cong) ).
thf(301,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: coinductive_llist @ TA,E: TB > TA > $o,F: TB > TA > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ ( coinductive_lset @ TB @ B ) )
=> ( ( member @ TA @ H @ ( coinductive_lset @ TA @ D ) )
=> ( ( E @ G @ H )
= ( F @ G @ H ) ) ) )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ E @ A @ C )
= ( coindu1486289336t_all2 @ TB @ TA @ F @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_lset__cases) ).
thf(320,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_split__llist__first) ).
thf(436,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ? [C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ C @ ( coinductive_LCons @ TA @ A @ D ) ) )
& ( coinductive_lfinite @ TA @ C )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(16,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( coindu1486289336t_all2 @ TA @ TA @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_llist__all2__reflI) ).
thf(257,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( coindu1486289336t_all2 @ TA @ TA @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD > TA > $o,C: TC > TB > $o,D: TC > TB > $o,E: TD > TC,F: TA > TB] :
( ! [G: TD,H: TA] :
( ( A @ G @ H )
=> ( B @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( C @ G @ H )
=> ( D @ G @ H ) )
=> ( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ B @ C @ E @ F )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__fun__mono_H) ).
thf(724,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD > TA > $o,C: TC > TB > $o,D: TC > TB > $o,E: TD > TC,F: TA > TB] :
( ! [G: TD,H: TA] :
( ( A @ G @ H )
=> ( B @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( C @ G @ H )
=> ( D @ G @ H ) )
=> ( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ B @ C @ E @ F )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: code_natural > TA > TA] :
( ( code_rec_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_natural_Osimps_I6_J) ).
thf(785,plain,
! [TA: $tType,A: TA,B: code_natural > TA > TA] :
( ( code_rec_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( coinductive_lfinite @ TB @ B )
= ( coinductive_lfinite @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_llist__all2__lfiniteD) ).
thf(504,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( coinductive_lfinite @ TB @ B )
= ( coinductive_lfinite @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_llength @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_llength @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_llength__lmap) ).
thf(838,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_llength @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_llength @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(153,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_ldrop @ TA @ ( zero_zero @ extended_enat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_ldrop__0) ).
thf(702,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_ldrop @ TA @ ( zero_zero @ extended_enat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
=> ? [E: TB] :
( ( member @ TB @ E @ ( coinductive_lset @ TB @ B ) )
& ( A @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_llist__all2__lsetD2) ).
thf(357,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
=> ? [E: TB] :
( ( member @ TB @ E @ ( coinductive_lset @ TB @ B ) )
& ( A @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) @ ( coinductive_lfinite @ TB ) @ ( coinductive_lfinite @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_lfinite__transfer) ).
thf(559,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) @ ( coinductive_lfinite @ TB ) @ ( coinductive_lfinite @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(30,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu501562517eWhile @ TA @ C @ A )
= ( coindu501562517eWhile @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_ltakeWhile__cong) ).
thf(325,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu501562517eWhile @ TA @ C @ A )
= ( coindu501562517eWhile @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(22,axiom,
canoni770627133id_add @ extended_enat @ ( type @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_1) ).
thf(284,plain,
canoni770627133id_add @ extended_enat @ ( type @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coindu218763757pWhile @ TB ) @ ( coindu218763757pWhile @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_ldropWhile__transfer) ).
thf(770,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coindu218763757pWhile @ TB ) @ ( coindu218763757pWhile @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_165_lprefix__lappendD) ).
thf(591,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)],[115]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( coinductive_llist @ TD ) > ( coinductive_llist @ TC ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( coinductive_llist @ TD ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ ( coindu1486289336t_all2 @ TD @ TA @ A ) @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( coinductive_lmap @ TD @ TC ) @ ( coinductive_lmap @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_llist_Omap__transfer) ).
thf(623,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( coinductive_llist @ TD ) > ( coinductive_llist @ TC ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( coinductive_llist @ TD ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ ( coindu1486289336t_all2 @ TD @ TA @ A ) @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( coinductive_lmap @ TD @ TC ) @ ( coinductive_lmap @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(77,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_add_Ogroup__left__neutral) ).
thf(485,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(88,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) @ ( coindu218763757pWhile @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_lappend__ltakeWhile__ldropWhile) ).
thf(514,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) @ ( coindu218763757pWhile @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TB,D: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lappend @ TB @ B @ C ) @ D )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ ( coinductive_ltake @ TA @ ( coinductive_llength @ TB @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_llist__all2__lappend1D_I1_J) ).
thf(806,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TB,D: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lappend @ TB @ B @ C ) @ D )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ ( coinductive_ltake @ TA @ ( coinductive_llength @ TB @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(199,axiom,
coinductive_lfinite @ a @ acca,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_local_OLNil_I3_J) ).
thf(821,plain,
coinductive_lfinite @ a @ acca,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(35,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coindu218763757pWhile @ TA @ A @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
& ~ ( A @ C ) )
=> ( coinductive_lfinite @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_lfinite__ldropWhile) ).
thf(348,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coindu218763757pWhile @ TA @ A @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
& ~ ( A @ C ) )
=> ( coinductive_lfinite @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(109,axiom,
! [TA: $tType,A: extended_enat,B: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_ltake @ TA @ A @ B ) @ ( coinductive_ldrop @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_lappend__ltake__ldrop) ).
thf(574,plain,
! [TA: $tType,A: extended_enat,B: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_ltake @ TA @ A @ B ) @ ( coinductive_ldrop @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > $o ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) ) @ ( coindu543516966_llist @ TB ) @ ( coindu543516966_llist @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_llist__all__transfer) ).
thf(602,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > $o ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) ) @ ( coindu543516966_llist @ TB ) @ ( coindu543516966_llist @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_llist_Oinject) ).
thf(453,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)],[66]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_rel__funD) ).
thf(774,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(48,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_lfilter__LCons__seek) ).
thf(396,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(12,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add_Oleft__cancel) ).
thf(243,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(59,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coindu218763757pWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coindu218763757pWhile @ TA @ A @ C ) ) )
& ( ~ ( A @ B )
=> ( ( coindu218763757pWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_ldropWhile__LCons) ).
thf(428,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coindu218763757pWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coindu218763757pWhile @ TA @ A @ C ) ) )
& ( ~ ( A @ B )
=> ( ( coindu218763757pWhile @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',fact_167_lprefix__lappend__sameI) ).
thf(507,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)],[85]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: nat > TA > TA] :
( ( rec_nat @ TA @ A @ B @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_old_Onat_Osimps_I6_J) ).
thf(527,plain,
! [TA: $tType,A: TA,B: nat > TA > TA] :
( ( rec_nat @ TA @ A @ B @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: TB,D: coinductive_llist @ TB] :
( ( ( coinductive_lmap @ TA @ TB @ A @ B )
= ( coinductive_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ E @ F ) )
& ( C
= ( A @ E ) )
& ( D
= ( coinductive_lmap @ TA @ TB @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_lmap__eq__LCons__conv) ).
thf(380,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: TB,D: coinductive_llist @ TB] :
( ( ( coinductive_lmap @ TA @ TB @ A @ B )
= ( coinductive_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ E @ F ) )
& ( C
= ( A @ E ) )
& ( D
= ( coinductive_lmap @ TA @ TB @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_lappend @ TB ) @ ( coinductive_lappend @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_lappend__transfer) ).
thf(512,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_lappend @ TB ) @ ( coinductive_lappend @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ TD @ TA @ ( ( TC > ( coinductive_llist @ TC ) > TD ) > ( coinductive_llist @ TC ) > TD ) @ ( ( TB > ( coinductive_llist @ TB ) > TA ) > ( coinductive_llist @ TB ) > TA ) @ A @ ( bNF_rel_fun @ ( TC > ( coinductive_llist @ TC ) > TD ) @ ( TB > ( coinductive_llist @ TB ) > TA ) @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ ( bNF_rel_fun @ TC @ TB @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ B @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( coindu1381640503_llist @ TD @ TC ) @ ( coindu1381640503_llist @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_case__llist__transfer) ).
thf(661,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ TD @ TA @ ( ( TC > ( coinductive_llist @ TC ) > TD ) > ( coinductive_llist @ TC ) > TD ) @ ( ( TB > ( coinductive_llist @ TB ) > TA ) > ( coinductive_llist @ TB ) > TA ) @ A @ ( bNF_rel_fun @ ( TC > ( coinductive_llist @ TC ) > TD ) @ ( TB > ( coinductive_llist @ TB ) > TA ) @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ ( bNF_rel_fun @ TC @ TB @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ B @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( coindu1381640503_llist @ TD @ TC ) @ ( coindu1381640503_llist @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_lfinite__lmap) ).
thf(546,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( E @ G @ H )
=> ( A @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( B @ G @ H )
=> ( F @ G @ H ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_rel__fun__mono) ).
thf(534,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( E @ G @ H )
=> ( A @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( B @ G @ H )
=> ( F @ G @ H ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > TC ) > ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TB ) > ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( bNF_rel_fun @ ( TD > TD ) @ ( TA > TA ) @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TD @ TA @ A @ A ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) ) ) ) ) @ ( coindu1259883913_llist @ TD @ TC ) @ ( coindu1259883913_llist @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_llist_Ocorec__transfer) ).
thf(714,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > TC ) > ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TB ) > ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( bNF_rel_fun @ ( TD > TD ) @ ( TA > TA ) @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TD @ TA @ A @ A ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) ) ) ) ) @ ( coindu1259883913_llist @ TD @ TC ) @ ( coindu1259883913_llist @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coindu218763757pWhile @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_in__lset__ldropWhileD) ).
thf(334,plain,
! [TA: $tType,A: TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coindu218763757pWhile @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ A @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_LCons @ TB ) @ ( coinductive_LCons @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_LCons__transfer) ).
thf(746,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ A @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_LCons @ TB ) @ ( coinductive_LCons @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_apply__rsp_H) ).
thf(598,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(104,axiom,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_natural_Osize_I3_J) ).
thf(561,plain,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_lset__induct_H) ).
thf(297,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(197,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( ( coinductive_llength @ TA @ A )
= ( coinductive_llength @ TA @ B ) )
=> ( ( ( coinductive_lappend @ TA @ A @ C )
= ( coinductive_lappend @ TA @ B @ D ) )
= ( ( A = B )
& ( ( coinductive_lfinite @ TA @ A )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_lappend__eq__lappend__conv) ).
thf(815,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( ( coinductive_llength @ TA @ A )
= ( coinductive_llength @ TA @ B ) )
=> ( ( ( coinductive_lappend @ TA @ A @ C )
= ( coinductive_lappend @ TA @ B @ D ) )
= ( ( A = B )
& ( ( coinductive_lfinite @ TA @ A )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( A @ E @ F )
=> ( D @ E @ F ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_llist__all2__mono) ).
thf(729,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( A @ E @ F )
=> ( D @ E @ F ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(150,axiom,
! [TA: $tType] :
( ( coinductive_llcp @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( coinductive_llcp @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_llcp__commute) ).
thf(693,plain,
! [TA: $tType] :
( ( coinductive_llcp @ TA )
= ( ^ [A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( coinductive_llcp @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > TC > $o ) @ ( TA > TB > $o ) @ ( ( coinductive_llist @ TD ) > ( coinductive_llist @ TC ) > $o ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TB ) > $o ) @ ( bNF_rel_fun @ TD @ TA @ ( TC > $o ) @ ( TB > $o ) @ A @ ( bNF_rel_fun @ TC @ TB @ $o @ $o @ B @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TD ) @ ( coinductive_llist @ TA ) @ ( ( coinductive_llist @ TC ) > $o ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( coindu1486289336t_all2 @ TD @ TA @ A ) @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ $o @ $o @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ ( (=) @ $o ) ) ) @ ( coindu1486289336t_all2 @ TD @ TC ) @ ( coindu1486289336t_all2 @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_llist_Orel__transfer) ).
thf(630,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > TC > $o ) @ ( TA > TB > $o ) @ ( ( coinductive_llist @ TD ) > ( coinductive_llist @ TC ) > $o ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TB ) > $o ) @ ( bNF_rel_fun @ TD @ TA @ ( TC > $o ) @ ( TB > $o ) @ A @ ( bNF_rel_fun @ TC @ TB @ $o @ $o @ B @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TD ) @ ( coinductive_llist @ TA ) @ ( ( coinductive_llist @ TC ) > $o ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( coindu1486289336t_all2 @ TD @ TA @ A ) @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ $o @ $o @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ ( (=) @ $o ) ) ) @ ( coindu1486289336t_all2 @ TD @ TC ) @ ( coindu1486289336t_all2 @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: extended_enat,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_ldrop @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_in__lset__ldropD) ).
thf(275,plain,
! [TA: $tType,A: TA,B: extended_enat,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_ldrop @ TA @ B @ C ) ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',fact_166_lprefix__conv__lappend) ).
thf(788,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)],[187]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: coinductive_llist @ TB,E: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( lMirro999291890or_aux @ TB @ B @ D ) @ ( lMirro999291890or_aux @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_llist__all2__lmirror__aux) ).
thf(625,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: coinductive_llist @ TB,E: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( lMirro999291890or_aux @ TB @ B @ D ) @ ( lMirro999291890or_aux @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(141,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_lappend @ TA @ C @ D ) )
=> ( ( coinductive_lfinite @ TA @ C )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ F ) )
& ( coinductive_lfinite @ TA @ E )
& ( C
= ( coinductive_lfilter @ TA @ A @ E ) )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_lfilter__eq__lappend__lfiniteD) ).
thf(665,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_lappend @ TA @ C @ D ) )
=> ( ( coinductive_lfinite @ TA @ C )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ F ) )
& ( coinductive_lfinite @ TA @ E )
& ( C
= ( coinductive_lfilter @ TA @ A @ E ) )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( nat > TB > TB ) > nat > TB ) @ ( ( nat > TA > TA ) > nat > TA ) @ A @ ( bNF_rel_fun @ ( nat > TB > TB ) @ ( nat > TA > TA ) @ ( nat > TB ) @ ( nat > TA ) @ ( bNF_rel_fun @ nat @ nat @ ( TB > TB ) @ ( TA > TA ) @ ( (=) @ nat ) @ ( bNF_rel_fun @ TB @ TA @ TB @ TA @ A @ A ) ) @ ( bNF_rel_fun @ nat @ nat @ TB @ TA @ ( (=) @ nat ) @ A ) ) @ ( rec_nat @ TB ) @ ( rec_nat @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_rec__nat__transfer) ).
thf(682,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( nat > TB > TB ) > nat > TB ) @ ( ( nat > TA > TA ) > nat > TA ) @ A @ ( bNF_rel_fun @ ( nat > TB > TB ) @ ( nat > TA > TA ) @ ( nat > TB ) @ ( nat > TA ) @ ( bNF_rel_fun @ nat @ nat @ ( TB > TB ) @ ( TA > TA ) @ ( (=) @ nat ) @ ( bNF_rel_fun @ TB @ TA @ TB @ TA @ A @ A ) ) @ ( bNF_rel_fun @ nat @ nat @ TB @ TA @ ( (=) @ nat ) @ A ) ) @ ( rec_nat @ TB ) @ ( rec_nat @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',fact_21_lprefix__trans) ).
thf(551,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)],[101]) ).
thf(67,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_lfilter__LCons__found) ).
thf(456,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coinductive_lfilter @ TA @ C @ A )
= ( coinductive_lfilter @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_lfilter__cong) ).
thf(229,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coinductive_lfilter @ TA @ C @ A )
= ( coinductive_lfilter @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(106,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lset @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) )
= ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_lset__lmirror__aux) ).
thf(566,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lset @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) )
= ( coinductive_lset @ TA @ ( coinductive_lappend @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(112,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_double__zero) ).
thf(583,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(91,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lappend @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_lappend__inf) ).
thf(522,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)],[91]) ).
thf(203,axiom,
( ( coinductive_llength @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) )
= ( coinductive_llength @ b @ ( lMirro999291890or_aux @ b @ acc_a @ xs_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_calculation) ).
thf(830,plain,
( ( coinductive_llength @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) )
= ( coinductive_llength @ b @ ( lMirro999291890or_aux @ b @ acc_a @ xs_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(23,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ( B @ C ) )
=> ( ( coindu501562517eWhile @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_ltakeWhile__all) ).
thf(285,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ( B @ C ) )
=> ( ( coindu501562517eWhile @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( member @ TB @ E @ ( coinductive_lset @ TB @ B ) )
=> ( ( member @ TA @ F @ ( coinductive_lset @ TA @ C ) )
=> ( ( A @ E @ F )
=> ( D @ E @ F ) ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_llist_Orel__mono__strong) ).
thf(224,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( member @ TB @ E @ ( coinductive_lset @ TB @ B ) )
=> ( ( member @ TA @ F @ ( coinductive_lset @ TA @ C ) )
=> ( ( A @ E @ F )
=> ( D @ E @ F ) ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( TA > TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_fun_Orel__eq) ).
thf(519,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( TA > TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > TC ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TB ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > TD ) @ ( TA > TA ) @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TD @ TA @ A @ A ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) ) ) @ ( coindu1441602521_llist @ TD @ TC ) @ ( coindu1441602521_llist @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_unfold__llist__transfer) ).
thf(650,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > TC ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TB ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > TD ) @ ( TA > TA ) @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TD @ TA @ A @ A ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) ) ) @ ( coindu1441602521_llist @ TD @ TC ) @ ( coindu1441602521_llist @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(123,axiom,
! [TA: $tType] :
( ( coindu1486289336t_all2 @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( coinductive_llist @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_llist_Orel__eq) ).
thf(615,plain,
! [TA: $tType] :
( ( coindu1486289336t_all2 @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( coinductive_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > $o,B: TC > TB > $o,C: TA > TC,D: TA > TB,E: TA] :
( ( bNF_rel_fun @ TA @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( B @ ( C @ E ) @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_rel__funD2) ).
thf(593,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > $o,B: TC > TB > $o,C: TA > TC,D: TA > TB,E: TA] :
( ( bNF_rel_fun @ TA @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( B @ ( C @ E ) @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_lfinite__LCons) ).
thf(420,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)],[56]) ).
thf(78,axiom,
! [TA: $tType,A: TA > ( coinductive_llist @ TA ),B: TA > TA] :
( ! [C: TA] :
( ( A @ C )
= ( coinductive_LCons @ TA @ C @ ( coinductive_lmap @ TA @ TA @ B @ ( A @ C ) ) ) )
=> ( A
= ( coinductive_iterates @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_iterates__equality) ).
thf(488,plain,
! [TA: $tType,A: TA > ( coinductive_llist @ TA ),B: TA > TA] :
( ! [C: TA] :
( ( A @ C )
= ( coinductive_LCons @ TA @ C @ ( coinductive_lmap @ TA @ TA @ B @ ( A @ C ) ) ) )
=> ( A
= ( coinductive_iterates @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TB,D: TA > TB] :
( ! [E: TA,F: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ A ) )
=> ( ( member @ TA @ F @ ( coinductive_lset @ TA @ B ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( coinductive_lmap @ TA @ TB @ C @ A )
= ( coinductive_lmap @ TA @ TB @ D @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_llist_Oinj__map__strong) ).
thf(339,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TB,D: TA > TB] :
( ! [E: TA,F: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ A ) )
=> ( ( member @ TA @ F @ ( coinductive_lset @ TA @ B ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( coinductive_lmap @ TA @ TB @ C @ A )
= ( coinductive_lmap @ TA @ TB @ D @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_lfilter @ TB ) @ ( coinductive_lfilter @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_lfilter__transfer) ).
thf(753,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_lfilter @ TB ) @ ( coinductive_lfilter @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(132,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
( ( coinductive_lmap @ TA @ TA @ A @ ( coinductive_iterates @ TA @ A @ B ) )
= ( coinductive_iterates @ TA @ A @ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_lmap__iterates) ).
thf(642,plain,
! [TA: $tType,A: TA > TA,B: TA] :
( ( coinductive_lmap @ TA @ TA @ A @ ( coinductive_iterates @ TA @ A @ B ) )
= ( coinductive_iterates @ TA @ A @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(147,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_plus__nat_Oadd__0) ).
thf(686,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coinductive_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ B )
= ( coinductive_LCons @ TB @ ( C @ B ) @ ( if @ ( coinductive_llist @ TB ) @ ( D @ B ) @ ( E @ B ) @ ( coindu1259883913_llist @ TA @ TB @ A @ C @ D @ E @ F @ ( F @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_llist_Ocorec_I2_J) ).
thf(476,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)],[74]) ).
thf(134,axiom,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coinductive_llist @ TA] :
( ( coinductive_ltake @ TA @ A @ ( coinductive_ldrop @ TA @ B @ C ) )
= ( coinductive_ldrop @ TA @ B @ ( coinductive_ltake @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_ltake__ldrop) ).
thf(647,plain,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coinductive_llist @ TA] :
( ( coinductive_ltake @ TA @ A @ ( coinductive_ldrop @ TA @ B @ C ) )
= ( coinductive_ldrop @ TA @ B @ ( coinductive_ltake @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_31_not__lfinite__lprefix__conv__eq) ).
thf(721,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)],[161]) ).
thf(107,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add__0__iff) ).
thf(569,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(183,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_lprefix__refl) ).
thf(779,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(42,axiom,
! [TA: $tType] :
( ( coinductive_iterates @ TA )
= ( ^ [A: TA > TA,B: TA] : ( coinductive_LCons @ TA @ B @ ( coinductive_iterates @ TA @ A @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_iterates_Ocode) ).
thf(371,plain,
! [TA: $tType] :
( ( coinductive_iterates @ TA )
= ( ^ [A: TA > TA,B: TA] : ( coinductive_LCons @ TA @ B @ ( coinductive_iterates @ TA @ A @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_llist_Oset__induct) ).
thf(237,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ $o @ $o @ ( TB > TB > TB ) @ ( TA > TA > TA ) @ ( (=) @ $o ) @ ( bNF_rel_fun @ TB @ TA @ ( TB > TB ) @ ( TA > TA ) @ A @ ( bNF_rel_fun @ TB @ TA @ TB @ TA @ A @ A ) ) @ ( if @ TB ) @ ( if @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_If__transfer) ).
thf(360,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ $o @ $o @ ( TB > TB > TB ) @ ( TA > TA > TA ) @ ( (=) @ $o ) @ ( bNF_rel_fun @ TB @ TA @ ( TB > TB ) @ ( TA > TA ) @ A @ ( bNF_rel_fun @ TB @ TA @ TB @ TA @ A @ A ) ) @ ( if @ TB ) @ ( if @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coinductive_lmap @ TA @ TB @ C @ A )
= ( coinductive_lmap @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_llist_Omap__cong) ).
thf(311,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coinductive_lmap @ TA @ TB @ C @ A )
= ( coinductive_lmap @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(98,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( coindu1486289336t_all2 @ TA @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_llist_Orel__refl) ).
thf(541,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( coindu1486289336t_all2 @ TA @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ extended_enat @ extended_enat @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( (=) @ extended_enat ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_ldrop @ TB ) @ ( coinductive_ldrop @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_ldrop__transfer) ).
thf(765,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ extended_enat @ extended_enat @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( (=) @ extended_enat ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_ldrop @ TB ) @ ( coinductive_ldrop @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(142,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_double__zero__sym) ).
thf(674,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(94,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ ( coinductive_lappend @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_lprefix__lappend) ).
thf(530,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)],[94]) ).
thf(160,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ B )
& ( coinductive_lfinite @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_lfinite__lmirror__aux) ).
thf(718,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( lMirro999291890or_aux @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ B )
& ( coinductive_lfinite @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(189,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_llcp @ TA @ B @ A )
= ( coinductive_llength @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_llcp__lprefix2) ).
thf(794,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_llcp @ TA @ B @ A )
= ( coinductive_llength @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_natural_Osimps_I4_J) ).
thf(586,plain,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( map_fun @ TA @ TB @ TD @ TC )
= ( ^ [A: TA > TB,B: TD > TC,C: TB > TD,D: TA] : ( B @ ( C @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_map__fun__apply) ).
thf(412,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( map_fun @ TA @ TB @ TD @ TC )
= ( ^ [A: TA > TB,B: TD > TC,C: TB > TD,D: TA] : ( B @ ( C @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(171,axiom,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coinductive_llist @ TA] :
( ( coinductive_ldrop @ TA @ A @ ( coinductive_ldrop @ TA @ B @ C ) )
= ( coinductive_ldrop @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_ldrop__ldrop) ).
thf(750,plain,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coinductive_llist @ TA] :
( ( coinductive_ldrop @ TA @ A @ ( coinductive_ldrop @ TA @ B @ C ) )
= ( coinductive_ldrop @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA > TF > $o,B: TD > TC > $o,C: TE > TB > $o,D: TA > TD > TE,E: TF > TC > TB] :
( ( bNF_rel_fun @ TA @ TF @ ( TD > TE ) @ ( TC > TB ) @ A @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C ) @ D @ E )
= ( ! [F: TA,G: TF] :
( ( A @ F @ G )
=> ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C @ ( D @ F ) @ ( E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rel__fun__def__butlast) ).
thf(618,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA > TF > $o,B: TD > TC > $o,C: TE > TB > $o,D: TA > TD > TE,E: TF > TC > TB] :
( ( bNF_rel_fun @ TA @ TF @ ( TD > TE ) @ ( TC > TB ) @ A @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C ) @ D @ E )
= ( ! [F: TA,G: TF] :
( ( A @ F @ G )
=> ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C @ ( D @ F ) @ ( E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',fact_117_lmirror__aux__simps_I2_J) ).
thf(425,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)],[58]) ).
thf(201,axiom,
! [TA: $tType] :
( ( coinductive_llength @ TA )
= ( coindu246717305length @ TA @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_llength__code) ).
thf(824,plain,
! [TA: $tType] :
( ( coinductive_llength @ TA )
= ( coindu246717305length @ TA @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_let__rsp) ).
thf(689,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(63,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_lfinite__lfilterI) ).
thf(444,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_lfilter @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC > $o,B: TE > TB > $o] : ( bNF_rel_fun @ ( TD > TE > $o ) @ ( TC > TB > $o ) @ ( ( TA > TD ) > ( TA > TE ) > $o ) @ ( ( TA > TC ) > ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TD @ TC @ ( TE > $o ) @ ( TB > $o ) @ A @ ( bNF_rel_fun @ TE @ TB @ $o @ $o @ B @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( TA > TD ) @ ( TA > TC ) @ ( ( TA > TE ) > $o ) @ ( ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TC @ ( (=) @ TA ) @ A ) @ ( bNF_rel_fun @ ( TA > TE ) @ ( TA > TB ) @ $o @ $o @ ( bNF_rel_fun @ TA @ TA @ TE @ TB @ ( (=) @ TA ) @ B ) @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TE @ ( (=) @ TA ) ) @ ( bNF_rel_fun @ TA @ TA @ TC @ TB @ ( (=) @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_fun_Orel__transfer) ).
thf(423,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC > $o,B: TE > TB > $o] : ( bNF_rel_fun @ ( TD > TE > $o ) @ ( TC > TB > $o ) @ ( ( TA > TD ) > ( TA > TE ) > $o ) @ ( ( TA > TC ) > ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TD @ TC @ ( TE > $o ) @ ( TB > $o ) @ A @ ( bNF_rel_fun @ TE @ TB @ $o @ $o @ B @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( TA > TD ) @ ( TA > TC ) @ ( ( TA > TE ) > $o ) @ ( ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TC @ ( (=) @ TA ) @ A ) @ ( bNF_rel_fun @ ( TA > TE ) @ ( TA > TB ) @ $o @ $o @ ( bNF_rel_fun @ TA @ TA @ TE @ TB @ ( (=) @ TA ) @ B ) @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TE @ ( (=) @ TA ) ) @ ( bNF_rel_fun @ TA @ TA @ TC @ TB @ ( (=) @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: coinductive_llist @ TA,C: TB,D: coinductive_llist @ TB] :
( ( coindu1486289336t_all2 @ TA @ TB @ A @ B @ ( coinductive_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ E @ F ) )
& ( A @ E @ C )
& ( coindu1486289336t_all2 @ TA @ TB @ A @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_llist__all2__LCons2) ).
thf(402,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: coinductive_llist @ TA,C: TB,D: coinductive_llist @ TB] :
( ( coindu1486289336t_all2 @ TA @ TB @ A @ B @ ( coinductive_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ E @ F ) )
& ( A @ E @ C )
& ( coindu1486289336t_all2 @ TA @ TB @ A @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(164,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfilter @ TA @ B @ ( coinductive_lappend @ TA @ A @ C ) )
= ( coinductive_lappend @ TA @ ( coinductive_lfilter @ TA @ B @ A ) @ ( coinductive_lfilter @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_lfilter__lappend__lfinite) ).
thf(732,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfilter @ TA @ B @ ( coinductive_lappend @ TA @ A @ C ) )
= ( coinductive_lappend @ TA @ ( coinductive_lfilter @ TA @ B @ A ) @ ( coinductive_lfilter @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',fact_30_lprefix__down__linear) ).
thf(772,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)],[180]) ).
thf(110,axiom,
! [TA: $tType] :
( ( coindu328551480prefix @ TA )
= ( coinductive_lprefix @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Coinductive__List_Ofinite__lprefix__def) ).
thf(577,plain,
! [TA: $tType] :
( ( coindu328551480prefix @ TA )
= ( coinductive_lprefix @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ A @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_LCons @ TB ) @ ( coinductive_LCons @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_llist_Octr__transfer_I2_J) ).
thf(711,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ A @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_LCons @ TB ) @ ( coinductive_LCons @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > TC ) > ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TB ) > ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( bNF_rel_fun @ ( TD > TD ) @ ( TA > TA ) @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TD @ TA @ A @ A ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) ) ) ) ) @ ( coindu1259883913_llist @ TD @ TC ) @ ( coindu1259883913_llist @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_llist__corec__transfer) ).
thf(572,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > TC ) > ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TB ) > ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( TD > $o ) > ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > $o ) > ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > $o ) @ ( TA > $o ) @ ( ( TD > ( coinductive_llist @ TC ) ) > ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > ( coinductive_llist @ TB ) ) > ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( ( TD > TD ) > TD > ( coinductive_llist @ TC ) ) @ ( ( TA > TA ) > TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( bNF_rel_fun @ ( TD > TD ) @ ( TA > TA ) @ ( TD > ( coinductive_llist @ TC ) ) @ ( TA > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TD @ TA @ A @ A ) @ ( bNF_rel_fun @ TD @ TA @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ A @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) ) ) ) ) @ ( coindu1259883913_llist @ TD @ TC ) @ ( coindu1259883913_llist @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(71,axiom,
! [TA: $tType,A: TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_llast__LCons2) ).
thf(466,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)],[71]) ).
thf(9,axiom,
canoni770627133id_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(236,plain,
canoni770627133id_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(157,axiom,
bNF_rel_fun @ nat @ nat @ ( nat > nat ) @ ( nat > nat ) @ ( (=) @ nat ) @ ( bNF_rel_fun @ nat @ nat @ nat @ nat @ ( (=) @ nat ) @ ( (=) @ nat ) ) @ ( plus_plus @ nat ) @ ( plus_plus @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_plus__natural_Orsp) ).
thf(713,plain,
bNF_rel_fun @ nat @ nat @ ( nat > nat ) @ ( nat > nat ) @ ( (=) @ nat ) @ ( bNF_rel_fun @ nat @ nat @ nat @ nat @ ( (=) @ nat ) @ ( (=) @ nat ) ) @ ( plus_plus @ nat ) @ ( plus_plus @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_lfinite__code_I2_J) ).
thf(498,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)],[82]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TB] :
( ! [C: TB] : ( A @ C @ C )
=> ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_fun_Orel__refl) ).
thf(604,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TB] :
( ! [C: TB] : ( A @ C @ C )
=> ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coinductive_llist @ TB,D: TA,E: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_LCons @ TB @ B @ C ) @ ( coinductive_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( coindu1486289336t_all2 @ TB @ TA @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_llist__all2__LCons__LCons) ).
thf(377,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coinductive_llist @ TB,D: TA,E: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_LCons @ TB @ B @ C ) @ ( coinductive_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( coindu1486289336t_all2 @ TB @ TA @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(39,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TA @ TA @ A @ B @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( A @ C @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_llist__all2__same) ).
thf(362,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TA @ TA @ A @ B @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( A @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(86,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Nat_Oadd__0__right) ).
thf(509,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1,conjecture,
( ( coinductive_llength @ a @ acca )
= ( coinductive_llength @ b @ acc_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( coinductive_llength @ a @ acca )
!= ( coinductive_llength @ b @ acc_a ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(208,plain,
( ( coinductive_llength @ a @ acca )
!= ( coinductive_llength @ b @ acc_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( lMirro999291890or_aux @ TA @ B @ C ) )
= ( lMirro999291890or_aux @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_lmap__lmirror__aux) ).
thf(737,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( lMirro999291890or_aux @ TA @ B @ C ) )
= ( lMirro999291890or_aux @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_lset__intros_I1_J) ).
thf(318,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(80,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
~ ( coinductive_lfinite @ TA @ ( coinductive_iterates @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_lfinite__iterates) ).
thf(494,plain,
! [TA: $tType,A: TA > TA,B: TA] :
~ ( coinductive_lfinite @ TA @ ( coinductive_iterates @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(174,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_lprefix__ltakeWhile) ).
thf(758,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)],[174]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB] :
( ! [E: TD,F: TA] :
( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rel__funI) ).
thf(609,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB] :
( ! [E: TD,F: TA] :
( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( coinductive_lmap @ TA @ TB @ B @ A )
= ( coinductive_lmap @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_llist_Omap__cong0) ).
thf(213,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( coinductive_lmap @ TA @ TB @ B @ A )
= ( coinductive_lmap @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__funE) ).
thf(621,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: coinductive_llist @ TB,E: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_LCons @ TB @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_llist_Orel__intros_I2_J) ).
thf(462,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: coinductive_llist @ TB,E: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_LCons @ TB @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',fact_110_LCons__lprefix__LCons) ).
thf(399,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)],[49]) ).
thf(202,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_llcp @ TA @ A @ B )
= ( coinductive_llength @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_llcp__lprefix1) ).
thf(827,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( coinductive_llcp @ TA @ A @ B )
= ( coinductive_llength @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(47,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_lfilter @ TA @ C @ A ) @ ( coinductive_lfilter @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_lprefix__lfilterI) ).
thf(394,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TA @ ( coinductive_lfilter @ TA @ C @ A ) @ ( coinductive_lfilter @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(105,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_lappend__assoc) ).
thf(563,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)],[105]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_llist_Oset__intros_I1_J) ).
thf(241,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,A: extended_enat,B: TA > TB,C: coinductive_llist @ TA] :
( ( coinductive_ltake @ TB @ A @ ( coinductive_lmap @ TA @ TB @ B @ C ) )
= ( coinductive_lmap @ TA @ TB @ B @ ( coinductive_ltake @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_ltake__lmap) ).
thf(658,plain,
! [TA: $tType,TB: $tType,A: extended_enat,B: TA > TB,C: coinductive_llist @ TA] :
( ( coinductive_ltake @ TB @ A @ ( coinductive_lmap @ TA @ TB @ B @ C ) )
= ( coinductive_lmap @ TA @ TB @ B @ ( coinductive_ltake @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > $o ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) ) @ ( coindu543516966_llist @ TB ) @ ( coindu543516966_llist @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_llist_Opred__transfer) ).
thf(589,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > $o ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) ) @ ( coindu543516966_llist @ TB ) @ ( coindu543516966_llist @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ TD @ TA @ ( ( TC > ( coinductive_llist @ TC ) > TD ) > ( coinductive_llist @ TC ) > TD ) @ ( ( TB > ( coinductive_llist @ TB ) > TA ) > ( coinductive_llist @ TB ) > TA ) @ A @ ( bNF_rel_fun @ ( TC > ( coinductive_llist @ TC ) > TD ) @ ( TB > ( coinductive_llist @ TB ) > TA ) @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ ( bNF_rel_fun @ TC @ TB @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ B @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( coindu1381640503_llist @ TD @ TC ) @ ( coindu1381640503_llist @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_llist_Ocase__transfer) ).
thf(680,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ TD @ TA @ ( ( TC > ( coinductive_llist @ TC ) > TD ) > ( coinductive_llist @ TC ) > TD ) @ ( ( TB > ( coinductive_llist @ TB ) > TA ) > ( coinductive_llist @ TB ) > TA ) @ A @ ( bNF_rel_fun @ ( TC > ( coinductive_llist @ TC ) > TD ) @ ( TB > ( coinductive_llist @ TB ) > TA ) @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ ( bNF_rel_fun @ TC @ TB @ ( ( coinductive_llist @ TC ) > TD ) @ ( ( coinductive_llist @ TB ) > TA ) @ B @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ TD @ TA @ ( coindu1486289336t_all2 @ TC @ TB @ B ) @ A ) ) @ ( coindu1381640503_llist @ TD @ TC ) @ ( coindu1381640503_llist @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > TB ) @ ( TA > TA ) @ ( TB > ( coinductive_llist @ TB ) ) @ ( TA > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ TB @ TA @ A @ A ) @ ( bNF_rel_fun @ TB @ TA @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ A @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_iterates @ TB ) @ ( coinductive_iterates @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_iterates__transfer) ).
thf(663,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > TB ) @ ( TA > TA ) @ ( TB > ( coinductive_llist @ TB ) ) @ ( TA > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ TB @ TA @ A @ A ) @ ( bNF_rel_fun @ TB @ TA @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ A @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_iterates @ TB ) @ ( coinductive_iterates @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(43,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( coindu543516966_llist @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A @ B )
& ( coindu543516966_llist @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_llist_Opred__inject_I2_J) ).
thf(374,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( coindu543516966_llist @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A @ B )
& ( coindu543516966_llist @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(196,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_llength @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( coinductive_llength @ TA @ B ) )
= ( ( coindu501562517eWhile @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_llength__ltakeWhile__all) ).
thf(812,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_llength @ TA @ ( coindu501562517eWhile @ TA @ A @ B ) )
= ( coinductive_llength @ TA @ B ) )
= ( ( coindu501562517eWhile @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(102,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ind__euclid) ).
thf(553,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_27_llist_Oleq__antisym) ).
thf(776,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)],[182]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',fact_23_llist_Oleq__trans) ).
thf(525,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)],[92]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_lappend @ TA @ B @ C ) )
= ( coinductive_lappend @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_lmap__lappend__distrib) ).
thf(580,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_lappend @ TA @ B @ C ) )
= ( coinductive_lappend @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',fact_159_lprefix__lappend__same) ).
thf(705,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)],[154]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',fact_123_LCons__lprefix__conv) ).
thf(409,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)],[53]) ).
thf(17,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( coindu1486289336t_all2 @ TA @ TA @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_llist_Orel__refl__strong) ).
thf(263,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( coindu1486289336t_all2 @ TA @ TA @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( coinductive_llength @ TB @ B )
= ( coinductive_llength @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_llist__all2__llengthD) ).
thf(791,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( coinductive_llength @ TB @ B )
= ( coinductive_llength @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coinductive_llist @ TA ) > TB,C: TA,D: coinductive_llist @ TA] :
( ( coindu1381640503_llist @ TB @ TA @ A @ B @ ( coinductive_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_llist_Osimps_I5_J) ).
thf(441,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coinductive_llist @ TA ) > TB,C: TA,D: coinductive_llist @ TA] :
( ( coindu1381640503_llist @ TB @ TA @ A @ B @ ( coinductive_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(194,axiom,
coindu1486289336t_all2 @ a @ b @ p @ ( lMirro999291890or_aux @ a @ acca @ xsa ) @ ( lMirro999291890or_aux @ b @ acc_a @ xs_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_local_OLNil_I1_J) ).
thf(808,plain,
coindu1486289336t_all2 @ a @ b @ p @ ( lMirro999291890or_aux @ a @ acca @ xsa ) @ ( lMirro999291890or_aux @ b @ acc_a @ xs_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TB] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TB @ ( coinductive_lmap @ TA @ TB @ C @ A ) @ ( coinductive_lmap @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lmap__lprefix) ).
thf(744,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TB] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( coinductive_lprefix @ TB @ ( coinductive_lmap @ TA @ TB @ C @ A ) @ ( coinductive_lmap @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(33,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add_Oright__cancel) ).
thf(336,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(118,axiom,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_natural_Osize_I1_J) ).
thf(600,plain,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > $o,E: TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [F: TB,G: TA] :
( ( A @ F @ G )
=> ( ( D @ F )
= ( E @ G ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lfilter @ TB @ D @ B ) @ ( coinductive_lfilter @ TA @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_llist__all2__lfilterI) ).
thf(446,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > $o,E: TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [F: TB,G: TA] :
( ( A @ F @ G )
=> ( ( D @ F )
= ( E @ G ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_lfilter @ TB @ D @ B ) @ ( coinductive_lfilter @ TA @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(122,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( ( coinductive_lfinite @ TA @ A )
& ( coinductive_lfinite @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_lfinite__lappend) ).
thf(612,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)],[122]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',fact_164_lappend__lprefixE) ).
thf(627,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)],[128]) ).
thf(65,axiom,
! [TA: $tType] :
( ( coinductive_iterates @ TA )
= ( ^ [A: TA > TA,B: TA] : ( coinductive_LCons @ TA @ B @ ( coinductive_lmap @ TA @ TA @ A @ ( coinductive_iterates @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_iterates__lmap) ).
thf(450,plain,
! [TA: $tType] :
( ( coinductive_iterates @ TA )
= ( ^ [A: TA > TA,B: TA] : ( coinductive_LCons @ TA @ B @ ( coinductive_lmap @ TA @ TA @ A @ ( coinductive_iterates @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ extended_enat @ extended_enat @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( (=) @ extended_enat ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_ltake @ TB ) @ ( coinductive_ltake @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_ltake__transfer) ).
thf(539,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ extended_enat @ extended_enat @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( (=) @ extended_enat ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coinductive_ltake @ TB ) @ ( coinductive_ltake @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(76,axiom,
! [TA: $tType,A: TA > TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_iterates @ TA @ A @ B ) @ C )
= ( coinductive_iterates @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_lappend__iterates) ).
thf(482,plain,
! [TA: $tType,A: TA > TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_iterates @ TA @ A @ B ) @ C )
= ( coinductive_iterates @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA > $o] :
( ( coindu543516966_llist @ TA @ A @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( coindu543516966_llist @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_llist_Opred__mono__strong) ).
thf(218,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA > $o] :
( ( coindu543516966_llist @ TA @ A @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( coindu543516966_llist @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( coinductive_LCons @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_lappend__code_I2_J) ).
thf(368,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)],[41]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: extended_enat] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_ltake @ TB @ D @ B ) @ ( coinductive_ltake @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_llist__all2__ltakeI) ).
thf(517,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: extended_enat] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_ltake @ TB @ D @ B ) @ ( coinductive_ltake @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Let__transfer) ).
thf(748,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(130,axiom,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coinductive_llist @ TA] :
( ( coinductive_ltake @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ ( coinductive_ltake @ TA @ A @ C ) @ ( coinductive_ltake @ TA @ B @ ( coinductive_ldrop @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_ltake__plus__conv__lappend) ).
thf(632,plain,
! [TA: $tType,A: extended_enat,B: extended_enat,C: coinductive_llist @ TA] :
( ( coinductive_ltake @ TA @ ( plus_plus @ extended_enat @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ ( coinductive_ltake @ TA @ A @ C ) @ ( coinductive_ltake @ TA @ B @ ( coinductive_ldrop @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(184,axiom,
( ( zero_zero @ nat )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_zero__natural_Orsp) ).
thf(781,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(136,axiom,
! [TA: $tType,A: TA,B: nat > TA] :
( ( case_nat @ TA @ A @ B @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_old_Onat_Osimps_I4_J) ).
thf(652,plain,
! [TA: $tType,A: TA,B: nat > TA] :
( ( case_nat @ TA @ A @ B @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(36,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_lset__induct) ).
thf(351,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(24,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu543516966_llist @ TA @ C @ A )
= ( coindu543516966_llist @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_llist_Opred__cong) ).
thf(290,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu543516966_llist @ TA @ C @ A )
= ( coindu543516966_llist @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coindu501562517eWhile @ TA @ B @ C ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) )
& ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_lset__ltakeWhileD) ).
thf(246,plain,
! [TA: $tType,A: TA,B: TA > $o,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coindu501562517eWhile @ TA @ B @ C ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) )
& ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ B )
= ( coinductive_LCons @ TB @ ( C @ B ) @ ( coindu1441602521_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_unfold__llist_Octr_I2_J) ).
thf(433,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)],[60]) ).
thf(19,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_lfilter__id__conv) ).
thf(272,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( coinductive_lset @ TA @ B ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ C @ F ) ) )
& ( coinductive_lfinite @ TA @ E )
& ! [G: TA] :
( ( member @ TA @ G @ ( coinductive_lset @ TA @ E ) )
=> ~ ( A @ G ) )
& ( A @ C )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_lfilter__eq__LConsD) ).
thf(383,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_lfilter @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
=> ? [E: coinductive_llist @ TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ C @ F ) ) )
& ( coinductive_lfinite @ TA @ E )
& ! [G: TA] :
( ( member @ TA @ G @ ( coinductive_lset @ TA @ E ) )
=> ~ ( A @ G ) )
& ( A @ C )
& ( D
= ( coinductive_lfilter @ TA @ A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coindu501562517eWhile @ TB ) @ ( coindu501562517eWhile @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_ltakeWhile__transfer) ).
thf(549,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > $o ) @ ( TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) ) @ ( coindu501562517eWhile @ TB ) @ ( coindu501562517eWhile @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(204,axiom,
coindu1486289336t_all2 @ a @ b @ p @ acca @ acc_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_local_OLNil_I2_J) ).
thf(832,plain,
coindu1486289336t_all2 @ a @ b @ p @ acca @ acc_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > TB > $o ) @ ( TA > TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) @ ( bNF_rel_fun @ TB @ TA @ ( TB > $o ) @ ( TA > $o ) @ A @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > $o ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) ) ) @ ( coindu1486289336t_all2 @ TB @ TB ) @ ( coindu1486289336t_all2 @ TA @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_llist__all2__transfer) ).
thf(684,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( TB > TB > $o ) @ ( TA > TA > $o ) @ ( ( coinductive_llist @ TB ) > ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) @ ( bNF_rel_fun @ TB @ TA @ ( TB > $o ) @ ( TA > $o ) @ A @ ( bNF_rel_fun @ TB @ TA @ $o @ $o @ A @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ ( ( coinductive_llist @ TB ) > $o ) @ ( ( coinductive_llist @ TA ) > $o ) @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ $o @ $o @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ $o ) ) ) @ ( coindu1486289336t_all2 @ TB @ TB ) @ ( coindu1486289336t_all2 @ TA @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( nat > TB ) > nat > TB ) @ ( ( nat > TA ) > nat > TA ) @ A @ ( bNF_rel_fun @ ( nat > TB ) @ ( nat > TA ) @ ( nat > TB ) @ ( nat > TA ) @ ( bNF_rel_fun @ nat @ nat @ TB @ TA @ ( (=) @ nat ) @ A ) @ ( bNF_rel_fun @ nat @ nat @ TB @ TA @ ( (=) @ nat ) @ A ) ) @ ( case_nat @ TB ) @ ( case_nat @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_case__nat__transfer) ).
thf(716,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ TB @ TA @ ( ( nat > TB ) > nat > TB ) @ ( ( nat > TA ) > nat > TA ) @ A @ ( bNF_rel_fun @ ( nat > TB ) @ ( nat > TA ) @ ( nat > TB ) @ ( nat > TA ) @ ( bNF_rel_fun @ nat @ nat @ TB @ TA @ ( (=) @ nat ) @ A ) @ ( bNF_rel_fun @ nat @ nat @ TB @ TA @ ( (=) @ nat ) @ A ) ) @ ( case_nat @ TB ) @ ( case_nat @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(191,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_llcp @ TA @ A @ A )
= ( coinductive_llength @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_llcp__same__conv__length) ).
thf(800,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_llcp @ TA @ A @ A )
= ( coinductive_llength @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(205,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > $o,E: TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [F: TB,G: TA] :
( ( A @ F @ G )
=> ( ( D @ F )
= ( E @ G ) ) )
=> ( ( coinductive_llength @ TB @ ( coindu501562517eWhile @ TB @ D @ B ) )
= ( coinductive_llength @ TA @ ( coindu501562517eWhile @ TA @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_llist__all2__llength__ltakeWhileD) ).
thf(833,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > $o,E: TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [F: TB,G: TA] :
( ( A @ F @ G )
=> ( ( D @ F )
= ( E @ G ) ) )
=> ( ( coinductive_llength @ TB @ ( coindu501562517eWhile @ TB @ D @ B ) )
= ( coinductive_llength @ TA @ ( coindu501562517eWhile @ TA @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(198,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_llcp @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ ( coinductive_lappend @ TA @ A @ C ) )
= ( plus_plus @ extended_enat @ ( coinductive_llength @ TA @ A ) @ ( coinductive_llcp @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_llcp__lappend__same) ).
thf(818,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_llcp @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ ( coinductive_lappend @ TA @ A @ C ) )
= ( plus_plus @ extended_enat @ ( coinductive_llength @ TA @ A ) @ ( coinductive_llcp @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coinductive_llist @ TB,D: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_LCons @ TB @ B @ C ) @ D )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ F ) )
& ( A @ B @ E )
& ( coindu1486289336t_all2 @ TB @ TA @ A @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_llist__all2__LCons1) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coinductive_llist @ TB,D: coinductive_llist @ TA] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coinductive_LCons @ TB @ B @ C ) @ D )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( D
= ( coinductive_LCons @ TA @ E @ F ) )
& ( A @ B @ E )
& ( coindu1486289336t_all2 @ TB @ TA @ A @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(165,axiom,
! [TA: $tType,A: extended_enat,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coinductive_ltake @ TA @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_ltake__is__lprefix) ).
thf(735,plain,
! [TA: $tType,A: extended_enat,B: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ ( coinductive_ltake @ TA @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > $o,D: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ~ ( C @ A )
=> ( ( coindu501562517eWhile @ TA @ C @ ( coinductive_lappend @ TA @ B @ D ) )
= ( coindu501562517eWhile @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_ltakeWhile__lappend1) ).
thf(210,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > $o,D: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ~ ( C @ A )
=> ( ( coindu501562517eWhile @ TA @ C @ ( coinductive_lappend @ TA @ B @ D ) )
= ( coindu501562517eWhile @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(178,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( lMirro999291890or_aux @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_lmirror__aux__inf) ).
thf(767,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ( lMirro999291890or_aux @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TB > $o,C: TA > TA > $o,D: coinductive_llist @ TB,E: coinductive_llist @ TA,F: coinductive_llist @ TB,G: coinductive_llist @ TA] :
( ! [H: TB,I: TA] :
( ( A @ H @ I )
=> ! [J: TB,K: TA] :
( ( A @ J @ K )
=> ( ( B @ H @ J )
= ( C @ I @ K ) ) ) )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ F @ G )
=> ( ( coindu1486289336t_all2 @ TB @ TB @ B @ D @ F )
= ( coindu1486289336t_all2 @ TA @ TA @ C @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_llist__all2__rsp) ).
thf(635,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TB > $o,C: TA > TA > $o,D: coinductive_llist @ TB,E: coinductive_llist @ TA,F: coinductive_llist @ TB,G: coinductive_llist @ TA] :
( ! [H: TB,I: TA] :
( ( A @ H @ I )
=> ! [J: TB,K: TA] :
( ( A @ J @ K )
=> ( ( B @ H @ J )
= ( C @ I @ K ) ) ) )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ D @ E )
=> ( ( coindu1486289336t_all2 @ TB @ TA @ A @ F @ G )
=> ( ( coindu1486289336t_all2 @ TB @ TB @ B @ D @ F )
= ( coindu1486289336t_all2 @ TA @ TA @ C @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,A: TH > TA > $o,B: TG > TB > $o,C: TF > TC > $o,D: TE > TD > $o] : ( bNF_rel_fun @ ( TH > TG ) @ ( TA > TB ) @ ( ( TF > TE ) > ( TG > TF ) > TH > TE ) @ ( ( TC > TD ) > ( TB > TC ) > TA > TD ) @ ( bNF_rel_fun @ TH @ TA @ TG @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TF > TE ) @ ( TC > TD ) @ ( ( TG > TF ) > TH > TE ) @ ( ( TB > TC ) > TA > TD ) @ ( bNF_rel_fun @ TF @ TC @ TE @ TD @ C @ D ) @ ( bNF_rel_fun @ ( TG > TF ) @ ( TB > TC ) @ ( TH > TE ) @ ( TA > TD ) @ ( bNF_rel_fun @ TG @ TB @ TF @ TC @ B @ C ) @ ( bNF_rel_fun @ TH @ TA @ TE @ TD @ A @ D ) ) ) @ ( map_fun @ TH @ TG @ TF @ TE ) @ ( map_fun @ TA @ TB @ TC @ TD ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_map__fun__parametric) ).
thf(532,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,A: TH > TA > $o,B: TG > TB > $o,C: TF > TC > $o,D: TE > TD > $o] : ( bNF_rel_fun @ ( TH > TG ) @ ( TA > TB ) @ ( ( TF > TE ) > ( TG > TF ) > TH > TE ) @ ( ( TC > TD ) > ( TB > TC ) > TA > TD ) @ ( bNF_rel_fun @ TH @ TA @ TG @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TF > TE ) @ ( TC > TD ) @ ( ( TG > TF ) > TH > TE ) @ ( ( TB > TC ) > TA > TD ) @ ( bNF_rel_fun @ TF @ TC @ TE @ TD @ C @ D ) @ ( bNF_rel_fun @ ( TG > TF ) @ ( TB > TC ) @ ( TH > TE ) @ ( TA > TD ) @ ( bNF_rel_fun @ TG @ TB @ TF @ TC @ B @ C ) @ ( bNF_rel_fun @ TH @ TA @ TE @ TD @ A @ D ) ) ) @ ( map_fun @ TH @ TG @ TF @ TE ) @ ( map_fun @ TA @ TB @ TC @ TD ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(151,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_llist_Oleq__refl) ).
thf(696,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coinductive_lprefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(55,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_lfilter__LCons) ).
thf(415,plain,
! [TA: $tType,A: TA > $o,B: TA,C: coinductive_llist @ TA] :
( ( ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TA @ B @ ( coinductive_lfilter @ TA @ A @ C ) ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_lfilter @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_lfilter @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > $o,E: TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [F: TB,G: TA] :
( ( A @ F @ G )
=> ( ( D @ F )
= ( E @ G ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coindu218763757pWhile @ TB @ D @ B ) @ ( coindu218763757pWhile @ TA @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_llist__all2__ldropWhileI) ).
thf(740,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB > $o,E: TA > $o] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [F: TB,G: TA] :
( ( A @ F @ G )
=> ( ( D @ F )
= ( E @ G ) ) )
=> ( coindu1486289336t_all2 @ TB @ TA @ A @ ( coindu218763757pWhile @ TB @ D @ B ) @ ( coindu218763757pWhile @ TA @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',fact_122_Le__LCons) ).
thf(464,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)],[70]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_llist_Oset__intros_I2_J) ).
thf(332,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coinductive_llist @ TB] :
( ( ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ D )
= ( coinductive_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1441602521_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_unfold__llist__eq__LCons) ).
thf(459,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)],[68]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ extended_enat @ extended_enat @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ extended_enat ) @ ( coinductive_llength @ TB ) @ ( coinductive_llength @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_llength__transfer) ).
thf(822,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( bNF_rel_fun @ ( coinductive_llist @ TB ) @ ( coinductive_llist @ TA ) @ extended_enat @ extended_enat @ ( coindu1486289336t_all2 @ TB @ TA @ A ) @ ( (=) @ extended_enat ) @ ( coinductive_llength @ TB ) @ ( coinductive_llength @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(83,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( lMirro999291890or_aux @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ ( lMirro999291890or_aux @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_lmirror__aux__acc) ).
thf(501,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( lMirro999291890or_aux @ TA @ ( coinductive_lappend @ TA @ A @ B ) @ C )
= ( coinductive_lappend @ TA @ ( lMirro999291890or_aux @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(21,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu218763757pWhile @ TA @ C @ A )
= ( coindu218763757pWhile @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_ldropWhile__cong) ).
thf(277,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( coindu218763757pWhile @ TA @ C @ A )
= ( coindu218763757pWhile @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( coinductive_llist @ TD ) > ( coinductive_llist @ TC ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( coinductive_llist @ TD ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ ( coindu1486289336t_all2 @ TD @ TA @ A ) @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( coinductive_lmap @ TD @ TC ) @ ( coinductive_lmap @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_lmap__transfer) ).
thf(691,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ ( ( coinductive_llist @ TD ) > ( coinductive_llist @ TC ) ) @ ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TB ) ) @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ ( bNF_rel_fun @ ( coinductive_llist @ TD ) @ ( coinductive_llist @ TA ) @ ( coinductive_llist @ TC ) @ ( coinductive_llist @ TB ) @ ( coindu1486289336t_all2 @ TD @ TA @ A ) @ ( coindu1486289336t_all2 @ TC @ TB @ B ) ) @ ( coinductive_lmap @ TD @ TC ) @ ( coinductive_lmap @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( member @ TB @ D @ ( coinductive_lset @ TB @ B ) )
=> ? [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ C ) )
& ( A @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_llist__all2__lsetD1) ).
thf(254,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coinductive_llist @ TB,C: coinductive_llist @ TA,D: TB] :
( ( coindu1486289336t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( member @ TB @ D @ ( coinductive_lset @ TB @ B ) )
=> ? [E: TA] :
( ( member @ TA @ E @ ( coinductive_lset @ TA @ C ) )
& ( A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(192,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( ( coinductive_llength @ TA @ A )
= ( coinductive_llength @ TA @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_lprefix__llength__eq__imp__eq) ).
thf(803,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lprefix @ TA @ A @ B )
=> ( ( ( coinductive_llength @ TA @ A )
= ( coinductive_llength @ TA @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(72,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_add__eq__0__iff__both__eq__0) ).
thf(469,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(173,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add__is__0) ).
thf(755,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(79,axiom,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_lfilter @ TA @ A @ B ) )
= ( coinductive_lfilter @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_lfilter__idem) ).
thf(491,plain,
! [TA: $tType,A: TA > $o,B: coinductive_llist @ TA] :
( ( coinductive_lfilter @ TA @ A @ ( coinductive_lfilter @ TA @ A @ B ) )
= ( coinductive_lfilter @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_lset__intros_I2_J) ).
thf(222,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(81,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_lfinite__LConsI) ).
thf(496,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)],[81]) ).
thf(155,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_llast @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) )
= ( coinductive_llast @ TA @ ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_llast__lappend__LCons) ).
thf(708,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)],[155]) ).
thf(847,plain,
$false,
inference(cvc4,[status(thm)],[645,809,365,760,479,249,408,762,655,269,677,797,472,698,782,841,301,320,436,257,724,785,504,838,702,357,559,325,284,770,591,623,485,514,806,821,348,574,602,453,774,396,243,428,507,527,380,512,661,546,534,714,334,746,598,561,297,815,729,693,630,275,788,625,665,682,551,456,229,566,583,522,830,285,224,519,650,615,593,420,488,339,753,642,686,476,647,721,569,779,371,237,360,311,541,765,674,530,718,794,586,412,750,618,425,824,689,444,423,402,732,772,577,711,572,466,236,713,498,604,377,362,509,208,737,318,494,758,609,213,621,462,399,827,394,563,241,658,589,680,663,374,812,553,776,525,580,705,409,263,791,441,808,744,336,600,446,612,627,450,539,482,218,368,517,748,632,781,652,351,290,246,433,272,383,549,832,684,716,800,833,818,405,735,210,767,635,532,696,415,740,464,332,459,822,501,277,691,254,803,469,755,491,222,496,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : DAT197^1 : TPTP v8.1.2. Released v7.0.0.
% 0.14/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 6 11:30:39 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/1.11 % [INFO] Parsing done (256ms).
% 1.82/1.12 % [INFO] Running in sequential loop mode.
% 2.58/1.33 % [INFO] eprover registered as external prover.
% 2.58/1.33 % [INFO] cvc4 registered as external prover.
% 2.58/1.33 % [INFO] Scanning for conjecture ...
% 2.73/1.43 % [INFO] Found a conjecture and 285 axioms. Running axiom selection ...
% 3.14/1.52 % [INFO] Axiom selection finished. Selected 205 axioms (removed 80 axioms).
% 3.80/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 3.80/1.75 % [INFO] Type checking passed.
% 3.80/1.75 % [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 ...
% 149.63/123.56 % External prover 'cvc4' found a proof!
% 149.63/123.56 % [INFO] Killing All external provers ...
% 149.63/123.56 % Time passed: 123041ms (effective reasoning time: 122442ms)
% 149.63/123.56 % 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)>
% 149.63/123.57 % Axioms used in derivation (205): fact_13_llist_Oleq__refl, fact_213_ldropWhile__cong, fact_104_llist_Octr__transfer_I2_J, fact_192_Nat_Oadd__0__right, fact_74_llist__all__transfer, fact_117_lmirror__aux__simps_I2_J, fact_247_lappend__ltake__ldrop, fact_1_local_OLNil_I3_J, fact_8_llength__ltakeWhile__all, fact_220_lfilter__cong, tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_1, fact_147_ldrop__ldrop, fact_143_natural_Osize_I3_J, fact_60_If__transfer, fact_94_llist__all2__lfilterI, fact_23_llist_Oleq__trans, fact_221_lfilter__id__conv, fact_12_lprefix__refl, fact_159_lprefix__lappend__same, fact_208_ltake__transfer, fact_243_lfinite__ldropWhile, fact_251_split__llist__first, fact_126_llist__all2__LCons2, fact_205_case__nat__transfer, fact_5_llcp__same__conv__length, fact_35_llist_Orel__refl, fact_202_rec__nat__transfer, fact_253_ltake__plus__conv__lappend, fact_142_llist__all2__lappend1D_I2_J, fact_185_lappend__iterates, fact_70_ldropWhile__transfer, fact_237_lset__induct, fact_130_llist__all2__ldropI, fact_134_iterates_Ocode, fact_129_lmap__eq__LCons__conv, fact_250_llist__all2__lappend1D_I1_J, fact_51_rel__fun__mono_H, fact_215_llist_Opred__cong, fact_76_lfilter__idem, fact_69_fun_Orel__transfer, fact_138_iterates__lmap, fact_59_rel__fun__def__butlast, fact_180_add_Oright__cancel, fact_236_lset__cases, fact_37_llist_Omap__transfer, fact_101_fun_Orel__eq, fact_163_lprefix__lappend, fact_19_lmap__lprefix, fact_56_Coinductive__List_Ofinite__lprefix__def, fact_111_llist__all2__LCons__LCons, fact_43_rel__funE, fact_48_apply__rsp_H, fact_218_ltakeWhile__cong, fact_50_rel__fun__mono, fact_160_lfilter__lappend__lfinite, fact_58_Let__transfer, fact_188_lappend__eq__lappend__conv, fact_140_natural_Osize_I1_J, fact_197_ind__euclid, fact_219_ltakeWhile__all, fact_49_rel__funD2, fact_252_split__llist, fact_110_LCons__lprefix__LCons, fact_53_llist_Orel__transfer, fact_217_lset__ltakeWhileD, fact_175_lappend__assoc, fact_249_ltake__ldrop, fact_20_lmap__transfer, fact_135_unfold__llist_Octr_I2_J, fact_187_llist__all2__lappendI, fact_52_llist__all2__transfer, fact_158_lfinite__lappend, fact_17_llcp__lprefix2, fact_227_llist_Orel__cong, fact_112_lfinite__code_I2_J, fact_30_lprefix__down__linear, fact_179_add_Oleft__cancel, fact_29_llist__all2__lfiniteD, fact_131_llist_Osimps_I5_J, fact_189_lfilter__eq__lappend__lfiniteD, fact_106_ldropWhile__eq__ldrop, fact_100_fun_Orel__refl, fact_238_lset__induct_H, fact_98_llist__all2__ldropWhileI, fact_233_lset__intros_I1_J, fact_33_lmap__lmirror__aux, fact_167_lprefix__lappend__sameI, fact_226_llist_Orel__mono__strong, fact_157_llength__lappend, fact_25_lprefix__antisym, fact_72_lfilter__transfer, fact_107_zero__natural_Orsp, fact_42_let__rsp, fact_127_lfinite__LConsI, fact_210_ltake__is__lprefix, fact_63_unfold__llist__transfer, fact_62_llist_Ocorec__transfer, fact_55_lfinite__transfer, fact_31_not__lfinite__lprefix__conv__eq, fact_18_llcp__commute, fact_27_llist_Oleq__antisym, fact_191_add__is__0, fact_105_LCons__transfer, fact_133_lfilter__LCons__seek, fact_153_double__zero, fact_24_llist__all2__mono, fact_223_llist_Omap__cong0, fact_39_Coinductive__List_Olprefix__nitpick__simps, fact_204_old_Onat_Osimps_I6_J, fact_241_llist_Oset__induct, fact_240_llist_Oset__cases, fact_3_local_OLNil_I1_J, fact_122_Le__LCons, fact_7_lprefix__llength__eq__imp__eq, fact_246_in__lset__lappend__iff, fact_128_llist_Osimps_I13_J, fact_73_llist_Opred__transfer, fact_6_llength__lmap, fact_26_lprefix__lfiniteD, fact_11_llength__transfer, fact_203_llast__LCons2, fact_225_llist_Orel__refl__strong, fact_97_lfinite__lfilterI, fact_231_llist__all2__ltakeI, fact_245_ltakeWhile__lappend1, fact_165_lprefix__lappendD, fact_216_llist_Opred__mono__strong, fact_222_llist_Oinj__map__strong, fact_172_lappend__inf, fact_170_add_Ogroup__left__neutral, fact_132_lfilter__LCons__found, fact_38_rel__funI, fact_186_lmirror__aux__acc, fact_68_lmap__iterates, fact_124_llist_Orel__intros_I2_J, fact_194_plus__natural_Orsp, fact_28_lprefix__ltakeWhile, fact_9_llist__all2__llength__ltakeWhileD, fact_54_ltakeWhile__transfer, fact_36_llist__all2__lmirror__aux, fact_123_LCons__lprefix__conv, fact_108_llist_Oinject, fact_211_llist__all2__same, fact_190_lappend__transfer, fact_242_lset__lmirror__aux, fact_201_llast__lappend__LCons, fact_171_add__eq__0__iff__both__eq__0, fact_119_llist_Opred__inject_I2_J, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_174_lmap__lappend__distrib, fact_0_local_OLNil_I2_J, fact_228_llist__all2__lsetD2, fact_193_natural_Osimps_I4_J, fact_2_calculation, fact_166_lprefix__conv__lappend, fact_156_lappend__code_I2_J, fact_234_llist_Oset__intros_I2_J, fact_139_ldrop__transfer, fact_65_case__llist__transfer, fact_198_add__0__iff, fact_21_lprefix__trans, fact_162_llcp__lappend__same, fact_109_ldrop__0, fact_4_llist__all2__llengthD, fact_102_map__fun__apply, fact_209_lfilter__eq__LConsD, fact_118_unfold__llist__eq__LCons, fact_230_llist__all2__reflI, fact_66_llist_Ocase__transfer, fact_164_lappend__lprefixE, fact_232_lset__intros_I2_J, fact_116_ldrop__lmap, fact_61_llist__corec__transfer, fact_34_llist_Orel__eq, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_206_natural_Osimps_I6_J, fact_212_ltake__lmap, fact_32_lmirror__aux__inf, fact_214_in__lset__ldropWhileD, fact_22_llist__all2__rsp, fact_229_llist__all2__lsetD1, fact_152_double__zero__sym, fact_224_llist_Omap__cong, fact_195_add__eq__self__zero, fact_15_lfinite__lmirror__aux, fact_10_llength__code, fact_136_llist_Ocorec_I2_J, fact_125_llist__all2__LCons1, fact_207_old_Onat_Osimps_I4_J, fact_93_lprefix__lfilterI, fact_16_llcp__lprefix1, fact_67_lfinite__iterates, fact_115_ldropWhile__LCons, fact_64_iterates__transfer, fact_137_iterates__equality, fact_114_lfilter__LCons, fact_244_lfinite__ltakeWhile, fact_235_llist_Oset__intros_I1_J, fact_41_rel__funD, fact_71_map__fun__parametric, fact_14_lfinite__lmap, fact_239_in__lset__ldropD, fact_113_lfinite__LCons, fact_161_lappend__ltakeWhile__ldropWhile, fact_196_plus__nat_Oadd__0
% 149.63/123.57 % No. of inferences in proof: 414
% 149.63/123.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 123041 ms resp. 122442 ms w/o parsing
% 150.38/123.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 150.38/123.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------