TSTP Solution File: DAT180^1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT180^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:41 EDT 2024
% Result : Theorem 14.16s 4.12s
% Output : Refutation 14.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 240
% Syntax : Number of formulae : 439 ( 195 unt; 43 typ; 0 def)
% Number of atoms : 1223 ( 462 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 5192 ( 108 ~; 20 |; 70 &;4666 @)
% ( 0 <=>; 328 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 7 con; 0-5 aty)
% Number of variables : 1199 ( 10 ^1120 !; 32 ?;1199 :)
% ( 37 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(ab_group_add_type,type,
ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_monoid_diff_type,type,
comm_monoid_diff:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordered_ab_group_add_type,type,
ordered_ab_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(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere516151231imp_le_type,type,
ordere516151231imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu328551480prefix_type,type,
coindu328551480prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lappend_type,type,
coinductive_lappend:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_LCons_type,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_LNil_type,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(coindu1478340336prefix_type,type,
coindu1478340336prefix:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lsublist_type,type,
coinductive_lsublist:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( set @ nat ) > ( coinductive_llist @ TA ) ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : 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(lList2435255213lllsts_type,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2236698231inlsts_type,type,
lList2236698231inlsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21916056377ts_rec_type,type,
lList21916056377ts_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coinductive_llist @ TA ) > TB > TB ) > ( coinductive_llist @ TA ) > TB ) ).
thf(lList22096119349pslsts_type,type,
lList22096119349pslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21612149805nflsts_type,type,
lList21612149805nflsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2370560421utlast_type,type,
lList2370560421utlast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList2508575361_ldrop_type,type,
lList2508575361_ldrop:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat > ( coinductive_llist @ TA ) ) ).
thf(lList2170638824_llast_type,type,
lList2170638824_llast:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA ) ).
thf(lList21232602520length_type,type,
lList21232602520length:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat ) ).
thf(lList2281150353e_lrev_type,type,
lList2281150353e_lrev:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList22119844313_ltake_type,type,
lList22119844313_ltake:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > nat > ( coinductive_llist @ TA ) ) ).
thf(lList21148268032oslsts_type,type,
lList21148268032oslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(nat_triangle_type,type,
nat_triangle: nat > nat ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_type,type,
a2: set @ a ).
thf(i_type,type,
i: nat ).
thf(t_type,type,
t: coinductive_llist @ a ).
thf(185,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
=> ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_lapp__inv2T) ).
thf(809,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
=> ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(110,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__diff__add) ).
thf(555,plain,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_old_Onat_Oinject) ).
thf(333,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(131,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_notinf__fin) ).
thf(628,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(78,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J) ).
thf(449,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( coindu328551480prefix @ TA @ ( coinductive_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(22,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ! [C: coinductive_llist @ TA] :
( ! [D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_llist__less__induct) ).
thf(247,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA] :
( ! [C: coinductive_llist @ TA] :
( ! [D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(75,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_n__not__Suc__n) ).
thf(440,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,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_72_ind__euclid) ).
thf(269,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)],[27]) ).
thf(62,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_diff__add__zero) ).
thf(385,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_llist_Odistinct_I1_J) ).
thf(533,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(148,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_alllsts_OLCons__all) ).
thf(670,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(34,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_old_Onat_Oexhaust) ).
thf(301,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(113,axiom,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_dependent__nat__choice) ).
thf(565,plain,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(127,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_UNIV__I) ).
thf(619,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(106,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Nat_Oadd__0__right) ).
thf(542,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( suc @ ( zero_zero @ nat ) ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_add__is__1) ).
thf(460,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( suc @ ( zero_zero @ nat ) ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(196,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( coinductive_LNil @ TA )
= ( lList2281150353e_lrev @ TA @ A ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_LNil__is__lrev__conv) ).
thf(853,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( coinductive_LNil @ TA )
= ( lList2281150353e_lrev @ TA @ A ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_nat__add__left__cancel__le) ).
thf(421,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(42,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ C @ B ) )
= ( minus_minus @ nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_diff__cancel2) ).
thf(325,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ C @ B ) )
= ( minus_minus @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [A: nat > $o] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_exists__least__lemma) ).
thf(289,plain,
! [A: nat > $o] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( minus_minus @ nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Nat_Odiff__cancel) ).
thf(316,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( minus_minus @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(86,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_lappend__snocL1__conv__LCons2) ).
thf(475,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ) @ C )
= ( coinductive_lappend @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(179,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= C ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( lList2170638824_llast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_LList2__Mirabelle__hamjzmohle_Ollast__LCons) ).
thf(789,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= C ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2170638824_llast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( lList2170638824_llast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_lstrict__prefix__code_I2_J) ).
thf(376,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(129,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_alllsts_Osimps) ).
thf(623,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_diff__add__eq) ).
thf(485,plain,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__diff__left) ).
thf(348,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(184,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_inflstsE) ).
thf(806,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(8,axiom,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(211,plain,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_old_Onat_Oinducts) ).
thf(253,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(173,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_lrev__is__LNil__conv) ).
thf(766,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(12,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_add__le__cancel__right) ).
thf(221,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(175,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_finlsts__rev__cases) ).
thf(774,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_lappend @ TA @ D @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(20,axiom,
semiri456707255roduct @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(243,plain,
semiri456707255roduct @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(194,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_inflstsI2) ).
thf(849,plain,
! [TA: $tType,A: TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_top__conj_I1_J) ).
thf(527,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(36,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_nat_Oinject) ).
thf(307,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(16,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_add__le__same__cancel2) ).
thf(233,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(96,axiom,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_lappend__LNil__LNil) ).
thf(512,plain,
! [TA: $tType] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(145,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( coinductive_lappend @ TA @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2508575361_ldrop @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_ltake__ldrop__id) ).
thf(661,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( coinductive_lappend @ TA @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2508575361_ldrop @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(4,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_double__zero__sym) ).
thf(201,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(171,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_lapp__fin__infT) ).
thf(761,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(61,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_Zero__not__Suc) ).
thf(381,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(181,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( lList22119844313_ltake @ TA @ A @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_llength__take) ).
thf(798,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( lList22119844313_ltake @ TA @ A @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(188,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( A
!= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_poslsts__UNIV) ).
thf(820,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( A
!= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(72,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_zero__induct__lemma) ).
thf(424,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_diff__commute) ).
thf(275,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(193,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_infsubsetall) ).
thf(847,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(54,axiom,
! [TA: $tType,A: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_LList2__Mirabelle__hamjzmohle_Oltake__LNil) ).
thf(361,plain,
! [TA: $tType,A: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(118,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( lList2508575361_ldrop @ TA @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_LList2__Mirabelle__hamjzmohle_Oldrop_Osimps_I1_J) ).
thf(583,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( lList2508575361_ldrop @ TA @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(92,axiom,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_lbutlast__LNil) ).
thf(493,plain,
! [TA: $tType] :
( ( lList2370560421utlast @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(152,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_app__invT) ).
thf(682,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(13,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_zero__le__double__add__iff__zero__le__single__add) ).
thf(224,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(116,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le0) ).
thf(578,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(155,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_lapp__allT__iff) ).
thf(697,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(140,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_alllstsE) ).
thf(650,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(125,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_UNIV__witness) ).
thf(615,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(63,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_top__conj_I2_J) ).
thf(388,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(94,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_diff__Suc__Suc) ).
thf(499,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_lstrict__prefix__code_I3_J) ).
thf(488,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(47,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J) ).
thf(339,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(135,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ldropT) ).
thf(637,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2508575361_ldrop @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(151,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ A ) @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_lrev__LCons) ).
thf(679,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ A ) @ ( coinductive_LCons @ TA @ C @ ( coinductive_LNil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(9,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_double__add__le__zero__iff__single__add__le__zero) ).
thf(212,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__add__left__cancel) ).
thf(328,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(85,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_nat_Odistinct_I1_J) ).
thf(471,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(139,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_lapp__fin__fin__iff) ).
thf(647,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(157,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_finsubsetall) ).
thf(701,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(97,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_top1I) ).
thf(515,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(142,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( coinductive_lappend @ TA @ A @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_lapp__inf) ).
thf(654,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( coinductive_lappend @ TA @ A @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(81,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_30_add__is__0) ).
thf(457,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)],[81]) ).
thf(18,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_le__add__same__cancel1) ).
thf(237,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le__zero__eq) ).
thf(244,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [TA: $tType] :
( ( lList21232602520length @ TA @ ( coinductive_LNil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_LList2__Mirabelle__hamjzmohle_Ollength__LNil) ).
thf(266,plain,
! [TA: $tType] :
( ( lList21232602520length @ TA @ ( coinductive_LNil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(133,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] : ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ltake__fin) ).
thf(633,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] : ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(143,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_finite__lemma) ).
thf(657,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(111,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_old_Onat_Odistinct_I2_J) ).
thf(558,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(102,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_not0__implies__Suc) ).
thf(530,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(119,axiom,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inflsts__def) ).
thf(586,plain,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(162,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_inflstsI) ).
thf(718,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(33,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_diff__0__eq__0) ).
thf(298,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(68,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_diff__self__eq__0) ).
thf(412,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(167,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_lappT) ).
thf(750,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(197,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2281150353e_lrev @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_lrevT) ).
thf(856,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList2281150353e_lrev @ TA @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(154,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ C ) ) )
& ( member @ TA @ F @ C ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_alllsts_Ocoinduct) ).
thf(689,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ C ) ) )
& ( member @ TA @ F @ C ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_add__Suc) ).
thf(444,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(166,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ D )
=> ( ( member @ TA @ E @ B )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_finlsts_Oinducts) ).
thf(733,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ D )
=> ( ( member @ TA @ E @ B )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(112,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_58_lappend__assoc) ).
thf(562,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)],[112]) ).
thf(191,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_fin__inf__cases) ).
thf(843,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(31,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__0__iff) ).
thf(286,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(161,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_alllsts_Ocases) ).
thf(711,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(5,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ 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_59_add__eq__0__iff__both__eq__0) ).
thf(204,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ 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)],[5]) ).
thf(107,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_plus__nat_Oadd__0) ).
thf(545,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(137,axiom,
! [TA: $tType,A: nat] :
( ( lList2508575361_ldrop @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_LList2__Mirabelle__hamjzmohle_Oldrop__LNil) ).
thf(641,plain,
! [TA: $tType,A: nat] :
( ( lList2508575361_ldrop @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(64,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Zero__neq__Suc) ).
thf(391,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_Suc__le__mono) ).
thf(572,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(38,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_top__set__def) ).
thf(313,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_DiffI) ).
thf(787,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_nat_OdiscI) ).
thf(466,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(17,axiom,
comm_monoid_diff @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(236,plain,
comm_monoid_diff @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(183,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_lapp__fin__fin__lemma) ).
thf(804,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2236698231inlsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(149,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Diff__iff) ).
thf(672,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TB,D: TA > ( coinductive_llist @ TA ) > TB > TB,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21916056377ts_rec @ TB @ TA @ C @ D @ ( coinductive_LCons @ TA @ E @ A ) )
= ( D @ E @ A @ ( lList21916056377ts_rec @ TB @ TA @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_finlsts__rec__LCons) ).
thf(784,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TB,D: TA > ( coinductive_llist @ TA ) > TB > TB,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21916056377ts_rec @ TB @ TA @ C @ D @ ( coinductive_LCons @ TA @ E @ A ) )
= ( D @ E @ A @ ( lList21916056377ts_rec @ TB @ TA @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(15,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_le__add__same__cancel2) ).
thf(230,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_add__Suc__right) ).
thf(451,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(73,axiom,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_lrev__LNil) ).
thf(434,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(132,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_alllsts_OLNil__all) ).
thf(631,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(170,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( coinductive_lappend @ TA @ A @ C )
= ( coinductive_lappend @ TA @ A @ D ) )
= ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_same__lappend__eq) ).
thf(758,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( coinductive_lappend @ TA @ A @ C )
= ( coinductive_lappend @ TA @ A @ D ) )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(123,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat,C: nat] :
( ( lList22119844313_ltake @ TA @ ( lList2508575361_ldrop @ TA @ A @ B ) @ C )
= ( lList2508575361_ldrop @ TA @ ( lList22119844313_ltake @ TA @ A @ ( plus_plus @ nat @ C @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_LList2__Mirabelle__hamjzmohle_Oltake__ldrop) ).
thf(609,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat,C: nat] :
( ( lList22119844313_ltake @ TA @ ( lList2508575361_ldrop @ TA @ A @ B ) @ C )
= ( lList2508575361_ldrop @ TA @ ( lList22119844313_ltake @ TA @ A @ ( plus_plus @ nat @ C @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(121,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
=> ( C @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_finlsts__induct) ).
thf(594,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
=> ( C @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(165,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_finlsts_Ocases) ).
thf(726,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(128,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_finlsts_OLCons__fin) ).
thf(621,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(156,axiom,
member @ ( coinductive_llist @ a ) @ t @ ( lList2236698231inlsts @ a @ a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(700,plain,
member @ ( coinductive_llist @ a ) @ t @ ( lList2236698231inlsts @ a @ a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_add__le__cancel__left) ).
thf(240,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(130,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finlsts_OLNil__fin) ).
thf(626,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(174,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ D ) )
=> ( ( member @ TA @ C @ B )
=> ~ ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_fpslsts__cases) ).
thf(769,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ D ) )
=> ( ( member @ TA @ C @ B )
=> ~ ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(49,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( A
!= ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_llistE) ).
thf(345,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( A
!= ( coinductive_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(198,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(858,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(56,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_lappend__code_I1_J) ).
thf(367,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_diffs0__imp__equal) ).
thf(552,plain,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_add__Suc__shift) ).
thf(521,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ C @ ( suc @ ( minus_minus @ nat @ B @ A ) ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ C @ A ) @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_diff__Suc__diff__eq1) ).
thf(278,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ C @ ( suc @ ( minus_minus @ nat @ B @ A ) ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ C @ A ) @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(195,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_alllsts__UNIV) ).
thf(851,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(120,axiom,
! [TA: $tType,A: set @ nat,B: TA] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( coinductive_lsublist @ TA @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) @ A )
= ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( coinductive_lsublist @ TA @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) @ A )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_lsublist__singleton) ).
thf(589,plain,
! [TA: $tType,A: set @ nat,B: TA] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( coinductive_lsublist @ TA @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) @ A )
= ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( coinductive_lsublist @ TA @ ( coinductive_LCons @ TA @ B @ ( coinductive_LNil @ TA ) ) @ A )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(180,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_fpslsts__iff) ).
thf(795,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(108,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Suc__neq__Zero) ).
thf(548,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(186,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LNil @ TA ) ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LCons @ TA @ C @ ( lList2370560421utlast @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_lbutlast__LCons) ).
thf(812,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( ( A
= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LNil @ TA ) ) )
& ( ( A
!= ( coinductive_LNil @ TA ) )
=> ( ( lList2370560421utlast @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( coinductive_LCons @ TA @ C @ ( lList2370560421utlast @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(126,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_lapp__all__invT) ).
thf(617,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(48,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(342,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(189,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_lrev__induct) ).
thf(823,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_lappend @ TA @ E @ ( coinductive_LCons @ TA @ D @ ( coinductive_LNil @ TA ) ) ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(91,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_lappend__eq__LNil__iff) ).
thf(490,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TA ) > TB,B: TB,C: TA > ( coinductive_llist @ TA ) > TB > TB,D: coinductive_llist @ TA,E: set @ TA,F: TA] :
( ( A
= ( lList21916056377ts_rec @ TB @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ E ) )
=> ( ( A @ ( coinductive_LCons @ TA @ F @ D ) )
= ( C @ F @ D @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_finlsts__rec__LCons__def) ).
thf(675,plain,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TA ) > TB,B: TB,C: TA > ( coinductive_llist @ TA ) > TB > TB,D: coinductive_llist @ TA,E: set @ TA,F: TA] :
( ( A
= ( lList21916056377ts_rec @ TB @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ E ) )
=> ( ( A @ ( coinductive_LCons @ TA @ F @ D ) )
= ( C @ F @ D @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ A @ ( plus_plus @ nat @ A @ B ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_diff__add__0) ).
thf(580,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ A @ ( plus_plus @ nat @ A @ B ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(67,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_lappend__is__LNil__conv) ).
thf(409,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lappend @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(159,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_DiffE) ).
thf(705,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TB ) > TA,B: TA,C: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( A
= ( lList21916056377ts_rec @ TA @ TB @ B @ C ) )
=> ( ( A @ ( coinductive_LNil @ TB ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_finlsts__rec__LNil__def) ).
thf(282,plain,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TB ) > TA,B: TA,C: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( A
= ( lList21916056377ts_rec @ TA @ TB @ B @ C ) )
=> ( ( A @ ( coinductive_LNil @ TB ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,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_92_llist_Oinject) ).
thf(263,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)],[25]) ).
thf(37,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1478340336prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_lstrict__prefix__code_I4_J) ).
thf(310,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( coindu1478340336prefix @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1478340336prefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1,conjecture,
member @ ( coinductive_llist @ a ) @ ( lList2508575361_ldrop @ a @ t @ i ) @ ( lList2236698231inlsts @ a @ a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( member @ ( coinductive_llist @ a ) @ ( lList2508575361_ldrop @ a @ t @ i ) @ ( lList2236698231inlsts @ a @ a2 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(199,plain,
~ ( member @ ( coinductive_llist @ a ) @ ( lList2508575361_ldrop @ a @ t @ i ) @ ( lList2236698231inlsts @ a @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
( ( nat_triangle @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_triangle__0) ).
thf(331,plain,
( ( nat_triangle @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_diff__add__inverse2) ).
thf(370,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(95,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_nat__induct) ).
thf(502,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(190,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_lapp__infT) ).
thf(840,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ B ) @ ( lList21612149805nflsts @ TA @ C ) )
= ( ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList21612149805nflsts @ TA @ C ) ) )
| ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(83,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_LNil__eq__lappend__iff) ).
thf(463,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(46,axiom,
! [A: nat] :
( ( nat_triangle @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_triangle @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_triangle__Suc) ).
thf(336,plain,
! [A: nat] :
( ( nat_triangle @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_triangle @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(158,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_infT__simp) ).
thf(703,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(124,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_UNIV__eq__I) ).
thf(612,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(192,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_fin__finite) ).
thf(845,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( suc @ C ) )
= ( coinductive_LCons @ TA @ A @ ( lList22119844313_ltake @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_ltake__LCons__Suc) ).
thf(250,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: nat] :
( ( lList22119844313_ltake @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ ( suc @ C ) )
= ( coinductive_LCons @ TA @ A @ ( lList22119844313_ltake @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_diff__add__inverse) ).
thf(539,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(88,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_LNil__is__lappend__conv) ).
thf(482,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_LNil @ TA )
= ( coinductive_lappend @ TA @ A @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
& ( B
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ A @ B ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_one__is__add) ).
thf(524,plain,
! [A: nat,B: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ A @ B ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(11,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_zero__diff) ).
thf(218,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Suc__inject) ).
thf(517,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(40,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_lappend__LNil2) ).
thf(319,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ A @ ( coinductive_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__add__right__cancel) ).
thf(418,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(176,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( member @ TA @ A @ C )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_LConsE) ).
thf(781,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( member @ TA @ A @ C )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(141,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_DiffD1) ).
thf(652,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(51,axiom,
! [TA: $tType,A: set @ nat] :
( ( coinductive_lsublist @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_lsublist__LNil) ).
thf(351,plain,
! [TA: $tType,A: set @ nat] :
( ( coinductive_lsublist @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( lList21916056377ts_rec @ TA @ TB @ A @ B @ ( coinductive_LNil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_finlsts__rec__LNil) ).
thf(378,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( lList21916056377ts_rec @ TA @ TB @ A @ B @ ( coinductive_LNil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(6,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_double__zero) ).
thf(207,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(147,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_top__empty__eq) ).
thf(667,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(87,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat] : ( A @ ( zero_zero @ nat ) @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_diff__induct) ).
thf(478,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat] : ( A @ ( zero_zero @ nat ) @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(172,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( suc @ ( lList21232602520length @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_LList2__Mirabelle__hamjzmohle_Ollength__LCons) ).
thf(763,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21232602520length @ TA @ ( coinductive_LCons @ TA @ C @ A ) )
= ( suc @ ( lList21232602520length @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(153,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_inflsts__cases) ).
thf(684,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(104,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Diff__idemp) ).
thf(536,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(168,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ B ) @ ( lList2281150353e_lrev @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_lrev__lappend) ).
thf(752,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( coinductive_lappend @ TA @ A @ B ) )
= ( coinductive_lappend @ TA @ ( lList2281150353e_lrev @ TA @ B ) @ ( lList2281150353e_lrev @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(77,axiom,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_lstrict__prefix__code_I1_J) ).
thf(447,plain,
! [TA: $tType] :
~ ( coindu1478340336prefix @ TA @ ( coinductive_LNil @ TA ) @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(187,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_take__fin) ).
thf(818,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: nat] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( lList22119844313_ltake @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(66,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_list__decode_Ocases) ).
thf(405,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(58,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_neq__LNil__conv) ).
thf(373,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(35,axiom,
( ( plus_plus @ nat )
= ( ^ [A: nat,B: nat] :
( if @ nat
@ ( A
= ( zero_zero @ nat ) )
@ B
@ ( suc @ ( plus_plus @ nat @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__eq__if) ).
thf(305,plain,
( ( plus_plus @ nat )
= ( ^ [A: nat,B: nat] :
( if @ nat
@ ( A
= ( zero_zero @ nat ) )
@ B
@ ( suc @ ( plus_plus @ nat @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(7,axiom,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(210,plain,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(182,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( lList2281150353e_lrev @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_lrev__lrev__ident) ).
thf(801,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( lList2281150353e_lrev @ TA @ ( lList2281150353e_lrev @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_diff__diff__cancel) ).
thf(358,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_add__eq__self__zero) ).
thf(437,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(664,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_DiffD2) ).
thf(635,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(163,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_notfin__inf) ).
thf(720,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(69,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ D ) )
& ( coindu328551480prefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J) ).
thf(415,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coindu328551480prefix @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ B @ D ) )
& ( coindu328551480prefix @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(65,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_zero__induct) ).
thf(395,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_diff__is__0__eq_H) ).
thf(575,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(138,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( lList2281150353e_lrev @ TA @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_lrev__is__lrev__conv) ).
thf(644,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( lList2281150353e_lrev @ TA @ A )
= ( lList2281150353e_lrev @ TA @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(164,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_poslsts__iff) ).
thf(723,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(3,axiom,
canoni770627133id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(200,plain,
canoni770627133id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(122,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_lappfin__finT) ).
thf(607,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_lappend @ TA @ A @ C ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(14,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_diff__ge__0__iff__ge) ).
thf(227,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(41,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_minus__nat_Odiff__0) ).
thf(322,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(52,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_old_Onat_Odistinct_I1_J) ).
thf(354,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(144,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finT__simp) ).
thf(659,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__le__same__cancel1) ).
thf(215,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(136,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_iso__tuple__UNIV__I) ).
thf(639,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(169,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat,C: nat] :
( ( lList2508575361_ldrop @ TA @ A @ ( plus_plus @ nat @ B @ C ) )
= ( lList2508575361_ldrop @ TA @ ( lList2508575361_ldrop @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_ldrop__add) ).
thf(755,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat,C: nat] :
( ( lList2508575361_ldrop @ TA @ A @ ( plus_plus @ nat @ B @ C ) )
= ( lList2508575361_ldrop @ TA @ ( lList2508575361_ldrop @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(55,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( lList22119844313_ltake @ TA @ A @ ( zero_zero @ nat ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_LList2__Mirabelle__hamjzmohle_Oltake_Osimps_I1_J) ).
thf(364,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( lList22119844313_ltake @ TA @ A @ ( zero_zero @ nat ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(160,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_finlsts_Osimps) ).
thf(708,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( coinductive_LCons @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_lappend__code_I2_J) ).
thf(496,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lappend @ TA @ ( coinductive_LCons @ TA @ A @ B ) @ C )
= ( coinductive_LCons @ TA @ A @ ( coinductive_lappend @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_Suc__diff__diff) ).
thf(454,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(870,plain,
$false,
inference(e,[status(thm)],[809,555,333,628,449,247,440,269,385,533,670,301,565,619,542,460,853,421,325,289,316,475,789,376,623,485,348,806,211,253,766,221,774,243,849,527,307,233,512,661,201,761,381,798,820,424,275,847,361,583,493,682,224,578,697,650,615,388,499,488,339,637,679,212,328,471,647,701,515,654,457,237,244,266,633,657,558,530,586,718,298,412,750,856,689,444,733,562,843,286,711,204,545,641,391,572,313,787,466,236,804,672,784,230,451,434,631,758,609,594,726,621,700,240,626,769,345,858,367,552,521,278,851,589,795,548,812,617,342,823,490,675,580,409,705,282,263,310,199,331,370,502,840,463,336,703,612,845,250,539,482,524,218,517,319,418,781,652,351,378,207,667,478,763,684,536,752,447,818,405,373,305,210,801,358,437,664,635,720,415,395,575,644,723,200,607,227,322,354,659,215,639,755,364,708,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT180^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 11:33:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.73/1.13 % [INFO] Parsing done (258ms).
% 1.73/1.13 % [INFO] Running in sequential loop mode.
% 2.64/1.36 % [INFO] eprover registered as external prover.
% 2.64/1.36 % [INFO] cvc4 registered as external prover.
% 2.64/1.36 % [INFO] Scanning for conjecture ...
% 3.00/1.47 % [INFO] Found a conjecture and 279 axioms. Running axiom selection ...
% 3.23/1.57 % [INFO] Axiom selection finished. Selected 196 axioms (removed 83 axioms).
% 3.89/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 3.89/1.75 % [INFO] Type checking passed.
% 3.89/1.75 % [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 ...
% 14.16/4.12 % External prover 'e' found a proof!
% 14.16/4.12 % [INFO] Killing All external provers ...
% 14.16/4.12 % Time passed: 3595ms (effective reasoning time: 2983ms)
% 14.16/4.12 % 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)>
% 14.16/4.12 % Axioms used in derivation (196): fact_138_lsublist__LNil, fact_135_lsublist__singleton, fact_249_add__le__same__cancel1, fact_66_iso__tuple__UNIV__I, fact_248_add__le__same__cancel2, fact_15_lrev__LNil, fact_25_lappfin__finT, fact_112_finlsts_Ocases, fact_200_ltake__LCons__Suc, fact_72_ind__euclid, fact_24_lapp__fin__fin__lemma, fact_214_diff__add__inverse2, fact_132_ltake__ldrop__id, fact_244_zero__le__double__add__iff__zero__le__single__add, fact_119_fin__inf__cases, fact_122_lapp__infT, fact_5_finite__lemma, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_207_Suc__diff__diff, fact_209_diffs0__imp__equal, fact_120_fpslsts__cases, fact_234_add__eq__if, fact_165_diff__add__zero, fact_179_nat__induct, fact_211_Nat_Odiff__cancel, fact_241_Suc__le__mono, fact_96_lapp__inf, fact_117_alllsts_Osimps, fact_231_finlsts__rec__LCons__def, fact_246_le__add__same__cancel2, fact_133_LList2__Mirabelle__hamjzmohle_Ollast__LCons, fact_18_lrev__is__LNil__conv, fact_93_top1I, fact_192_DiffD2, fact_129_inflstsE, fact_164_lstrict__prefix__code_I1_J, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_127_lrev__induct, fact_65_lappend__LNil__LNil, fact_194_n__not__Suc__n, fact_64_plus__nat_Oadd__0, fact_35_double__zero__sym, fact_83_UNIV__witness, fact_136_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, fact_106_llistE, fact_233_finlsts__rec__LNil__def, fact_125_alllstsE, fact_34_double__zero, fact_216_diff__add__0, fact_113_finlsts_Osimps, fact_251_diff__is__0__eq_H, fact_130_lapp__allT__iff, fact_183_Zero__neq__Suc, fact_171_diff__add__eq, fact_73_LList2__Mirabelle__hamjzmohle_Ollength__LNil, fact_128_LList2__Mirabelle__hamjzmohle_Oltake_Osimps_I1_J, fact_116_alllsts_Ocoinduct, fact_150_Diff__idemp, fact_63_add__eq__self__zero, fact_217_triangle__Suc, fact_109_infT__simp, fact_115_finlsts_Oinducts, fact_193_Suc__inject, fact_100_llength__take, fact_153_zero__diff, fact_94_lappend__code_I2_J, fact_143_lstrict__prefix__code_I2_J, fact_243_diff__diff__cancel, fact_20_lrev__lappend, fact_4_ldrop__add, fact_205_diff__self__eq__0, fact_176_old_Onat_Odistinct_I2_J, fact_21_lappT, fact_188_add__Suc__shift, fact_210_minus__nat_Odiff__0, fact_107_finlsts_OLCons__fin, fact_16_lrev__is__lrev__conv, fact_204_diff__0__eq__0, fact_105_llist_Odistinct_I1_J, fact_235_diff__Suc__diff__eq1, fact_1_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, fact_148_DiffI, fact_110_infsubsetall, fact_26_lappend__code_I1_J, fact_69_poslsts__iff, fact_86_lbutlast__LNil, fact_104_neq__LNil__conv, fact_7_same__lappend__eq, fact_201_list__decode_Ocases, fact_103_inflstsI2, fact_134_top__empty__eq, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_203_exists__least__lemma, fact_232_finlsts__rec__LNil, fact_182_Suc__neq__Zero, fact_162_add__Suc__right, fact_126_finlsts__rev__cases, fact_208_diff__diff__left, fact_101_lbutlast__LCons, fact_238_add__le__cancel__right, fact_95_LConsE, fact_131_LList2__Mirabelle__hamjzmohle_Oltake__ldrop, fact_23_alllsts_OLNil__all, fact_8_lapp__fin__fin__iff, fact_10_fin__finite, fact_27_lappend__LNil2, fact_213_diff__add__inverse, fact_14_alllsts__UNIV, fact_191_DiffD1, fact_11_finlsts_OLNil__fin, fact_215_zero__induct__lemma, fact_190_DiffE, fact_12_LNil__is__lappend__conv, fact_82_UNIV__eq__I, fact_250_diff__ge__0__iff__ge, fact_74_add__0__iff, fact_102_inflsts__cases, fact_75_top__set__def, fact_237_le__zero__eq, fact_181_zero__induct, fact_242_nat__add__left__cancel__le, fact_22_lapp__all__invT, fact_2_ldropT, fact_178_nat_OdiscI, fact_31_Nat_Oadd__0__right, fact_111_lappend__snocL1__conv__LCons2, fact_58_lappend__assoc, fact_88_lrev__LCons, fact_240_le0, fact_137_top__conj_I1_J, fact_218_add__diff__add, fact_141_top__conj_I2_J, fact_187_not0__implies__Suc, fact_57_nat__add__left__cancel, fact_180_diff__induct, fact_139_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, fact_189_add__Suc, fact_140_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, fact_177_old_Onat_Odistinct_I1_J, fact_67_UNIV__I, fact_198_one__is__add, fact_28_LNil__eq__lappend__iff, fact_45_Collect__mem__eq, fact_219_triangle__0, fact_247_le__add__same__cancel1, fact_220_diff__commute, fact_186_old_Onat_Oinducts, fact_97_LList2__Mirabelle__hamjzmohle_Oltake__LNil, fact_71_poslsts__UNIV, fact_184_Zero__not__Suc, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_118_alllsts_Ocases, fact_90_inflstsI, fact_29_lappend__eq__LNil__iff, fact_0_lrevT, fact_199_add__is__1, fact_149_Diff__iff, fact_121_app__invT, fact_147_old_Onat_Oinject, fact_114_finlsts__induct, fact_19_LNil__is__lrev__conv, fact_30_add__is__0, fact_202_dependent__nat__choice, fact_195_llist__less__induct, fact_245_double__add__le__zero__iff__single__add__le__zero, fact_142_lstrict__prefix__code_I3_J, fact_17_lrev__lrev__ident, fact_3_LList2__Mirabelle__hamjzmohle_Oldrop_Osimps_I1_J, fact_123_lapp__inv2T, fact_13_lappend__is__LNil__conv, fact_230_finlsts__rec__LCons, fact_56_nat__add__right__cancel, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_239_add__le__cancel__left, fact_145_LList2__Mirabelle__hamjzmohle_Ollength__LCons, fact_146_nat_Oinject, fact_59_add__eq__0__iff__both__eq__0, fact_163_lstrict__prefix__code_I4_J, conj_0, fact_70_fpslsts__iff, fact_185_old_Onat_Oexhaust, fact_6_finsubsetall, fact_87_take__fin, fact_92_llist_Oinject, fact_99_notinf__fin, fact_212_diff__cancel2, fact_46_Collect__cong, fact_44_mem__Collect__eq, fact_124_lapp__fin__infT, fact_9_finT__simp, fact_206_diff__Suc__Suc, fact_98_notfin__inf, fact_108_alllsts_OLCons__all, fact_144_inflsts__def, fact_175_nat_Odistinct_I1_J, fact_89_ltake__fin
% 14.16/4.12 % No. of inferences in proof: 396
% 14.16/4.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3595 ms resp. 2983 ms w/o parsing
% 14.91/4.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.91/4.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------