TSTP Solution File: LCL816_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL816_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 11:32:02 EDT 2023
% Result : Theorem 72.72s 34.13s
% Output : Refutation 72.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 170
% Syntax : Number of formulae : 287 ( 83 unt; 55 typ; 0 def)
% Number of atoms : 2266 ( 200 equ; 0 cnn)
% Maximal formula atoms : 108 ( 9 avg)
% Number of connectives : 9486 ( 68 ~; 22 |; 61 &;9182 @)
% ( 15 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 27 con; 0-5 aty)
% Number of variables : 691 ( 0 ^; 626 !; 34 ?; 691 :)
% ( 31 !>; 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 @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( 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(cons_type,type,
cons:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(listset_type,type,
listset:
!>[TA: $tType] : ( ( list @ ( fun @ TA @ bool ) ) > ( fun @ ( list @ TA ) @ bool ) ) ).
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(set_Cons_type,type,
set_Cons:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( list @ TA ) @ bool ) > ( fun @ ( list @ TA ) @ bool ) ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
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 ) > ( fun @ 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(fEx_type,type,
fEx:
!>[TA: $tType] : ( fun @ ( fun @ TA @ bool ) @ bool ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ 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(ts_type,type,
ts: list @ 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(t3_type,type,
t3: dB ).
thf(u_type,type,
u: dB ).
thf(ua_type,type,
ua: dB ).
thf(85,axiom,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( abs @ B ) ) @ A ) )
=> ~ ! [D: type,E: type] :
~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_abs__typeE) ).
thf(403,plain,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( abs @ B ) ) @ A ) )
=> ~ ! [D: type,E: type] :
~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(65,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_73_foldl__map) ).
thf(328,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)],[65]) ).
thf(9,axiom,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( ( aa @ nat @ type @ C @ B )
= A )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( var @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_typing_OVar) ).
thf(139,plain,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( ( aa @ nat @ type @ C @ B )
= A )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( var @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,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 @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ D @ C @ F ) ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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_25_MI2) ).
thf(222,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 @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ D @ C @ F ) ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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)],[31]) ).
thf(37,axiom,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( var @ B ) ) @ A ) )
=> ( ( aa @ nat @ type @ C @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_typing__elims_I1_J) ).
thf(249,plain,
! [A: type,B: nat,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( var @ B ) ) @ A ) )
=> ( ( aa @ nat @ type @ C @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(481,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(67,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ea ) @ ua ) @ t1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Var_I4_J) ).
thf(352,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ea ) @ ua ) @ t1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(29,axiom,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Var__IT) ).
thf(217,plain,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(105,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_23_type_Osimps_I2_J) ).
thf(449,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)],[105]) ).
thf(36,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_98_appR) ).
thf(247,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)],[36]) ).
thf(25,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_15_lift_Osimps_I2_J) ).
thf(202,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)],[25]) ).
thf(77,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(384,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)],[77]) ).
thf(13,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_36_shift__eq) ).
thf(153,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)],[13]) ).
thf(51,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_nT) ).
thf(288,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(56,axiom,
! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ G ) @ F ) @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) @ B ) )
=> ( ( G
= ( shift @ type @ D @ A @ B ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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_44_subst__lemma) ).
thf(301,plain,
! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ G ) @ F ) @ E ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) @ B ) )
=> ( ( G
= ( shift @ type @ D @ A @ B ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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)],[56]) ).
thf(61,axiom,
listsp @ dB @ it @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( 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_49__096listsp_AIT_A_Imap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
thf(320,plain,
listsp @ dB @ it @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( 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)],[61]) ).
thf(100,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_75_ext) ).
thf(436,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)],[100]) ).
thf(79,axiom,
! [A: type,B: dB,C: type,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ D @ ( zero_zero @ nat ) @ C ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( abs @ B ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Abs) ).
thf(389,plain,
! [A: type,B: dB,C: type,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ D @ ( zero_zero @ nat ) @ C ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( abs @ B ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB,C: list @ TB,D: TB] :
( ( ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ D ) @ C )
= ( map @ TA @ TB @ B @ A ) )
<=> ? [E: TA,F: list @ TA] :
( ( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ E ) @ F ) )
& ( D
= ( aa @ TA @ TB @ B @ E ) )
& ( C
= ( map @ TA @ TB @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Cons__eq__map__conv) ).
thf(184,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB,C: list @ TB,D: TB] :
( ( ( ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ D ) @ C )
= ( map @ TA @ TB @ B @ A ) )
=> ? [E: TA,F: list @ TA] :
( ( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ E ) @ F ) )
& ( D
= ( aa @ TA @ TB @ B @ E ) )
& ( C
= ( map @ TA @ TB @ B @ F ) ) ) )
& ( ? [E: TA,F: list @ TA] :
( ( A
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ E ) @ F ) )
& ( D
= ( aa @ TA @ TB @ B @ E ) )
& ( C
= ( map @ TA @ TB @ B @ F ) ) )
=> ( ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ D ) @ C )
= ( map @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(107,axiom,
listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) ) @ as,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Aas_096) ).
thf(460,plain,
listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) ) @ as,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(14,axiom,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_list__app__typeE) ).
thf(157,plain,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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)],[14]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_68_not__Cons__self) ).
thf(416,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)],[92]) ).
thf(33,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zero__reorient) ).
thf(228,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)],[33]) ).
thf(52,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_dB_Osimps_I6_J) ).
thf(289,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(60,axiom,
~ ! [A: type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ A ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ a ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(316,plain,
~ ! [A: type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ A ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ a ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(40,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_55_lifts__IT) ).
thf(261,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)],[40]) ).
thf(62,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(321,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)],[62]) ).
thf(68,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 @ ( 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 ) @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) ) ) @ ( typings @ D @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_typings_Osimps_I2_J) ).
thf(353,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 @ ( 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 ) @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) ) ) @ ( typings @ D @ B ) ) @ A ) ) )
& ( ( pp @ ( list_case @ bool @ type @ fFalse @ ( 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 ) @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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)],[68]) ).
thf(47,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(280,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)],[47]) ).
thf(53,axiom,
! [A: list @ type,B: list @ dB,C: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ C @ B ) @ A ) )
=> ( listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( typing @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_lists__typings) ).
thf(293,plain,
! [A: list @ type,B: list @ dB,C: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ C @ B ) @ A ) )
=> ( listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( typing @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',fact_70_foldl__Cons) ).
thf(132,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)],[6]) ).
thf(82,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_34_app__Var__IT) ).
thf(396,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)],[82]) ).
thf(89,axiom,
! [TA: $tType,A: list @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
( ( listset @ TA @ ( aa @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) ) @ ( cons @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
= ( set_Cons @ TA @ B @ ( listset @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_listset_Osimps_I2_J) ).
thf(411,plain,
! [TA: $tType,A: list @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
( ( listset @ TA @ ( aa @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) ) @ ( cons @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
= ( set_Cons @ TA @ B @ ( listset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(97,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Lambda) ).
thf(428,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(42,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(265,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)],[42]) ).
thf(59,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_21_dB_Osimps_I2_J) ).
thf(307,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)],[59]) ).
thf(101,axiom,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ~ ! [E: type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_typing__elims_I2_J) ).
thf(439,plain,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ~ ! [E: type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(75,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(381,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(74,axiom,
pp @ ( aa @ dB @ bool @ it @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT) ).
thf(380,plain,
pp @ ( aa @ dB @ bool @ it @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1,conjecture,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ ( zero_zero @ nat ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ) @ ( foldl @ dB @ dB @ app @ ( var @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) ) ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ ( zero_zero @ nat ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ) @ ( foldl @ dB @ dB @ app @ ( var @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) ) ) @ t ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ ( zero_zero @ nat ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ) @ ( foldl @ dB @ dB @ app @ ( var @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) ) ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [A: list @ type,B: list @ dB,C: nat,D: type,E: dB,F: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ F ) @ E ) @ D ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ F @ C @ D ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( 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_42_substs__lemma) ).
thf(160,plain,
! [A: list @ type,B: list @ dB,C: nat,D: type,E: dB,F: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ F ) @ E ) @ D ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ F @ C @ D ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( 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)],[15]) ).
thf(87,axiom,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ? [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
& ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_list__app__typeD) ).
thf(407,plain,
! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ? [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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)],[87]) ).
thf(45,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_11_subst__map) ).
thf(275,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)],[45]) ).
thf(17,axiom,
( rs
= ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ a ) @ as ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Cons) ).
thf(165,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)],[17]) ).
thf(116,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_87_dB_Osimps_I8_J) ).
thf(484,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)],[116]) ).
thf(38,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_19_apps__eq__tail__conv) ).
thf(252,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)],[38]) ).
thf(108,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_97_beta) ).
thf(461,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)],[108]) ).
thf(63,axiom,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_map__ident) ).
thf(324,plain,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(5,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/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)],[5]) ).
thf(73,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_84_Abs__apps__eq__Abs__apps__conv) ).
thf(371,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)],[73]) ).
thf(35,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_18_subst__App) ).
thf(244,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)],[35]) ).
thf(70,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_56_IT_OVar) ).
thf(360,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)],[70]) ).
thf(26,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_91_Abs__App__neq__Var__apps) ).
thf(205,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)],[26]) ).
thf(83,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ ( zero_zero @ nat ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ) @ ( var @ ( zero_zero @ nat ) ) ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096e_0600_058Ts_A_061_062_062_AT_H_062_A_092_060turnstile_062_AVar_A0_A_058_ATs_A_061_062_062_AT_H_096) ).
thf(398,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ ( zero_zero @ nat ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ) @ ( var @ ( zero_zero @ nat ) ) ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_71_foldr_Osimps_I2_J) ).
thf(430,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)],[98]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(180,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(103,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(444,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(12,axiom,
~ ! [A: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ A @ t ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ e @ i @ t1 ) @ as ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(149,plain,
~ ! [A: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ A @ t ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ e @ i @ t1 ) @ as ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(95,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_37_dB_Osimps_I5_J) ).
thf(423,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)],[95]) ).
thf(49,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ e ) @ u ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_uT_H) ).
thf(286,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ e ) @ u ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_dB_Osimps_I3_J) ).
thf(118,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)],[3]) ).
thf(39,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_81_Beta) ).
thf(259,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)],[39]) ).
thf(80,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(391,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(111,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_dB_Osimps_I1_J) ).
thf(466,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)],[111]) ).
thf(86,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_varT) ).
thf(406,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(30,axiom,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ B ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_var__app__type__eq) ).
thf(219,plain,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ B ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(93,axiom,
! [A: type,B: list @ dB,C: nat,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( var @ C ) ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
=> ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_var__app__typesE) ).
thf(419,plain,
! [A: type,B: list @ dB,C: nat,D: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ D ) @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ~ ! [E: list @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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)],[93]) ).
thf(71,axiom,
pp @ ( aa @ dB @ bool @ it @ t3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096IT_At_096) ).
thf(362,plain,
pp @ ( aa @ dB @ bool @ it @ t3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(44,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_90_Var__apps__neq__Abs__apps) ).
thf(271,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)],[44]) ).
thf(113,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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/sandbox/benchmark/theBenchmark.p',fact_46__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
thf(477,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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)],[113]) ).
thf(28,axiom,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( abs @ B ) ) @ A ) )
=> ~ ! [D: type,E: type] :
( ( A
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ E ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) ) @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_typing__elims_I3_J) ).
thf(213,plain,
! [A: type,B: dB,C: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ C ) @ ( abs @ B ) ) @ A ) )
=> ~ ! [D: type,E: type] :
( ( A
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ E ) )
=> ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ C @ ( zero_zero @ nat ) @ D ) ) @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24,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_86_dB_Osimps_I9_J) ).
thf(198,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)],[24]) ).
thf(84,axiom,
! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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 @ ( aa @ dB @ ( fun @ 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/sandbox/benchmark/theBenchmark.p',fact_59_var__app__types) ).
thf(399,plain,
! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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 @ ( aa @ dB @ ( fun @ 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)],[84]) ).
thf(46,axiom,
! [A: type,B: nat,C: type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ D ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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_12_lift__type) ).
thf(278,plain,
! [A: type,B: nat,C: type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ D ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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)],[46]) ).
thf(7,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ a ) @ t2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_argT) ).
thf(135,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ a ) @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(55,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_27_lift__IT) ).
thf(299,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)],[55]) ).
thf(32,axiom,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ D ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_App) ).
thf(226,plain,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ D ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dB_Osimps_I7_J) ).
thf(267,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: list @ TB,D: fun @ TB @ TA] :
( ( ( map @ TB @ TA @ D @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
<=> ? [E: TB,F: list @ TB] :
( ( C
= ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ E ) @ F ) )
& ( ( aa @ TB @ TA @ D @ E )
= B )
& ( ( map @ TB @ TA @ D @ F )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_map__eq__Cons__conv) ).
thf(167,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: list @ TB,D: fun @ TB @ TA] :
( ( ( ( map @ TB @ TA @ D @ C )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
=> ? [E: TB,F: list @ TB] :
( ( C
= ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ E ) @ F ) )
& ( ( aa @ TB @ TA @ D @ E )
= B )
& ( ( map @ TB @ TA @ D @ F )
= A ) ) )
& ( ? [E: TB,F: list @ TB] :
( ( C
= ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ E ) @ F ) )
& ( ( aa @ TB @ TA @ D @ E )
= B )
& ( ( map @ TB @ TA @ D @ F )
= A ) )
=> ( ( map @ TB @ 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)],[18]) ).
thf(81,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_35_subst__Var__IT) ).
thf(394,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)],[81]) ).
thf(58,axiom,
pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ e @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) @ ts ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096e_A_124_124_N_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_A_058_ATs_096) ).
thf(306,plain,
pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ e @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) @ ts ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(16,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_10_lift__map) ).
thf(162,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)],[16]) ).
thf(27,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_38_dB_Osimps_I4_J) ).
thf(209,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)],[27]) ).
thf(106,axiom,
! [A: type,B: nat,C: list @ type,D: list @ dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ D ) @ C ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( 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_41_lift__types) ).
thf(458,plain,
! [A: type,B: nat,C: list @ type,D: list @ dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ D ) @ C ) )
=> ( pp @ ( aa @ ( list @ type ) @ bool @ ( 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)],[106]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
( ( listsp @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( 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_65_listsp__conj__eq) ).
thf(194,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
( ( ( listsp @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( 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 @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( 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)],[23]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(295,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(90,axiom,
pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ e @ i @ t1 ) @ as ) @ ts ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_argsT) ).
thf(414,plain,
pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ e @ i @ t1 ) @ as ) @ ts ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(64,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ e ) @ u ) @ t1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_uT) ).
thf(327,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ e ) @ u ) @ t1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(41,axiom,
( t1
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_T) ).
thf(263,plain,
( t1
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: fun @ TA @ bool] :
( ( set_Cons @ TA @ B @ A )
= ( collect @ ( list @ TA ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ ( list @ TA ) ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ bool @ TA ) @ ( fEx @ ( list @ TA ) ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combs @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combs @ ( list @ TA ) @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ ( list @ TA ) ) @ fconj ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( list @ TA ) ) @ ( combb @ ( list @ TA ) @ bool @ ( list @ TA ) ) ) @ ( fequal @ ( list @ TA ) ) ) ) @ ( cons @ TA ) ) ) ) ) @ ( combc @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combb @ bool @ bool @ ( list @ TA ) ) ) @ ( 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 ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ bool @ ( member @ ( list @ TA ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_set__Cons__def) ).
thf(177,plain,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: fun @ TA @ bool] :
( ( set_Cons @ TA @ B @ A )
= ( collect @ ( list @ TA ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ ( list @ TA ) ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ bool @ TA ) @ ( fEx @ ( list @ TA ) ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combs @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combs @ ( list @ TA ) @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ ( list @ TA ) ) @ fconj ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( list @ TA ) ) @ ( combb @ ( list @ TA ) @ bool @ ( list @ TA ) ) ) @ ( fequal @ ( list @ TA ) ) ) ) @ ( cons @ TA ) ) ) ) ) @ ( combc @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combb @ bool @ bool @ ( list @ TA ) ) ) @ ( 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 ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ bool @ ( member @ ( list @ TA ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(66,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_94_IT_Osimps) ).
thf(331,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)],[66]) ).
thf(109,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
thf(463,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_72_list_Osimps_I5_J) ).
thf(386,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)],[78]) ).
thf(104,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_40_subst__lift) ).
thf(446,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)],[104]) ).
thf(10,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_dB_Osize_I1_J) ).
thf(143,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(110,axiom,
pp @ ( aa @ dB @ bool @ it @ ua ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Var_I3_J) ).
thf(465,plain,
pp @ ( aa @ dB @ bool @ it @ ua ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_67_list_Oinject) ).
thf(363,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)],[72]) ).
thf(34,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_14_Var__apps__eq__Var__apps__conv) ).
thf(235,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)],[34]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ 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 @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ ( aa @ TA @ TB @ C @ B ) ) @ ( map @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_map_Osimps_I2_J) ).
thf(433,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ 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 @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ ( aa @ TA @ TB @ C @ B ) ) @ ( map @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ 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(478,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ 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)],[114]) ).
thf(76,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ ea @ ia @ t1 ) ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Var_I2_J) ).
thf(383,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ 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)],[76]) ).
thf(50,axiom,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( 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_9__096IT_A_IVar_A0_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
thf(287,plain,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( 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)],[50]) ).
thf(88,axiom,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ u ) @ ( 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',fact_48__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
thf(410,plain,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ u ) @ ( 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)],[88]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',fact_69_not__Cons__self2) ).
thf(146,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)],[11]) ).
thf(21,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(183,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(94,axiom,
pp @ ( aa @ dB @ bool @ it @ ( 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 @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ u ) @ ( zero_zero @ nat ) ) ) @ ( var @ ( zero_zero @ nat ) ) ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
thf(422,plain,
pp @ ( aa @ dB @ bool @ it @ ( 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 @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ u ) @ ( zero_zero @ nat ) ) ) @ ( var @ ( zero_zero @ nat ) ) ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(57,axiom,
pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ e @ ( zero_zero @ nat ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) ) @ ts ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096e_0600_058Ts_A_061_062_062_AT_H_062_A_124_124_N_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_A_058_ATs_096) ).
thf(305,plain,
pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( shift @ type @ e @ ( zero_zero @ nat ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ lift @ ( zero_zero @ nat ) ) @ ( map @ dB @ dB @ ( combc @ dB @ nat @ dB @ ( combc @ dB @ dB @ ( fun @ nat @ dB ) @ subst @ u ) @ i ) @ as ) ) ) @ ts ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(69,axiom,
! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ D ) @ ( foldr @ type @ type @ fun1 @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( foldl @ dB @ dB @ app @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_list__app__typeI) ).
thf(358,plain,
! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ D ) @ ( foldr @ type @ type @ fun1 @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ A ) @ C ) )
=> ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ E ) @ ( foldl @ dB @ dB @ app @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(112,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_39_subst__eq) ).
thf(474,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)],[112]) ).
thf(48,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(283,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(91,axiom,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_headT) ).
thf(415,plain,
pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ e @ i @ t1 ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ ts @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(4,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(126,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,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 @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ D @ C @ G ) ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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_26_MI1) ).
thf(136,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 @ ( aa @ dB @ ( fun @ type @ bool ) @ ( typing @ ( shift @ type @ D @ C @ G ) ) @ E ) @ B ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( 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)],[8]) ).
thf(96,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(427,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(102,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
thf(442,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(490,plain,
$false,
inference(cvc4,[status(thm)],[403,328,139,222,249,481,352,217,449,247,202,384,153,288,301,320,436,389,184,460,157,416,228,289,316,261,321,353,280,293,132,396,411,428,265,307,439,381,380,117,160,407,275,165,484,252,461,324,129,371,244,360,205,398,430,180,444,149,423,286,118,259,391,466,406,219,419,362,271,477,213,198,399,278,135,299,226,267,167,394,306,162,209,458,194,295,414,327,263,177,331,463,386,446,143,465,363,235,433,478,383,287,410,146,183,422,305,358,474,283,415,126,136,427,442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL816_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n018.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 16:21:28 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.04 % [INFO] Parsing done (195ms).
% 1.64/1.04 % [INFO] Running in sequential loop mode.
% 2.23/1.24 % [INFO] eprover registered as external prover.
% 2.23/1.24 % [INFO] cvc4 registered as external prover.
% 2.23/1.25 % [INFO] Scanning for conjecture ...
% 2.77/1.38 % [INFO] Found a conjecture and 114 axioms. Running axiom selection ...
% 3.17/1.47 % [INFO] Axiom selection finished. Selected 114 axioms (removed 0 axioms).
% 3.55/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.55/1.65 % [INFO] Type checking passed.
% 3.55/1.66 % [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 ...
% 4.28/1.82 % [INFO] [Domain constraints] Detected constraint on bool
% 4.28/1.83 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 72.72/34.12 % External prover 'cvc4' found a proof!
% 72.72/34.13 % [INFO] Killing All external provers ...
% 72.72/34.13 % Time passed: 33608ms (effective reasoning time: 33079ms)
% 72.72/34.13 % 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)>
% 72.72/34.13 % Axioms used in derivation (114): help_fequal_1_1_T, fact_27_lift__IT, fact_46__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096, fact_61_list__app__typeE, fact_79_zero__reorient, fact_96_listset_Osimps_I2_J, help_COMBS_1_1_U, fact_89_dB_Osimps_I6_J, fact_81_Beta, fact_78_map__eq__Cons__conv, fact_34_app__Var__IT, help_fconj_3_1_U, fact_21_dB_Osimps_I2_J, fact_30_nT, fact_82_dB_Osimps_I3_J, fact_20_Var_I3_J, fact_36_shift__eq, fact_16_typing_OVar, fact_22_dB_Osimps_I1_J, help_COMBI_1_1_U, fact_72_list_Osimps_I5_J, fact_17_typing__elims_I1_J, fact_50__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_80_dB_Osize_I1_J, fact_73_foldl__map, fact_41_lift__types, fact_9__096IT_A_IVar_A0_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096, fact_88_dB_Osimps_I7_J, fact_19_apps__eq__tail__conv, fact_54_Cons, fact_40_subst__lift, fact_42_substs__lemma, fact_63_typings_Osimps_I2_J, fact_69_not__Cons__self2, fact_14_Var__apps__eq__Var__apps__conv, fact_52_Var_I2_J, fact_18_subst__App, help_fFalse_1_1_T, fact_44_subst__lemma, fact_47__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096, fact_93_abs__typeE, fact_97_beta, fact_62_list__app__typeD, help_COMBB_1_1_U, fact_10_lift__map, fact_24_Var_I4_J, fact_45_var__app__type__eq, fact_68_not__Cons__self, fact_55_lifts__IT, fact_91_Abs__App__neq__Var__apps, help_fconj_2_1_U, fact_71_foldr_Osimps_I2_J, fact_8_argsT, fact_13_App, fact_23_type_Osimps_I2_J, fact_74_Cons__eq__map__conv, fact_85_Abs, fact_64_map_Osimps_I2_J, fact_53_typing__elims_I2_J, fact_29_T, fact_95_set__Cons__def, fact_48__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096, fact_43_list__app__typeI, fact_49__096listsp_AIT_A_Imap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096, fact_28_varT, fact_76_mem__def, arity_Nat_Onat___Groups_Ozero, fact_25_MI2, fact_87_dB_Osimps_I8_J, fact_31_argT, fact_6_uT, fact_32_headT, fact_92_typing__elims_I3_J, fact_11_subst__map, fact_58_var__app__typesE, help_COMBC_1_1_U, fact_26_MI1, fact_5__096e_A_124_124_N_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_A_058_ATs_096, fact_37_dB_Osimps_I5_J, fact_3_uIT, help_fequal_2_1_T, fact_59_var__app__types, fact_67_list_Oinject, help_fconj_1_1_U, fact_56_IT_OVar, fact_94_IT_Osimps, fact_38_dB_Osimps_I4_J, fact_7_uT_H, fact_70_foldl__Cons, fact_66_map__ident, fact_90_Var__apps__neq__Abs__apps, help_fFalse_1_1_U, fact_86_dB_Osimps_I9_J, fact_65_listsp__conj__eq, fact_77_Collect__def, fact_98_appR, fact_4__096e_0600_058Ts_A_061_062_062_AT_H_062_A_124_124_N_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_A_058_ATs_096, fact_2__096e_0600_058Ts_A_061_062_062_AT_H_062_A_092_060turnstile_062_AVar_A0_A_058_ATs_A_061_062_062_AT_H_096, help_pp_1_1_U, fact_83_Lambda, fact_35_subst__Var__IT, fact_1__096IT_At_096, fact_33_Var__IT, fact_0_True, fact_75_ext, fact_12_lift__type, fact_51__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_57__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Aas_096, help_pp_2_1_U, fact_15_lift_Osimps_I2_J, fact_60_lists__typings, help_fEx_1_1_U, fact_39_subst__eq, fact_84_Abs__apps__eq__Abs__apps__conv
% 72.72/34.13 % No. of inferences in proof: 232
% 72.72/34.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 33608 ms resp. 33079 ms w/o parsing
% 72.72/34.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 72.72/34.23 % [INFO] Killing All external provers ...
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