TSTP Solution File: LCL840_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL840_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:32:17 EDT 2023
% Result : Theorem 17.52s 7.05s
% Output : Refutation 18.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 156
% Syntax : Number of formulae : 267 ( 87 unt; 47 typ; 0 def)
% Number of atoms : 852 ( 181 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 5209 ( 86 ~; 14 |; 40 &;4884 @)
% ( 11 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 26 con; 0-5 aty)
% Number of variables : 622 ( 0 ^; 578 !; 22 ?; 622 :)
% ( 22 !>; 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(zero_type,type,
zero:
!>[TA: $tType] : $o ).
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 ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combi_type,type,
combi:
!>[TA: $tType] : ( fun @ TA @ TA ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_type,type,
it: fun @ dB @ bool ).
thf(beta_type,type,
beta: dB > dB > $o ).
thf(abs_type,type,
abs: dB > dB ).
thf(app_type,type,
app: fun @ dB @ ( fun @ dB @ dB ) ).
thf(var_type,type,
var: nat > dB ).
thf(dB_size_type,type,
dB_size: dB > nat ).
thf(lift_type,type,
lift: fun @ dB @ ( fun @ nat @ dB ) ).
thf(subst_type,type,
subst: fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ).
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(listsp_type,type,
listsp:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(map_type,type,
map:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(suc_type,type,
suc: nat > nat ).
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(typing_type,type,
typing: ( fun @ nat @ type ) > dB > type > $o ).
thf(typings_type,type,
typings: ( fun @ nat @ type ) > ( list @ dB ) > ( list @ type ) > $o ).
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(t2_type,type,
t2: type ).
thf(t_type,type,
t: type ).
thf(t_a_type,type,
t_a: type ).
thf(t1_type,type,
t1: type ).
thf(ua1_type,type,
ua1: 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(r_type,type,
r: dB ).
thf(t3_type,type,
t3: dB ).
thf(u_type,type,
u: dB ).
thf(ua_type,type,
ua: dB ).
thf(78,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_dB_Osimps_I5_J) ).
thf(340,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)],[78]) ).
thf(72,axiom,
! [A: dB,B: type,C: nat,D: fun @ nat @ type] :
( ( typing @ ( shift @ type @ D @ C @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ t1 )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_SI1) ).
thf(317,plain,
! [A: dB,B: type,C: nat,D: fun @ nat @ type] :
( ( typing @ ( shift @ type @ D @ C @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ t1 )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(225,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)],[36]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(295,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ 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)],[63]) ).
thf(29,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_nat_Osimps_I3_J) ).
thf(203,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(80,axiom,
! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ ( foldr @ type @ type @ fun1 @ C @ B ) )
=> ( ( typings @ E @ A @ C )
=> ( typing @ E @ ( foldl @ dB @ dB @ app @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_list__app__typeI) ).
thf(347,plain,
! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ ( foldr @ type @ type @ fun1 @ C @ B ) )
=> ( ( typings @ E @ A @ C )
=> ( typing @ E @ ( foldl @ dB @ dB @ app @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(249,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(109,axiom,
! [A: list @ type,B: list @ dB,C: nat,D: type,E: dB,F: fun @ nat @ type] :
( ( typing @ F @ E @ D )
=> ( ( typings @ ( shift @ type @ F @ C @ D ) @ B @ A )
=> ( typings @ F @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ E ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_substs__lemma) ).
thf(468,plain,
! [A: list @ type,B: list @ dB,C: nat,D: type,E: dB,F: fun @ nat @ type] :
( ( typing @ F @ E @ D )
=> ( ( typings @ ( shift @ type @ F @ C @ D ) @ B @ A )
=> ( typings @ F @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ E ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(82,axiom,
pp @ ( aa @ dB @ bool @ it @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Beta_I3_J) ).
thf(352,plain,
pp @ ( aa @ dB @ bool @ it @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(408,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)],[96]) ).
thf(69,axiom,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_dB_Osimps_I8_J) ).
thf(308,plain,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(91,axiom,
! [A: dB,B: nat,C: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ B ) ) @ A ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_subst__lift) ).
thf(379,plain,
! [A: dB,B: nat,C: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ B ) ) @ A ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(52,axiom,
! [A: nat,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_lift__preserves__beta) ).
thf(269,plain,
! [A: nat,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(21,axiom,
typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_T) ).
thf(185,plain,
typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(99,axiom,
! [A: dB,B: dB] : ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ A ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_beta) ).
thf(417,plain,
! [A: dB,B: dB] : ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ A ) @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(47,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 ) )
=> ( ( typing @ ( shift @ type @ D @ C @ F ) @ E @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ F )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_MI2) ).
thf(257,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 ) )
=> ( ( typing @ ( shift @ type @ D @ C @ F ) @ E @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ F )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(20,axiom,
typing @ e @ u @ t1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uT) ).
thf(184,plain,
typing @ e @ u @ t1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(79,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(344,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)],[79]) ).
thf(85,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 ) )
=> ( ( typing @ ( shift @ type @ D @ C @ G ) @ E @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ G )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MI1) ).
thf(357,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 ) )
=> ( ( typing @ ( shift @ type @ D @ C @ G ) @ E @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ G )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(26,axiom,
beta @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35__096Abs_Ar_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_092_060rightarrow_062_092_060_094sub_062_092_060beta_062r_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_096) ).
thf(196,plain,
beta @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(107,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Suc__neq__Zero) ).
thf(460,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(12,axiom,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_abs) ).
thf(152,plain,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_appL) ).
thf(289,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(103,axiom,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Abs__App__neq__Var__apps) ).
thf(448,plain,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(48,axiom,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dB_Osimps_I9_J) ).
thf(261,plain,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',fact_90_IT_OVar) ).
thf(353,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)],[83]) ).
thf(32,axiom,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( typing @ C @ ( abs @ B ) @ A )
=> ~ ! [D: type,E: type] :
( ( A
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ E ) )
=> ~ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_typing__elims_I3_J) ).
thf(211,plain,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( typing @ C @ ( abs @ B ) @ A )
=> ~ ! [D: type,E: type] :
( ( A
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ E ) )
=> ~ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(45,axiom,
typing @ ( shift @ type @ e @ i @ t1 ) @ a @ t2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096e_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_096) ).
thf(253,plain,
typing @ ( shift @ type @ e @ i @ t1 ) @ a @ t2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',fact_19_type_Osimps_I2_J) ).
thf(397,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)],[94]) ).
thf(35,axiom,
~ ! [A: type] :
~ ( typing @ ( shift @ type @ e @ i @ t1 ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(221,plain,
~ ! [A: type] :
~ ( typing @ ( shift @ type @ e @ i @ t1 ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(105,axiom,
! [A: nat,B: list @ dB,C: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_lift__map) ).
thf(453,plain,
! [A: nat,B: list @ dB,C: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(8,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_n__not__Suc__n) ).
thf(132,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(97,axiom,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Var__IT) ).
thf(411,plain,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(49,axiom,
typing @ ( shift @ type @ e @ i @ t1 ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ ua1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096) ).
thf(265,plain,
typing @ ( shift @ type @ e @ i @ t1 ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ ua1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(70,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(312,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)],[70]) ).
thf(4,axiom,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_beta__cases_I1_J) ).
thf(116,plain,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(243,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)],[41]) ).
thf(62,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_not0__implies__Suc) ).
thf(292,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(104,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(452,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(28,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_appR) ).
thf(201,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(81,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_lift_Osimps_I2_J) ).
thf(349,plain,
! [A: nat,B: dB,C: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Var__apps__neq__Abs__apps) ).
thf(192,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(44,axiom,
pp @ ( aa @ dB @ bool @ it @ t3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(252,plain,
pp @ ( aa @ dB @ bool @ it @ t3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(27,axiom,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( ( aa @ nat @ type @ C @ B )
= A )
=> ( typing @ C @ ( var @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_typing_OVar) ).
thf(197,plain,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( ( aa @ nat @ type @ C @ B )
= A )
=> ( typing @ C @ ( var @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(106,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Zero__neq__Suc) ).
thf(456,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(59,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Suc__not__Zero) ).
thf(285,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(50,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Lambda) ).
thf(266,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_36_Var__apps__eq__Var__apps__conv) ).
thf(360,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)],[86]) ).
thf(64,axiom,
typing @ ( shift @ type @ ea @ ia @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Beta_I5_J) ).
thf(298,plain,
typing @ ( shift @ type @ ea @ ia @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Suc__inject) ).
thf(148,plain,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: dB,B: type,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ C @ B )
=> ( ( beta @ C @ A )
=> ( typing @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subject__reduction) ).
thf(161,plain,
! [A: dB,B: type,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ C @ B )
=> ( ( beta @ C @ A )
=> ( typing @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,axiom,
! [A: type,B: nat,C: list @ type,D: list @ dB,E: fun @ nat @ type] :
( ( typings @ E @ D @ C )
=> ( typings @ ( shift @ type @ E @ B @ A ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ B ) @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_lift__types) ).
thf(279,plain,
! [A: type,B: nat,C: list @ type,D: list @ dB,E: fun @ nat @ type] :
( ( typings @ E @ D @ C )
=> ( typings @ ( shift @ type @ E @ B @ A ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ B ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(102,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nat_Oexhaust) ).
thf(444,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(101,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
<=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_IT_Osimps) ).
thf(423,plain,
! [A: dB] :
( ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) )
& ( ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) )
=> ( pp @ ( aa @ dB @ bool @ it @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(24,axiom,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ u ) @ ( zero_zero @ nat ) ) ) @ ( suc @ i ) ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66__096IT_A_Ir_091lift_Au_A0_PSuc_Ai_093_091a_091u_Pi_093_P0_093_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_096) ).
thf(191,plain,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ u ) @ ( zero_zero @ nat ) ) ) @ ( suc @ i ) ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
pp @ ( aa @ dB @ bool @ it @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(291,plain,
pp @ ( aa @ dB @ bool @ it @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(57,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_IT_OBeta) ).
thf(281,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_92_listsp__conj__eq) ).
thf(413,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)],[98]) ).
thf(92,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ( ! [D: dB] :
( ( A
= ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( beta @ C @ D ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( beta @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_beta__cases_I3_J) ).
thf(382,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ( ! [D: dB] :
( ( A
= ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( beta @ C @ D ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( beta @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(10,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_dB_Osimps_I7_J) ).
thf(144,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__induct) ).
thf(335,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(19,axiom,
! [A: nat,B: dB,C: list @ dB,D: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( foldl @ dB @ dB @ app @ D @ C ) ) @ B ) @ A )
= ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_subst__map) ).
thf(181,plain,
! [A: nat,B: dB,C: list @ dB,D: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( foldl @ dB @ dB @ app @ D @ C ) ) @ B ) @ A )
= ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(95,axiom,
! [A: type,B: nat,C: type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ C )
=> ( typing @ ( shift @ type @ E @ B @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ D ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_lift__type) ).
thf(406,plain,
! [A: type,B: nat,C: type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ C )
=> ( typing @ ( shift @ type @ E @ B @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ D ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(34,axiom,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ ( var @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_subst__Var__IT) ).
thf(219,plain,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ ( var @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(54,axiom,
~ ! [A: type] :
~ ( typing @ ( shift @ type @ e @ i @ t1 ) @ a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096_B_Bthesis_O_A_I_B_BT_H_H_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(274,plain,
~ ! [A: type] :
~ ( typing @ ( shift @ type @ e @ i @ t1 ) @ a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(100,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dB_Osimps_I4_J) ).
thf(419,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)],[100]) ).
thf(90,axiom,
! [A: type,B: dB,C: type,D: fun @ nat @ type] :
( ( typing @ ( shift @ type @ D @ ( zero_zero @ nat ) @ C ) @ B @ A )
=> ( typing @ D @ ( abs @ B ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Abs) ).
thf(377,plain,
! [A: type,B: dB,C: type,D: fun @ nat @ type] :
( ( typing @ ( shift @ type @ D @ ( zero_zero @ nat ) @ C ) @ B @ A )
=> ( typing @ D @ ( abs @ B ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_40_dB_Osimps_I2_J) ).
thf(230,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)],[38]) ).
thf(67,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(303,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(53,axiom,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( typing @ C @ ( abs @ B ) @ A )
=> ~ ! [D: type,E: type] :
~ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_abs__typeE) ).
thf(271,plain,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( typing @ C @ ( abs @ B ) @ A )
=> ~ ! [D: type,E: type] :
~ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(55,axiom,
pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) ) @ u ) @ i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096) ).
thf(278,plain,
pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) ) @ u ) @ i ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(93,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__induct) ).
thf(394,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(65,axiom,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Beta_I1_J) ).
thf(299,plain,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(40,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( beta @ D @ C )
=> ( beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_subst__preserves__beta) ).
thf(241,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( beta @ D @ C )
=> ( beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TA,B: fun @ TA @ TB,C: TC,D: fun @ TC @ ( fun @ TB @ TC )] :
( ( foldl @ TC @ TB @ D @ C @ ( map @ TA @ TB @ B @ A ) )
= ( foldl @ TC @ TA @ ( combc @ TC @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ TC ) ) @ ( fun @ TC @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) ) @ ( aa @ ( fun @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) ) @ ( fun @ ( fun @ TC @ ( fun @ TB @ TC ) ) @ ( fun @ TC @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) ) ) @ ( combb @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ TC ) @ ( combb @ TB @ TC @ TA ) ) @ D ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_foldl__map) ).
thf(374,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TA,B: fun @ TA @ TB,C: TC,D: fun @ TC @ ( fun @ TB @ TC )] :
( ( foldl @ TC @ TB @ D @ C @ ( map @ TA @ TB @ B @ A ) )
= ( foldl @ TC @ TA @ ( combc @ TC @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ TC ) ) @ ( fun @ TC @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) ) @ ( aa @ ( fun @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) ) @ ( fun @ ( fun @ TC @ ( fun @ TB @ TC ) ) @ ( fun @ TC @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) ) ) @ ( combb @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ TC ) @ ( combb @ TB @ TC @ TA ) ) @ D ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(31,axiom,
! [A: nat,B: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lift__IT) ).
thf(209,plain,
! [A: nat,B: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3,axiom,
! [A: dB,B: dB] :
( ( beta @ ( abs @ B ) @ A )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( beta @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_beta__cases_I2_J) ).
thf(112,plain,
! [A: dB,B: dB] :
( ( beta @ ( abs @ B ) @ A )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( beta @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_nat_Oinject) ).
thf(123,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( suc @ B )
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact_31_app__Var__IT) ).
thf(355,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)],[84]) ).
thf(77,axiom,
! [A: dB,B: type,C: nat,D: fun @ nat @ type] :
( ( typing @ ( shift @ type @ D @ C @ t1 ) @ a @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ t1 )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_SI2) ).
thf(338,plain,
! [A: dB,B: type,C: nat,D: fun @ nat @ type] :
( ( typing @ ( shift @ type @ D @ C @ t1 ) @ a @ B )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( typing @ D @ A @ t1 )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_43_apps__eq__tail__conv) ).
thf(470,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)],[110]) ).
thf(13,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Suc__n__not__n) ).
thf(154,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(71,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_subst__App) ).
thf(314,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(73,axiom,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ~ ! [E: type] :
( ( typing @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) )
=> ~ ( typing @ D @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_typing__elims_I2_J) ).
thf(319,plain,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ~ ! [E: type] :
( ( typing @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) )
=> ~ ( typing @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(14,axiom,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_map__ident) ).
thf(158,plain,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
( ( typing @ G @ ( foldl @ dB @ dB @ app @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ D ) @ C )
=> ( ( typings @ G @ E @ B )
=> ( ( typing @ G @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ A )
=> ? [H: list @ type] :
( ( A
= ( foldr @ type @ type @ fun1 @ H @ C ) )
& ( typings @ G @ D @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_var__app__types) ).
thf(186,plain,
! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
( ( typing @ G @ ( foldl @ dB @ dB @ app @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ D ) @ C )
=> ( ( typings @ G @ E @ B )
=> ( ( typing @ G @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ A )
=> ? [H: list @ type] :
( ( A
= ( foldr @ type @ type @ fun1 @ H @ C ) )
& ( typings @ G @ D @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(17,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zero__reorient) ).
thf(171,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_dB_Osimps_I6_J) ).
thf(119,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA,C: nat,D: fun @ nat @ TA] :
( ( shift @ TA @ ( shift @ TA @ D @ C @ B ) @ ( zero_zero @ nat ) @ A )
= ( shift @ TA @ ( shift @ TA @ D @ ( zero_zero @ nat ) @ A ) @ ( suc @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_shift__commute) ).
thf(246,plain,
! [TA: $tType,A: TA,B: TA,C: nat,D: fun @ nat @ TA] :
( ( shift @ TA @ ( shift @ TA @ D @ C @ B ) @ ( zero_zero @ nat ) @ A )
= ( shift @ TA @ ( shift @ TA @ D @ ( zero_zero @ nat ) @ A ) @ ( suc @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(30,axiom,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) )
=> ( ( typing @ E @ A @ C )
=> ( typing @ E @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_App) ).
thf(207,plain,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) )
=> ( ( typing @ E @ A @ C )
=> ( typing @ E @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(66,axiom,
! [A: dB,B: nat] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( var @ B ) ) @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_subst__eq) ).
thf(300,plain,
! [A: dB,B: nat] :
( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( var @ B ) ) @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(23,axiom,
pp @ ( aa @ dB @ bool @ it @ ua ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Beta_I6_J) ).
thf(190,plain,
pp @ ( aa @ dB @ bool @ it @ ua ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(88,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(373,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(68,axiom,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( typing @ C @ ( var @ B ) @ A )
=> ( ( aa @ nat @ type @ C @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_typing__elims_I1_J) ).
thf(305,plain,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( typing @ C @ ( var @ B ) @ A )
=> ( ( aa @ nat @ type @ C @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(75,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Abs__apps__eq__Abs__apps__conv) ).
thf(326,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(39,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( foldl @ dB @ dB @ app @ C @ A ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_apps__preserves__beta) ).
thf(239,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( foldl @ dB @ dB @ app @ C @ A ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(9,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_dB_Osimps_I3_J) ).
thf(136,plain,
! [A: dB,B: dB] :
( ( ( ( abs @ B )
= ( abs @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( abs @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__096e_060i_058T_062_A_092_060turnstile_062_Ar_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
thf(268,plain,
typing @ ( shift @ type @ e @ i @ t1 ) @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ r ) @ a ) @ ( zero_zero @ nat ) ) @ as ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(58,axiom,
! [A: list @ dB] :
( ( listsp @ dB @ it @ A )
=> ( listsp @ dB @ it @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( zero_zero @ nat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_lifts__IT) ).
thf(283,plain,
! [A: list @ dB] :
( ( listsp @ dB @ it @ A )
=> ( listsp @ dB @ it @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( zero_zero @ nat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(108,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Zero__not__Suc) ).
thf(464,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(7,axiom,
typing @ ea @ ua @ t1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Beta_I7_J) ).
thf(131,plain,
typing @ ea @ ua @ t1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_dB_Osimps_I1_J) ).
thf(163,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)],[16]) ).
thf(18,axiom,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ B )
=> ( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_var__app__type__eq) ).
thf(178,plain,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ B )
=> ( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(87,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat_Osimps_I2_J) ).
thf(369,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1,conjecture,
pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(111,plain,
~ ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',fact_29_shift__eq) ).
thf(322,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)],[74]) ).
thf(33,axiom,
! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
( ( typing @ G @ F @ E )
=> ( ( typing @ D @ C @ B )
=> ( ( G
= ( shift @ type @ D @ A @ B ) )
=> ( typing @ D @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ F ) @ C ) @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__lemma) ).
thf(215,plain,
! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
( ( typing @ G @ F @ E )
=> ( ( typing @ D @ C @ B )
=> ( ( G
= ( shift @ type @ D @ A @ B ) )
=> ( typing @ D @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ F ) @ C ) @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(46,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(254,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(37,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_dB_Osize_I1_J) ).
thf(227,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(477,plain,
$false,
inference(e,[status(thm)],[340,317,225,295,203,347,249,468,352,408,308,379,269,185,417,257,184,344,357,196,460,152,289,448,261,353,211,253,397,221,453,132,411,265,312,116,243,292,452,201,349,192,252,197,456,285,266,360,298,148,161,279,444,423,191,291,281,413,382,144,335,181,406,219,274,419,377,230,303,271,278,394,299,241,374,209,112,123,355,338,470,154,314,319,158,186,171,119,246,207,300,190,373,305,326,239,136,268,283,464,131,163,178,369,111,322,215,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL840_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n015.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 16:01:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/1.03 % [INFO] Parsing done (192ms).
% 1.56/1.04 % [INFO] Running in sequential loop mode.
% 2.20/1.24 % [INFO] eprover registered as external prover.
% 2.20/1.24 % [INFO] cvc4 registered as external prover.
% 2.20/1.24 % [INFO] Scanning for conjecture ...
% 2.55/1.35 % [INFO] Found a conjecture and 108 axioms. Running axiom selection ...
% 2.82/1.43 % [INFO] Axiom selection finished. Selected 108 axioms (removed 0 axioms).
% 3.56/1.57 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.56/1.59 % [INFO] Type checking passed.
% 3.56/1.59 % [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 ...
% 17.52/7.05 % External prover 'e' found a proof!
% 17.52/7.05 % [INFO] Killing All external provers ...
% 17.52/7.05 % Time passed: 6534ms (effective reasoning time: 6010ms)
% 17.52/7.05 % 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)>
% 17.52/7.05 % Axioms used in derivation (108): fact_44_appR, help_COMBS_1_1_U, fact_35__096Abs_Ar_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_092_060rightarrow_062_092_060_094sub_062_092_060beta_062r_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_096, fact_54_dB_Osimps_I9_J, help_fconj_1_1_U, help_fconj_3_1_U, fact_15__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096, fact_36_Var__apps__eq__Var__apps__conv, fact_66__096IT_A_Ir_091lift_Au_A0_PSuc_Ai_093_091a_091u_Pi_093_P0_093_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_096, fact_30_var__app__type__eq, fact_75_Suc__n__not__n, fact_58_dB_Osimps_I6_J, fact_80_nat_Osimps_I3_J, fact_26_Abs, fact_69_subst__map, help_COMBI_1_1_U, fact_14_subst__lemma, fact_85_zero__reorient, fact_93_lift__types, fact_61_Var__apps__neq__Abs__apps, fact_17_Beta_I1_J, fact_46_subst__App, fact_96_list__app__typeI, fact_88_nat__induct, fact_22_App, fact_70_lift__map, fact_64_abs__typeE, fact_31_app__Var__IT, fact_71_map__ident, fact_45_appL, fact_2_uIT, fact_40_dB_Osimps_I2_J, fact_59_dB_Osimps_I7_J, fact_43_apps__eq__tail__conv, fact_5__096e_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_096, fact_89_dB_Osize_I1_J, fact_73_Suc__inject, fact_0__096IT_At_096, fact_12_SI2, fact_72_nat_Oinject, fact_74_ext, fact_92_listsp__conj__eq, fact_91_substs__lemma, fact_41_dB_Osimps_I3_J, fact_84_not0__implies__Suc, fact_27_Beta_I5_J, fact_77_Zero__not__Suc, fact_8_MI2, help_COMBB_1_1_U, fact_3_uT, fact_78_nat_Osimps_I2_J, fact_95_IT_Osimps, fact_97_var__app__types, fact_67_beta__cases_I3_J, fact_47_abs, fact_21_typing__elims_I1_J, fact_62_Abs__App__neq__Var__apps, fact_52_subject__reduction, help_fconj_2_1_U, fact_28__096e_060i_058T_062_A_092_060turnstile_062_Ar_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096, fact_25_SI1, fact_51_lift__preserves__beta, fact_9_subst__Var__IT, fact_1_Beta_I6_J, fact_57_subst__eq, fact_42_dB_Osimps_I1_J, fact_37_Abs__apps__eq__Abs__apps__conv, arity_Nat_Onat___Groups_Ozero, fact_24_lift__type, fact_19_type_Osimps_I2_J, fact_55_dB_Osimps_I5_J, fact_6__096_B_Bthesis_O_A_I_B_BT_H_H_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_90_IT_OVar, fact_4_Beta_I3_J, fact_39_lift_Osimps_I2_J, fact_38_Lambda, fact_23_T, fact_79_Suc__not__Zero, fact_29_shift__eq, help_COMBC_1_1_U, fact_65_apps__preserves__beta, fact_86_nat_Oexhaust, fact_87_zero__induct, fact_11__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096, fact_76_n__not__Suc__n, fact_34_typing__elims_I2_J, fact_56_dB_Osimps_I4_J, fact_83_foldl__map, fact_10_lift__IT, fact_33_typing__elims_I3_J, fact_20_typing_OVar, fact_13_Var__IT, fact_32_IT_OBeta, fact_16__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, help_pp_1_1_U, fact_18_Beta_I7_J, fact_81_Zero__neq__Suc, fact_7_MI1, fact_48_beta__cases_I1_J, fact_68_shift__commute, fact_60_subst__lift, fact_63_beta__cases_I2_J, fact_49_beta, help_pp_2_1_U, fact_94_lifts__IT, fact_50_subst__preserves__beta, fact_82_Suc__neq__Zero, fact_53_dB_Osimps_I8_J
% 17.52/7.05 % No. of inferences in proof: 220
% 17.52/7.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6534 ms resp. 6010 ms w/o parsing
% 18.28/7.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.28/7.14 % [INFO] Killing All external provers ...
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