TSTP Solution File: LCL785_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL785_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 : Fri May 19 11:31:41 EDT 2023
% Result : Theorem 27.88s 15.18s
% Output : Refutation 28.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 158
% Syntax : Number of formulae : 271 ( 99 unt; 47 typ; 0 def)
% Number of atoms : 2264 ( 342 equ; 0 cnn)
% Maximal formula atoms : 116 ( 10 avg)
% Number of connectives : 8384 ( 66 ~; 22 |; 97 &;8003 @)
% ( 28 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 23 con; 0-5 aty)
% Number of variables : 839 ( 0 ^; 782 !; 28 ?; 839 :)
% ( 29 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(type_type,type,
type: $tType ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(it_type,type,
it: fun @ dB @ bool ).
thf(app_type,type,
app: fun @ dB @ ( fun @ dB @ dB ) ).
thf(var_type,type,
var: nat > dB ).
thf(dB_case_type,type,
dB_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ TA ) ) > ( fun @ dB @ TA ) > dB > TA ) ).
thf(subst_type,type,
subst: dB > dB > nat > dB ).
thf(append_type,type,
append:
!>[TA: $tType] : ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) ).
thf(foldl_type,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).
thf(foldr_type,type,
foldr:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TA ) ) > ( list @ TB ) > TA > TA ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(listsp_type,type,
listsp:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(maps_type,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( list @ TA ) ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(rotate1_type,type,
rotate1:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(shift_type,type,
shift:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > nat > TA > ( fun @ nat @ TA ) ) ).
thf(fun1_type,type,
fun1: fun @ type @ ( fun @ type @ type ) ).
thf(type_case_type,type,
type_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ type @ ( fun @ type @ TA ) ) > type > TA ) ).
thf(typing_type,type,
typing: ( fun @ nat @ type ) > dB > ( fun @ type @ bool ) ).
thf(typings_type,type,
typings: ( fun @ nat @ type ) > ( list @ dB ) > ( fun @ ( list @ type ) @ bool ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(t_type,type,
t: type ).
thf(t_a_type,type,
t_a: type ).
thf(t1_type,type,
t1: type ).
thf(a_type,type,
a: dB ).
thf(as_type,type,
as: list @ dB ).
thf(e_type,type,
e: fun @ nat @ type ).
thf(ea_type,type,
ea: fun @ nat @ type ).
thf(i_type,type,
i: nat ).
thf(ia_type,type,
ia: nat ).
thf(n_type,type,
n: nat ).
thf(rs_type,type,
rs: list @ dB ).
thf(t2_type,type,
t2: dB ).
thf(u_type,type,
u: dB ).
thf(ua_type,type,
ua: dB ).
thf(33,axiom,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( ( aa @ nat @ type @ C @ B )
= A )
=> ( pp @ ( aa @ type @ bool @ ( typing @ C @ ( var @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_typing_OVar) ).
thf(234,plain,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( ( aa @ nat @ type @ C @ B )
= A )
=> ( pp @ ( aa @ type @ bool @ ( typing @ C @ ( var @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(71,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
<=> ( ( ( B
= ( nil @ TA ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ E )
= B )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Cons__eq__append__conv) ).
thf(389,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
=> ( ( ( B
= ( nil @ TA ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ E )
= B )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ A ) ) ) ) )
& ( ( ( ( B
= ( nil @ TA ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ E )
= B )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ A ) ) ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(103,axiom,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ E ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_App__eq__foldl__conv) ).
thf(519,plain,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ E ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) ) )
& ( ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ E ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(7,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(129,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_insert__Nil) ).
thf(143,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_splice_Osimps_I1_J) ).
thf(120,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_list_Osimps_I5_J) ).
thf(379,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(25,axiom,
pp @ ( aa @ dB @ bool @ it @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_uIT) ).
thf(202,plain,
pp @ ( aa @ dB @ bool @ it @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(80,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(440,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(99,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(511,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: fun @ nat @ TA,C: nat,D: nat] :
( ( D = C )
=> ( ( aa @ nat @ TA @ ( shift @ TA @ B @ D @ A ) @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_shift__eq) ).
thf(385,plain,
! [TA: $tType,A: TA,B: fun @ nat @ TA,C: nat,D: nat] :
( ( D = C )
=> ( ( aa @ nat @ TA @ ( shift @ TA @ B @ D @ A ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(97,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_list_Oinject) ).
thf(500,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(46,axiom,
pp @ ( aa @ type @ bool @ ( typing @ ea @ ua ) @ t1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Var_I4_J) ).
thf(288,plain,
pp @ ( aa @ type @ bool @ ( typing @ ea @ ua ) @ t1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(79,axiom,
! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ G @ F ) @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ B ) )
=> ( ( G
= ( shift @ type @ D @ A @ B ) )
=> ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( subst @ F @ C @ A ) ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_subst__lemma) ).
thf(436,plain,
! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ G @ F ) @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ B ) )
=> ( ( G
= ( shift @ type @ D @ A @ B ) )
=> ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( subst @ F @ C @ A ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_dB_Osimps_I1_J) ).
thf(174,plain,
! [A: nat,B: nat] :
( ( ( ( var @ B )
= ( var @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( var @ B )
= ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(72,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(404,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(47,axiom,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_IT_OVar) ).
thf(289,plain,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(41,axiom,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Var__IT) ).
thf(261,plain,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_subst__App) ).
thf(216,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ D )
= C )
=> ( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ A ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_append__eq__appendI) ).
thf(443,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ D )
= C )
=> ( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ A ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rev__exhaust2) ).
thf(321,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(253,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,axiom,
pp @ ( aa @ type @ bool @ ( typing @ e @ u ) @ t1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_uT) ).
thf(238,plain,
pp @ ( aa @ type @ bool @ ( typing @ e @ u ) @ t1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(101,axiom,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_subst__Var__IT) ).
thf(514,plain,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(63,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( listsp @ TA @ B @ A )
<=> ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_listsp_Osimps) ).
thf(348,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( listsp @ TA @ B @ A )
=> ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) ) )
& ( ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) )
=> ( listsp @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(480,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(84,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
<=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Nil__is__append__conv) ).
thf(453,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( nil @ TA )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) )
& ( ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) )
=> ( ( nil @ TA )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(8,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_listsp_ONil) ).
thf(132,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
! [A: type,B: type,C: type,D: type] :
( ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_type_Osimps_I2_J) ).
thf(312,plain,
! [A: type,B: type,C: type,D: type] :
( ( ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(37,axiom,
! [A: list @ type,B: dB,C: list @ dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ C ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ B ) @ ( nil @ dB ) ) ) ) @ A ) )
=> ~ ! [E: list @ type,F: type] :
( ( A
= ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ ( list @ type ) @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( append @ type ) @ E ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ type @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( cons @ type ) @ F ) @ ( nil @ type ) ) ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ C ) @ E ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( typing @ D @ B ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_types__snocE) ).
thf(248,plain,
! [A: list @ type,B: dB,C: list @ dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ C ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ B ) @ ( nil @ dB ) ) ) ) @ A ) )
=> ~ ! [E: list @ type,F: type] :
( ( A
= ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ ( list @ type ) @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( append @ type ) @ E ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ type @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( cons @ type ) @ F ) @ ( nil @ type ) ) ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ C ) @ E ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( typing @ D @ B ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA )] :
( ( foldr @ TB @ TA @ B @ ( nil @ TB ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_foldr_Osimps_I1_J) ).
thf(117,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA )] :
( ( foldr @ TB @ TA @ B @ ( nil @ TB ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,axiom,
! [TA: $tType,A: type,B: type,C: fun @ type @ ( fun @ type @ TA ),D: fun @ nat @ TA] :
( ( type_case @ TA @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
= ( aa @ type @ TA @ ( aa @ type @ ( fun @ type @ TA ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_type_Osimps_I6_J) ).
thf(270,plain,
! [TA: $tType,A: type,B: type,C: fun @ type @ ( fun @ type @ TA ),D: fun @ nat @ TA] :
( ( type_case @ TA @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
= ( aa @ type @ TA @ ( aa @ type @ ( fun @ type @ TA ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(106,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_list_Osimps_I2_J) ).
thf(546,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(50,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) @ ( nil @ TA ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_splice_Osimps_I2_J) ).
thf(297,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) @ ( nil @ TA ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_list_Osimps_I4_J) ).
thf(137,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: type,B: list @ type,C: dB,D: list @ dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ D ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ ( nil @ dB ) ) ) ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ ( list @ type ) @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( append @ type ) @ B ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ type @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( cons @ type ) @ A ) @ ( nil @ type ) ) ) ) )
<=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ D ) @ B ) )
& ( pp @ ( aa @ type @ bool @ ( typing @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_types__snoc__eq) ).
thf(165,plain,
! [A: type,B: list @ type,C: dB,D: list @ dB,E: fun @ nat @ type] :
( ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ D ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ ( nil @ dB ) ) ) ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ ( list @ type ) @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( append @ type ) @ B ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ type @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( cons @ type ) @ A ) @ ( nil @ type ) ) ) ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ D ) @ B ) )
& ( pp @ ( aa @ type @ bool @ ( typing @ E @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ D ) @ B ) )
& ( pp @ ( aa @ type @ bool @ ( typing @ E @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ D ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ ( nil @ dB ) ) ) ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ ( list @ type ) @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( append @ type ) @ B ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ type @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( cons @ type ) @ A ) @ ( nil @ type ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(87,axiom,
! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
( ( t1
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ D @ C @ G ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ D @ A ) @ G ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ E @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_MI1) ).
thf(467,plain,
! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
( ( t1
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ D @ C @ G ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ D @ A ) @ G ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ E @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(64,axiom,
! [A: nat,B: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ ( var @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_app__Var__IT) ).
thf(361,plain,
! [A: nat,B: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ ( var @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_list_Osimps_I3_J) ).
thf(461,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(57,axiom,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_subst__eq) ).
thf(324,plain,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(39,axiom,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ? [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
& ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_list__app__typeD) ).
thf(256,plain,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ? [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
& ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_same__append__eq) ).
thf(193,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(90,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(476,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(95,axiom,
! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ E @ D ) @ ( foldr @ type @ type @ fun1 @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( foldl @ dB @ dB @ app @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_list__app__typeI) ).
thf(489,plain,
! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ E @ D ) @ ( foldr @ type @ type @ fun1 @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( foldl @ dB @ dB @ app @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_maps__simps_I2_J) ).
thf(134,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(98,axiom,
! [TA: $tType,A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_append__Nil2) ).
thf(508,plain,
! [TA: $tType,A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(54,axiom,
pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nT) ).
thf(311,plain,
pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(108,axiom,
( rs
= ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ a ) @ as ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Cons) ).
thf(558,plain,
( rs
= ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ a ) @ as ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(16,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ E ) @ D )
= C )
=> ( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ A ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ E ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Cons__eq__appendI) ).
thf(161,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ E ) @ D )
= C )
=> ( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ A ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ E ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: list @ dB,B: dB,C: nat] :
( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Var__eq__apps__conv) ).
thf(149,plain,
! [A: list @ dB,B: dB,C: nat] :
( ( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) )
& ( ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) )
=> ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(100,axiom,
pp @ ( aa @ dB @ bool @ it @ t2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(513,plain,
pp @ ( aa @ dB @ bool @ it @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(77,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_not__Cons__self) ).
thf(430,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(48,axiom,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ B ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_var__app__type__eq) ).
thf(291,plain,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ B ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= A )
<=> ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_append__self__conv2) ).
thf(204,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= A )
=> ( B
= ( nil @ TA ) ) )
& ( ( B
= ( nil @ TA ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(40,axiom,
! [A: type,B: dB,C: list @ type,D: list @ dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ D ) @ C ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ E @ B ) @ A ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ D ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ B ) @ ( nil @ dB ) ) ) ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ ( list @ type ) @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( append @ type ) @ C ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ type @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( cons @ type ) @ A ) @ ( nil @ type ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_types__snoc) ).
thf(259,plain,
! [A: type,B: dB,C: list @ type,D: list @ dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ D ) @ C ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ E @ B ) @ A ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ D ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ B ) @ ( nil @ dB ) ) ) ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ ( list @ type ) @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( append @ type ) @ C ) @ ( aa @ ( list @ type ) @ ( list @ type ) @ ( aa @ type @ ( fun @ ( list @ type ) @ ( list @ type ) ) @ ( cons @ type ) @ A ) @ ( nil @ type ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(75,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(413,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(69,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_rev__cases) ).
thf(382,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(60,axiom,
! [A: list @ type,B: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ B @ ( nil @ dB ) ) @ A ) )
<=> ( A
= ( nil @ type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_typings_Osimps_I1_J) ).
thf(335,plain,
! [A: list @ type,B: fun @ nat @ type] :
( ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ B @ ( nil @ dB ) ) @ A ) )
=> ( A
= ( nil @ type ) ) )
& ( ( A
= ( nil @ type ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ B @ ( nil @ dB ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( combc @ TC @ TA @ TB @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(540,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( combc @ TC @ TA @ TB @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(22,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_append__same__eq) ).
thf(187,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TB,C: list @ TB,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( foldr @ TB @ TA @ D @ ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ ( list @ TB ) @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( append @ TB ) @ C ) @ B ) @ A )
= ( foldr @ TB @ TA @ D @ C @ ( foldr @ TB @ TA @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_foldr__append) ).
thf(406,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TB,C: list @ TB,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( foldr @ TB @ TA @ D @ ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ ( list @ TB ) @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( append @ TB ) @ C ) @ B ) @ A )
= ( foldr @ TB @ TA @ D @ C @ ( foldr @ TB @ TA @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1,conjecture,
pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) @ as ) ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) @ as ) ) @ t ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) @ as ) ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ ( nil @ TA ) ) ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_append1__eq__conv) ).
thf(219,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ ( nil @ TA ) ) ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
( ( t1
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ D @ C @ F ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ D @ A ) @ F ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ E @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_MI2) ).
thf(230,plain,
! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
( ( t1
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ D @ C @ F ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ D @ A ) @ F ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ E @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(111,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= ( nil @ TA ) )
<=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_append__is__Nil__conv) ).
thf(567,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= ( nil @ TA ) )
=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) )
& ( ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(52,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_True) ).
thf(303,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( list @ TB )] :
( ( maps @ TA @ TB @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ ( list @ TB ) @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( append @ TB ) @ ( aa @ TA @ ( list @ TB ) @ C @ B ) ) @ ( maps @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_maps__simps_I1_J) ).
thf(477,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( list @ TB )] :
( ( maps @ TA @ TB @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ ( list @ TB ) @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( append @ TB ) @ ( aa @ TA @ ( list @ TB ) @ C @ B ) ) @ ( maps @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(62,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_append__assoc) ).
thf(345,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA] :
( ( rotate1 @ TA @ A )
= ( list_case @ ( list @ TA ) @ TA @ ( nil @ TA ) @ ( aa @ ( fun @ TA @ ( list @ TA ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ ( fun @ TA @ ( list @ TA ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) ) @ ( combb @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ TA ) @ ( combc @ ( list @ TA ) @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA ) ) ) @ ( aa @ ( list @ TA ) @ ( fun @ TA @ ( list @ TA ) ) @ ( combc @ TA @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA ) ) @ ( nil @ TA ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_rotate1__def) ).
thf(140,plain,
! [TA: $tType,A: list @ TA] :
( ( rotate1 @ TA @ A )
= ( list_case @ ( list @ TA ) @ TA @ ( nil @ TA ) @ ( aa @ ( fun @ TA @ ( list @ TA ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ ( fun @ TA @ ( list @ TA ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) ) @ ( combb @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ TA ) @ ( combc @ ( list @ TA ) @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA ) ) ) @ ( aa @ ( list @ TA ) @ ( fun @ TA @ ( list @ TA ) ) @ ( combc @ TA @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA ) ) @ ( nil @ TA ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(93,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ TA @ bool] :
( ( listsp @ TA @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
<=> ( ( listsp @ TA @ C @ B )
& ( listsp @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_append__in__listsp__conv) ).
thf(483,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ TA @ bool] :
( ( ( listsp @ TA @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
=> ( ( listsp @ TA @ C @ B )
& ( listsp @ TA @ C @ A ) ) )
& ( ( ( listsp @ TA @ C @ B )
& ( listsp @ TA @ C @ A ) )
=> ( listsp @ TA @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(110,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
( ( listsp @ TA @ ( combs @ TA @ bool @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) @ A ) @ C )
<=> ( ( listsp @ TA @ B @ C )
& ( listsp @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_listsp__conj__eq) ).
thf(563,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
( ( ( listsp @ TA @ ( combs @ TA @ bool @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) @ A ) @ C )
=> ( ( listsp @ TA @ B @ C )
& ( listsp @ TA @ A @ C ) ) )
& ( ( ( listsp @ TA @ B @ C )
& ( listsp @ TA @ A @ C ) )
=> ( listsp @ TA @ ( combs @ TA @ bool @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(267,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_apps__eq__tail__conv) ).
thf(241,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(89,axiom,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ C @ ( var @ B ) ) @ A ) )
=> ( ( aa @ nat @ type @ C @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_typing__elims_I1_J) ).
thf(473,plain,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ C @ ( var @ B ) ) @ A ) )
=> ( ( aa @ nat @ type @ C @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(94,axiom,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ E @ D ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ E @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_App) ).
thf(487,plain,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ E @ D ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ E @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( typing @ E @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(102,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_list_Oexhaust) ).
thf(516,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(61,axiom,
! [TA: $tType,A: list @ TA,B: fun @ ( list @ TA ) @ bool] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rev__induct) ).
thf(342,plain,
! [TA: $tType,A: list @ TA,B: fun @ ( list @ TA ) @ bool] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( nil @ TA ) ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rotate1__is__Nil__conv) ).
thf(123,plain,
! [TA: $tType,A: list @ TA] :
( ( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( rotate1 @ TA @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(58,axiom,
! [A: list @ type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ B ) ) @ A ) )
<=> ( pp @ ( list_case @ bool @ type @ fFalse @ ( aa @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) @ ( combc @ type @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) @ ( aa @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ type ) @ ( combb @ bool @ bool @ ( list @ type ) ) ) @ ( aa @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ type ) @ fconj ) @ ( typing @ D @ C ) ) ) ) @ ( typings @ D @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_typings_Osimps_I2_J) ).
thf(327,plain,
! [A: list @ type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( list_case @ bool @ type @ fFalse @ ( aa @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) @ ( combc @ type @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) @ ( aa @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ type ) @ ( combb @ bool @ bool @ ( list @ type ) ) ) @ ( aa @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ type ) @ fconj ) @ ( typing @ D @ C ) ) ) ) @ ( typings @ D @ B ) ) @ A ) ) )
& ( ( pp @ ( list_case @ bool @ type @ fFalse @ ( aa @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) @ ( combc @ type @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) @ ( aa @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ type ) @ ( combb @ bool @ bool @ ( list @ type ) ) ) @ ( aa @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ type ) @ fconj ) @ ( typing @ D @ C ) ) ) ) @ ( typings @ D @ B ) ) @ A ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(74,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_dB_Osimps_I4_J) ).
thf(409,plain,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(42,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_dB_Osimps_I5_J) ).
thf(263,plain,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24,axiom,
! [TA: $tType,A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( nil @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_append__Nil) ).
thf(199,plain,
! [TA: $tType,A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( nil @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
pp @ ( aa @ dB @ bool @ it @ ua ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Var_I3_J) ).
thf(182,plain,
pp @ ( aa @ dB @ bool @ it @ ua ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
= ( foldl @ TB @ TA @ D @ ( foldl @ TB @ TA @ D @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_foldl__append) ).
thf(470,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
= ( foldl @ TB @ TA @ D @ ( foldl @ TB @ TA @ D @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(83,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_dB_Osimps_I11_J) ).
thf(450,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ B ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_self__append__conv2) ).
thf(363,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ B ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(26,axiom,
pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ ea @ ia @ t1 ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Var_I2_J) ).
thf(203,plain,
pp @ ( aa @ type @ bool @ ( typing @ ( shift @ type @ ea @ ia @ t1 ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ C @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ B ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ A ) @ ( nil @ dB ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_app__last) ).
thf(158,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ C @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( append @ dB ) @ B ) @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ A ) @ ( nil @ dB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_splice__Nil2) ).
thf(114,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_list__app__typeE) ).
thf(171,plain,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ ( splice @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_splice_Osimps_I3_J) ).
thf(433,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ ( splice @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(107,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_dB_Osimps_I2_J) ).
thf(549,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(51,axiom,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ~ ! [E: type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( typing @ D @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_typing__elims_I2_J) ).
thf(300,plain,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ~ ! [E: type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ C ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( typing @ D @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(82,axiom,
! [A: type,B: list @ dB,C: nat,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( var @ C ) ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_var__app__typesE) ).
thf(447,plain,
! [A: type,B: list @ dB,C: nat,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ D @ ( var @ C ) ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TB,C: TB,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( foldr @ TB @ TA @ D @ ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ C ) @ ( foldr @ TB @ TA @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_foldr_Osimps_I2_J) ).
thf(146,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TB,C: TB,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( foldr @ TB @ TA @ D @ ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ C ) @ ( foldr @ TB @ TA @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ G @ ( foldl @ dB @ dB @ app @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ E ) @ B ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ G @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) ) @ A ) )
=> ? [H: list @ type] :
( ( A
= ( foldr @ type @ type @ fun1 @ H @ C ) )
& ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ D ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_var__app__types) ).
thf(183,plain,
! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( typing @ G @ ( foldl @ dB @ dB @ app @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ E ) @ B ) )
=> ( ( pp @ ( aa @ type @ bool @ ( typing @ G @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) ) @ A ) )
=> ? [H: list @ type] :
( ( A
= ( foldr @ type @ type @ fun1 @ H @ C ) )
& ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ D ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(45,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
<=> ( ( ( D
= ( nil @ TA ) )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ E ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_append__eq__Cons__conv) ).
thf(273,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
=> ( ( ( D
= ( nil @ TA ) )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ E ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ C )
= A ) ) ) )
& ( ( ( ( D
= ( nil @ TA ) )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ E ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ C )
= A ) ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(67,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_self__append__conv) ).
thf(373,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA] :
( ( ( rotate1 @ TB @ ( nil @ TB ) )
= ( nil @ TB ) )
& ( ( rotate1 @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_rotate__simps) ).
thf(305,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA] :
( ( ( rotate1 @ TB @ ( nil @ TB ) )
= ( nil @ TB ) )
& ( ( rotate1 @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ A ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(28,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_neq__Nil__conv) ).
thf(210,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(35,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(239,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_foldl__Cons) ).
thf(294,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(76,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
<=> ? [E: list @ TA] :
( ( ( D
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ E ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ C )
= A ) )
| ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ E )
= B )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_append__eq__append__conv2) ).
thf(415,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) )
=> ? [E: list @ TA] :
( ( ( D
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ E ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ C )
= A ) )
| ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ E )
= B )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ A ) ) ) ) )
& ( ? [E: list @ TA] :
( ( ( D
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ E ) )
& ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ C )
= A ) )
| ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ E )
= B )
& ( C
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ E ) @ A ) ) ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ D ) @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_foldl__Nil) ).
thf(464,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_foldl__fun__comm) ).
thf(332,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(112,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= B )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_append__self__conv) ).
thf(575,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= B )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B = A )
=> ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( nil @ TA ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_eq__Nil__appendI) ).
thf(369,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B = A )
=> ( B
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( nil @ TA ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(31,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Osimps_I10_J) ).
thf(227,plain,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_not__Cons__self2) ).
thf(543,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(109,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_append__Cons) ).
thf(560,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( append @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(96,axiom,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Var__apps__eq__Var__apps__conv) ).
thf(491,plain,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(581,plain,
$false,
inference(e,[status(thm)],[234,389,519,129,143,120,379,202,440,511,385,500,288,436,174,404,289,261,216,443,321,253,238,514,348,480,453,132,312,248,117,270,546,297,137,165,467,361,461,324,256,193,476,489,134,508,311,558,161,149,513,430,291,204,259,413,382,335,540,187,406,113,219,230,567,303,477,345,140,483,563,267,241,473,487,516,342,123,327,409,263,199,182,470,450,363,203,158,114,171,433,549,300,447,146,183,273,373,305,210,239,294,415,464,332,575,369,227,543,560,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL785_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 16:20:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/1.03 % [INFO] Parsing done (198ms).
% 1.46/1.04 % [INFO] Running in sequential loop mode.
% 2.18/1.24 % [INFO] eprover registered as external prover.
% 2.18/1.25 % [INFO] cvc4 registered as external prover.
% 2.18/1.25 % [INFO] Scanning for conjecture ...
% 2.61/1.37 % [INFO] Found a conjecture and 110 axioms. Running axiom selection ...
% 2.95/1.45 % [INFO] Axiom selection finished. Selected 110 axioms (removed 0 axioms).
% 3.55/1.61 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.55/1.63 % [INFO] Type checking passed.
% 3.55/1.63 % [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 ...
% 4.27/1.80 % [INFO] [Domain constraints] Detected constraint on bool
% 4.27/1.80 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 27.88/15.18 % External prover 'e' found a proof!
% 27.88/15.18 % [INFO] Killing All external provers ...
% 27.88/15.18 % Time passed: 14657ms (effective reasoning time: 14131ms)
% 27.88/15.18 % 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)>
% 27.88/15.18 % Axioms used in derivation (110): fact_17_Var_I4_J, fact_88_types__snocE, fact_28_App, fact_44_neq__Nil__conv, fact_85_list_Osimps_I5_J, help_COMBS_1_1_U, fact_43_listsp_Osimps, help_fconj_3_1_U, fact_11_Var_I3_J, fact_67_append__Nil, fact_1_True, fact_16_Var_I2_J, fact_31_listsp_ONil, fact_70_append__eq__append__conv2, fact_32_subst__App, fact_71_append__eq__appendI, fact_65_append1__eq__conv, fact_18_Var__IT, fact_77_rev__induct, fact_12_dB_Osimps_I1_J, fact_37_subst__Var__IT, fact_33_list_Osimps_I2_J, fact_13_dB_Osimps_I2_J, fact_60_append__self__conv, fact_0__096IT_At_096, fact_10_uIT, fact_90_list__app__typeI, fact_2_Cons, help_fFalse_1_1_T, fact_27_dB_Osimps_I10_J, fact_72_append__eq__Cons__conv, fact_57_self__append__conv, fact_52_append__assoc, fact_91_var__app__types, fact_96_list__app__typeE, fact_50_app__last, help_COMBB_1_1_U, fact_3_uT, fact_81_rotate1__is__Nil__conv, fact_7_typing__elims_I1_J, fact_49_splice_Osimps_I2_J, fact_82_rotate1__def, fact_86_list_Osimps_I4_J, fact_61_append__self__conv2, fact_38_subst__lemma, fact_98_maps__simps_I1_J, fact_48_foldl__fun__comm, help_fconj_2_1_U, fact_35_foldl__Nil, fact_76_splice_Osimps_I1_J, fact_55_append__Cons, fact_20_shift__eq, fact_21_list_Oinject, fact_83_types__snoc, fact_19_app__Var__IT, fact_47_type_Osimps_I6_J, fact_8_apps__eq__tail__conv, fact_40_not__Cons__self, fact_14_dB_Osimps_I4_J, fact_41_dB_Osimps_I11_J, fact_93_foldr_Osimps_I1_J, fact_53_same__append__eq, fact_23_MI2, fact_89_typings_Osimps_I2_J, fact_29_type_Osimps_I2_J, fact_6_typing_OVar, fact_92_foldr__append, fact_34_list_Osimps_I3_J, fact_63_append__in__listsp__conv, fact_22_foldl__Cons, help_COMBC_1_1_U, fact_99_maps__simps_I2_J, fact_9_var__app__type__eq, fact_69_eq__Nil__appendI, fact_45_list_Oexhaust, fact_58_self__append__conv2, fact_97_list__app__typeD, fact_68_append__Nil2, help_fconj_1_1_U, fact_95_var__app__typesE, fact_42_typing__elims_I2_J, fact_59_append__is__Nil__conv, fact_26_Var__eq__apps__conv, help_fFalse_1_1_U, fact_51_App__eq__foldl__conv, fact_87_types__snoc__eq, fact_39_not__Cons__self2, fact_56_Nil__is__append__conv, help_pp_1_1_U, fact_79_rev__exhaust2, fact_74_splice__Nil2, fact_46_insert__Nil, fact_15_dB_Osimps_I5_J, fact_75_ext, fact_24_MI1, fact_78_rev__cases, help_pp_2_1_U, fact_25_IT_OVar, fact_54_append__same__eq, fact_5_Var__apps__eq__Var__apps__conv, fact_30_listsp__conj__eq, fact_4_nT, fact_66_Cons__eq__appendI, fact_64_splice_Osimps_I3_J, fact_62_foldl__append, fact_36_subst__eq, fact_84_typings_Osimps_I1_J, fact_73_Cons__eq__append__conv, fact_80_rotate__simps, fact_94_foldr_Osimps_I2_J
% 27.88/15.18 % No. of inferences in proof: 224
% 27.88/15.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14657 ms resp. 14131 ms w/o parsing
% 28.30/15.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.30/15.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------