TSTP Solution File: LCL805_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL805_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:53 EDT 2023
% Result : Theorem 21.97s 11.65s
% Output : Refutation 22.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 161
% Syntax : Number of formulae : 275 ( 121 unt; 49 typ; 0 def)
% Number of atoms : 845 ( 261 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 5235 ( 74 ~; 19 |; 66 &;4940 @)
% ( 20 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 19 con; 0-5 aty)
% Number of variables : 720 ( 0 ^; 656 !; 28 ?; 720 :)
% ( 36 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[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(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(equal_equal_type,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(it_type,type,
it: fun @ dB @ bool ).
thf(beta_type,type,
beta: fun @ dB @ ( fun @ dB @ bool ) ).
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_case_type,type,
dB_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ TA ) ) > ( fun @ dB @ TA ) > dB > TA ) ).
thf(dB_size_type,type,
dB_size: dB > nat ).
thf(lift_type,type,
lift: fun @ dB @ ( fun @ nat @ dB ) ).
thf(liftn_type,type,
liftn: nat > dB > nat > dB ).
thf(subst_type,type,
subst: fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ).
thf(substn_type,type,
substn: dB > dB > nat > dB ).
thf(step1_type,type,
step1:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ bool ) ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(foldl_type,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(list_rec_type,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) ) > ( list @ TA ) > TB ) ).
thf(list_size_type,type,
list_size:
!>[TA: $tType] : ( ( fun @ TA @ nat ) > ( list @ TA ) > nat ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
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(monoid_add_listsum_type,type,
monoid_add_listsum:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(null_type,type,
null:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(a_type,type,
a: dB ).
thf(as_type,type,
as: list @ dB ).
thf(i_type,type,
i: nat ).
thf(n_type,type,
n: nat ).
thf(rs_type,type,
rs: list @ dB ).
thf(t_type,type,
t: dB ).
thf(u_type,type,
u: dB ).
thf(ua_type,type,
ua: dB ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',fact_58_Abs__apps__eq__Abs__apps__conv) ).
thf(176,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)],[18]) ).
thf(59,axiom,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_IT_OVar) ).
thf(347,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)],[59]) ).
thf(95,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) )
<=> ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_apps__eq__Abs__conv) ).
thf(468,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) )
=> ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) ) )
& ( ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(61,axiom,
pp @ ( aa @ dB @ bool @ it @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(352,plain,
pp @ ( aa @ dB @ bool @ it @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(170,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)],[16]) ).
thf(106,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zero__reorient) ).
thf(523,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)],[106]) ).
thf(3,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dB_Osimps_I7_J) ).
thf(115,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dB_Osimps_I8_J) ).
thf(202,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)],[25]) ).
thf(89,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_apps__preserves__beta) ).
thf(440,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_list_Orecs_I1_J) ).
thf(511,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_47_lift__map) ).
thf(384,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)],[74]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
( ( listsp @ TA @ ( combs @ TA @ bool @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) @ A ) @ C )
<=> ( ( listsp @ TA @ B @ C )
& ( listsp @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_listsp__conj__eq) ).
thf(500,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
( ( ( listsp @ TA @ ( combs @ TA @ bool @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) @ A ) @ C )
=> ( ( listsp @ TA @ B @ C )
& ( listsp @ TA @ A @ C ) ) )
& ( ( ( listsp @ TA @ B @ C )
& ( listsp @ TA @ A @ C ) )
=> ( listsp @ TA @ ( combs @ TA @ bool @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_foldl__Nil) ).
thf(185,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_apps__eq__tail__conv) ).
thf(257,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)],[30]) ).
thf(76,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_dB_Osimps_I10_J) ).
thf(389,plain,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',fact_66_Var__apps__neq__Abs__apps) ).
thf(504,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)],[101]) ).
thf(21,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
= ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_eq__Nil__null) ).
thf(189,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( map @ TA @ TB @ B @ A )
= ( nil @ TB ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_map__is__Nil__conv) ).
thf(289,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( ( map @ TA @ TB @ B @ A )
= ( nil @ TB ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( map @ TA @ TB @ B @ A )
= ( nil @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(91,axiom,
! [A: dB,B: nat] :
~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_beta__cases_I1_J) ).
thf(448,plain,
! [A: dB,B: nat] :
~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(321,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)],[49]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',fact_16_subst__Var__IT) ).
thf(376,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)],[71]) ).
thf(104,axiom,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Osize_I4_J) ).
thf(514,plain,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(62,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 @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_list_Osimps_I5_J) ).
thf(353,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 @ ( 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)],[62]) ).
thf(97,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ E @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
<=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( step1 @ TA @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Cons__step1__Cons) ).
thf(480,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( ( step1 @ TA @ E @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( step1 @ TA @ E @ C @ A ) ) ) )
& ( ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( step1 @ TA @ E @ C @ A ) ) )
=> ( step1 @ TA @ E @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(79,axiom,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Var__IT) ).
thf(397,plain,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(7,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(132,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Osimps_I2_J) ).
thf(312,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)],[48]) ).
thf(26,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Abs__eq__apps__conv) ).
thf(206,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) ) )
& ( ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) )
=> ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(46,axiom,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_null__rec_I2_J) ).
thf(307,plain,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fact_67_Abs__App__neq__Var__apps) ).
thf(380,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)],[73]) ).
thf(33,axiom,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_map__ident) ).
thf(270,plain,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ D @ B ) ) )
=> ( ! [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
=> ( A
!= ( foldl @ dB @ dB @ app @ C @ D ) ) )
=> ~ ! [D: dB] :
( ( C
= ( abs @ D ) )
=> ! [E: dB,F: list @ dB] :
( ( B
= ( cons @ dB @ E @ F ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ E ) @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_apps__betasE) ).
thf(220,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ D @ B ) ) )
=> ( ! [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
=> ( A
!= ( foldl @ dB @ dB @ app @ C @ D ) ) )
=> ~ ! [D: dB] :
( ( C
= ( abs @ D ) )
=> ! [E: dB,F: list @ dB] :
( ( B
= ( cons @ dB @ E @ F ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ E ) @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(67,axiom,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_beta__cases_I2_J) ).
thf(366,plain,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(54,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_not__step1__Nil) ).
thf(334,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_map_Osimps_I1_J) ).
thf(349,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(77,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(392,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)],[77]) ).
thf(35,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_dB_Osimps_I11_J) ).
thf(275,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_20_lift_Osimps_I2_J) ).
thf(435,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)],[87]) ).
thf(50,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_not__Nil__step1) ).
thf(324,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(39,axiom,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_dB_Osimps_I9_J) ).
thf(285,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)],[39]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_foldl__fun__comm) ).
thf(403,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(20,axiom,
pp @ ( aa @ dB @ bool @ it @ ua ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
thf(188,plain,
pp @ ( aa @ dB @ bool @ it @ ua ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(63,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_True) ).
thf(356,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(52,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_substn_Osimps_I2_J) ).
thf(328,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_equal__Nil__null) ).
thf(339,plain,
! [TA: $tType,A: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( map @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_map_Osimps_I2_J) ).
thf(173,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( map @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_not__Cons__self) ).
thf(129,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',fact_5_lifts__IT) ).
thf(371,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)],[69]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(360,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)],[65]) ).
thf(102,axiom,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_substn__subst__n) ).
thf(508,plain,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(107,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_listsp_ONil) ).
thf(530,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_52_Beta) ).
thf(298,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)],[42]) ).
thf(85,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_subst__preserves__beta) ).
thf(430,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(11,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(148,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_dB_Osimps_I5_J) ).
thf(264,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)],[31]) ).
thf(14,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(161,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',fact_19_subst__App) ).
thf(279,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)],[37]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_68_IT_Osimps) ).
thf(236,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)],[29]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_foldl__Cons) ).
thf(540,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( 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)],[112]) ).
thf(82,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_beta__cases_I3_J) ).
thf(406,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(92,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_dB_Osimps_I4_J) ).
thf(451,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)],[92]) ).
thf(44,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ 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/sandbox2/benchmark/theBenchmark.p',fact_72_appR) ).
thf(303,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ 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)],[44]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_43_foldl__map) ).
thf(477,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)],[96]) ).
thf(75,axiom,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_abs) ).
thf(387,plain,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_list_Orecs_I2_J) ).
thf(494,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(58,axiom,
! [A: dB,B: list @ dB,C: list @ dB] :
( ( step1 @ dB @ beta @ C @ B )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_apps__preserves__betas) ).
thf(345,plain,
! [A: dB,B: list @ dB,C: list @ dB] :
( ( step1 @ dB @ beta @ C @ B )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',fact_14__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
thf(535,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)],[109]) ).
thf(23,axiom,
( rs
= ( cons @ dB @ a @ as ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Cons) ).
thf(198,plain,
( rs
= ( cons @ dB @ a @ as ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(80,axiom,
! [A: dB,B: list @ dB,C: nat] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ? [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
& ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_head__Var__reduction) ).
thf(399,plain,
! [A: dB,B: list @ dB,C: nat] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ? [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
& ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(36,axiom,
pp @ ( aa @ dB @ bool @ it @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(278,plain,
pp @ ( aa @ dB @ bool @ it @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(93,axiom,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Var__apps__eq__Var__apps__conv) ).
thf(455,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)],[93]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_dB_Osimps_I1_J) ).
thf(135,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)],[8]) ).
thf(88,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_appL) ).
thf(438,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(15,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_list_Oinject) ).
thf(162,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_not__Cons__self2) ).
thf(145,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(57,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_liftn_Osimps_I2_J) ).
thf(342,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ B @ A )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_equal__list__def) ).
thf(123,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( equal_equal @ ( list @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_list_Osimps_I4_J) ).
thf(295,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TB] :
( ( monoid_add_listsum @ TA @ ( map @ TB @ TA @ ( combk @ TA @ TB @ ( zero_zero @ TA ) ) @ A ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_listsum__0) ).
thf(282,plain,
! [TA: $tType,TB: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TB] :
( ( monoid_add_listsum @ TA @ ( map @ TB @ TA @ ( combk @ TA @ TB @ ( zero_zero @ TA ) ) @ A ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(12,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dB_Osimps_I3_J) ).
thf(150,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)],[12]) ).
thf(53,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_dB_Osimps_I12_J) ).
thf(331,plain,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fact_13__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
thf(370,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)],[68]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_12_subst__lift) ).
thf(336,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)],[55]) ).
thf(9,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_null__rec_I1_J) ).
thf(143,plain,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_48_subst__map) ).
thf(497,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)],[99]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_list_Osimps_I3_J) ).
thf(363,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(111,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(539,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA] :
( ( null @ TA @ A )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_List_Onull__def) ).
thf(517,plain,
! [TA: $tType,A: list @ TA] :
( ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(158,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
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 ) @ ( nil @ dB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( 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 ) @ ( nil @ dB ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(114,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 ) @ ( nil @ dB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(83,axiom,
! [A: list @ dB,B: dB,C: nat] :
( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Var__eq__apps__conv) ).
thf(418,plain,
! [A: list @ dB,B: dB,C: nat] :
( ( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) )
& ( ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) )
=> ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(110,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_dB_Osize_I1_J) ).
thf(536,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(4,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_dB_Osimps_I6_J) ).
thf(119,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(72,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(378,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)],[72]) ).
thf(43,axiom,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ A ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_substn__subst__0) ).
thf(300,plain,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( 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)],[43]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_24_subst__eq) ).
thf(432,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)],[86]) ).
thf(34,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_list__ex1__simps_I1_J) ).
thf(273,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(70,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_list_Osimps_I2_J) ).
thf(373,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(45,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(305,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)],[45]) ).
thf(51,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Lambda) ).
thf(326,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',fact_4_lift__IT) ).
thf(268,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)],[32]) ).
thf(64,axiom,
! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ 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/sandbox2/benchmark/theBenchmark.p',fact_69_beta) ).
thf(358,plain,
! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ 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)],[64]) ).
thf(22,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ( ( monoid_add_listsum @ TA @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_listsum__simps_I1_J) ).
thf(195,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ( ( monoid_add_listsum @ TA @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(108,axiom,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_liftn__0) ).
thf(532,plain,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(78,axiom,
! [A: nat,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_lift__preserves__beta) ).
thf(395,plain,
! [A: nat,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ C ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ lift @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(94,axiom,
! [A: dB] :
( ! [B: nat] :
( A
!= ( var @ B ) )
=> ( ! [B: dB,C: dB] :
( A
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ C ) )
=> ~ ! [B: dB] :
( A
!= ( abs @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dB_Oexhaust) ).
thf(464,plain,
! [A: dB] :
( ! [B: nat] :
( A
!= ( var @ B ) )
=> ( ! [B: dB,C: dB] :
( A
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ C ) )
=> ~ ! [B: dB] :
( A
!= ( abs @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(84,axiom,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_list_Osize_I1_J) ).
thf(427,plain,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(24,axiom,
! [A: nat,B: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ ( var @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_app__Var__IT) ).
thf(200,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)],[24]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( nil @ TB )
= ( map @ TA @ TB @ B @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Nil__is__map__conv) ).
thf(442,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( ( nil @ TB )
= ( map @ TA @ TB @ B @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( nil @ TB )
= ( map @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(309,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(113,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(543,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(27,axiom,
! [A: dB] :
? [B: list @ dB,C: dB] :
( ( A
= ( foldl @ dB @ dB @ app @ C @ B ) )
& ( ? [D: nat] :
( C
= ( var @ D ) )
| ? [D: dB] :
( C
= ( abs @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ex__head__tail) ).
thf(215,plain,
! [A: dB] :
? [B: list @ dB,C: dB] :
( ( A
= ( foldl @ dB @ dB @ app @ C @ B ) )
& ( ? [D: nat] :
( C
= ( var @ D ) )
| ? [D: dB] :
( C
= ( abs @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(544,plain,
$false,
inference(e,[status(thm)],[176,347,468,352,170,523,115,202,440,511,384,500,185,257,389,504,189,289,448,321,376,514,353,480,397,132,312,206,307,380,270,220,366,334,349,392,275,435,324,285,403,188,356,328,339,173,129,371,360,508,530,298,430,148,264,161,279,236,540,406,451,303,477,387,494,345,535,198,399,278,455,135,438,162,145,342,123,295,282,150,331,370,336,143,497,363,539,517,158,114,418,536,119,378,300,432,273,373,305,326,268,358,195,532,395,464,427,200,442,309,543,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL805_5 : TPTP v8.1.2. Released v6.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n019.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 15:46:43 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.99/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.10 % [INFO] Parsing done (207ms).
% 1.65/1.11 % [INFO] Running in sequential loop mode.
% 2.31/1.32 % [INFO] eprover registered as external prover.
% 2.31/1.32 % [INFO] cvc4 registered as external prover.
% 2.31/1.32 % [INFO] Scanning for conjecture ...
% 2.55/1.44 % [INFO] Found a conjecture and 111 axioms. Running axiom selection ...
% 3.03/1.51 % [INFO] Axiom selection finished. Selected 111 axioms (removed 0 axioms).
% 3.37/1.65 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.37/1.67 % [INFO] Type checking passed.
% 3.37/1.68 % [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 ...
% 21.97/11.65 % External prover 'e' found a proof!
% 21.97/11.65 % [INFO] Killing All external provers ...
% 21.97/11.65 % Time passed: 11134ms (effective reasoning time: 10535ms)
% 21.97/11.65 % 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)>
% 21.97/11.65 % Axioms used in derivation (111): fact_33_dB_Osimps_I11_J, arity_Nat_Onat___Groups_Ozero, fact_81_apps__preserves__betas, fact_85_apps__betasE, fact_82_head__Var__reduction, fact_36_list_Orecs_I1_J, fact_77_subst__preserves__beta, help_COMBS_1_1_U, fact_67_Abs__App__neq__Var__apps, fact_10_listsp__conj__eq, fact_29_list_Osize_I1_J, fact_59_apps__eq__Abs__conv, fact_18_dB_Osimps_I1_J, fact_66_Var__apps__neq__Abs__apps, fact_6_listsp_ONil, help_fconj_3_1_U, fact_65_dB_Osimps_I12_J, fact_46_List_Onull__def, fact_38_IT_OVar, fact_94_not__Cons__self2, fact_45_eq__Nil__null, help_COMBI_1_1_U, fact_54_foldl__fun__comm, fact_14__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096, fact_52_Beta, fact_69_beta, fact_11_map__ident, fact_9_map__is__Nil__conv, fact_40_liftn_Osimps_I2_J, fact_95_list_Osimps_I5_J, fact_44_liftn__0, fact_91_list_Osimps_I3_J, fact_47_lift__map, fact_43_foldl__map, fact_48_subst__map, fact_50_Var__apps__eq__Var__apps__conv, fact_28_list_Osimps_I4_J, fact_32_dB_Osimps_I10_J, fact_20_lift_Osimps_I2_J, fact_2_uIT, fact_89_Cons__step1__Cons, fact_0__096IT_At_096, fact_87_list_Oinject, fact_21_dB_Osimps_I4_J, fact_62_dB_Osimps_I6_J, fact_57_Lambda, fact_74_ext, fact_72_appR, help_COMBB_1_1_U, fact_56_dB_Osimps_I3_J, fact_3_True, fact_17_dB_Osimps_I2_J, fact_92_list_Osimps_I2_J, fact_63_dB_Osimps_I7_J, fact_42_foldl__Nil, fact_15_zero__reorient, fact_41_listsum__simps_I1_J, help_fconj_2_1_U, fact_16_subst__Var__IT, fact_58_Abs__apps__eq__Abs__apps__conv, fact_83_not__step1__Nil, fact_60_dB_Osimps_I8_J, fact_98_Cons, fact_22_dB_Osimps_I5_J, fact_1_Var_I3_J, fact_86_ex__head__tail, fact_97_list_Orecs_I2_J, fact_76_lift__preserves__beta, fact_7_Nil__is__map__conv, fact_79_apps__preserves__beta, fact_80_beta__cases_I3_J, help_COMBK_1_1_U, fact_64_equal__list__def, fact_90_null__rec_I1_J, fact_93_not__Cons__self, fact_12_subst__lift, fact_71_appL, help_COMBC_1_1_U, fact_34_substn_Osimps_I2_J, fact_84_not__Nil__step1, fact_49_Var__eq__apps__conv, help_fconj_1_1_U, fact_25_Var__IT, fact_55_Abs__eq__apps__conv, fact_27_dB_Osize_I4_J, fact_5_lifts__IT, fact_23_app__Var__IT, fact_4_lift__IT, fact_35_substn__subst__n, fact_88_map_Osimps_I2_J, fact_96_foldl__Cons, fact_73_beta__cases_I1_J, fact_53_equal__Nil__null, help_pp_1_1_U, fact_26_dB_Osize_I1_J, fact_37_listsum__0, fact_31_list__ex1__simps_I1_J, fact_39_null__rec_I2_J, arity_Nat_Onat___Groups_Omonoid__add, fact_61_dB_Osimps_I9_J, fact_8_map_Osimps_I1_J, fact_13__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096, fact_68_IT_Osimps, fact_75_abs, fact_30_substn__subst__0, fact_78_beta__cases_I2_J, help_pp_2_1_U, fact_51_apps__eq__tail__conv, fact_19_subst__App, fact_24_subst__eq, fact_70_dB_Oexhaust
% 21.97/11.65 % No. of inferences in proof: 226
% 21.97/11.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11134 ms resp. 10535 ms w/o parsing
% 22.45/11.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.45/11.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------